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How to Calculate Osmolarity in 4 Easy Steps

Osmolarity is a measure of concentration. Concentration, regardless of the different units that can be used, is the ratio of mass and quantity. When concentration is expressed as osmolarity, mass is the number of osmoles and quantity is volume in liters.

image displays an equation for calculating osmolarity as the number of osmoles divided by the volume in liters.

When is Osmolarity Useful

Osmolarity permeates many aspects of medicine:

Homeostasis

The concept of osmolarity is relevant in medicine because it influences how fluids moves through the body. Whether its intravascular to extravascular, intracellular to extracellular, osmolarity helps to maintain homeostasis. It keeps fluids where they need to be, in the appropriate quantities throughout the body.

image showing the importance of osmolarity in medicine, pharmacy and nursing

Pathologies

When homeostasis is disrupted by pathologies like intracranial hemorrhages, ascites and acute congestive heart failure we can leverage the force of osmotic pull to reestablish fluid balances.

Intravenous Compounding

There are limitations on the osmolarity of compounded solutions that can be administered via central versus peripheral lines. We must know how to calculate osmolarity when compounding TPNs and other non-standard concentrations of intravenous solutions. Both hyperosmostic and hypo-osmotic solutions can have adverse outcomes.

Oral Compounding

The osmolarity of oral solutions must be considered as hyperosmotic oral solutions can cause adverse gastrointestinal effects like diarrhea and cramping.

Plasma

Plasma is one of the most important “solutions” we work with in medicine. The osmolarity of blood is maintained within a narrow range of 275-290 mOsm/ml.

Osmotic Pressure

Osmolarity influences all of those facets of medicine just discussed because of osmotic pressure. This pressure is what determines how water will or will not move across the semi permeable membranes that creates compartments throughout the body.

The pressure is the results of the differences in the amount of solute on either side of the membrane. Water will always move in the direction of higher osmolarity i.e. it will move to the side of the membrane that has a higher number of solutes. The higher the concentration of solutes, the higher the osmotic pressure.

The amount of pressure the solute will create is also dependent on how the solute interacts with each other once in solution. The interactions can be ionic or non-ionic.

Ionic versus Non Ionic Solutes

Whether a solute is ionic or non-ionic has to be determined before osmolarity can be calculated. Ionic solutes will require the use of an osmotic coefficient. Non-ionic solutes have an “ideal” osmotic coefficient of 1 and therefore not necessary for the calculation of osmolarity.

Osmotic Coefficient

The osmotic coefficient tells us the degree to which particles of a solute will interaction in solution. It ranges from 0 to 1.

A osmotic coefficient of 1 indicates the “ideal” of particles existing independently in solution i.e. there is minimal, near zero, interaction between the particles. You can think of an osmotic coefficient of 1 meaning that the particles are providing their maximum osmotic pressure.

Any deviation from 1 means that there are other factors, like electric charges and attraction, that are affecting the “ideal” osmotic pressure. This deviation is represented by the osmotic coefficient moving away from 1. It must be accounted for when calculating osmolarity.

Image showing factors affecting osmotic coefficient

Non-ionic solutes like dextrose or albumin maintain the covalent bonds that hold them together when in solution. There is minimal interaction between the solute particles. The osmotic coefficient for non-ionic solutes are closer to 1 or assumed to be 1.

Ionic solutes dissolve in solution for form ions. These ions maintain some degree of interaction with each other due to their opposing charges. The osmotic coefficient on ionic solution will be less than 1.

Osmotic coefficients are calculated experimentally and can be found in various reference sources. The Journal of Physical and Chemical Reference Data is a useful resource for osmotic coefficients.

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What are Osmoles?

An (os)mole is the osmotic pressure produced by each mole of a substance in solution.

image showing that an osmole is the osmotic pressure per mole of substance

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Moles to Osmoles

In the unit Calculating Milliequivalents we explain the concepts of mole and equivalent weight. If you are unsure about either of those you will need to review that unit to track along with calculation of osmolarity.

Briefly, 1 mole is a surrogate marker for a very large number of particles, 6.002 x10²³ to be exact.

illustration showing the concept of 1 mole and it's relation to Avogadro's number

It would be very hard to use such a large number in practice so we use 1 mole instead.

Equivalent weight is a way to standardize moles. It accounts for the differences in mass and valence when elements interact with each other. This affects their behavior including how they interact with each other in solution which affects osmolarity.

When elements interact with each other, the goal is to form a stable atom or molecule that has a low level of reactivity. They do this by sharing electrons in a way that allows all atoms involved to achieve a stable outershell. If any of this sounds foreign to you please stop and review the unit on How to Read Valence. The stability of valence electrons is the basis of formation of osmoles when calculating osmolarity for ionic solutions.

Image showing how atoms interact to form stable molecules that then have some degree of dissociation

In this example using sodium chloride (NaCl):

imaging showing how atoms create 1 mole and moles convert to osmoles

In an “ideal” solution the particles exist independently of each other, there is little to no interaction between them i.e. an osmotic coefficient of 1. In reality differing molecular weights and valence contribute to the attraction that is maintained between ions in solution.

NaCl has an osmotic coefficient (OC) of 0.93 (less than 1) indicating that there are interactions that cause a less than “ideal” solution.

The "ideal" osmole for Na-Cl would be: 2 osmoles x 1 OC

The "true" osmole for Na-Cl would be: 2 osmoles x 0.93 OC

Calculate Osmolarity in 4 Steps

We can organize all this foundational information into 4 easy steps to calculate the osmolarity of any solutions. There are slight differences when the solute is ionic versus non-ionic.

Use equivalent weight if ionic to calculate the weight of one mole
Use the given weight in solution to calculate the number of moles
Assume “ideal” osmoles x osmotic coefficient to determine the true number of osmoles
Express the number of osmoles per liter of volume: osmolarity

Use molecular weight to calculate the weight of one mole
Use the given weight in solution to calculate the number of moles
For non-ionic solutes there is minimal to no interaction in solution. The osmotic coefficient is assumed to be 1. Therefore # of moles = # of osmoles
Express the number of osmoles per liter of volume: osmolarity

Calculations

Let’s look at some sample questions. One example uses an ionic solute and the other a non-ionic solute.

Calculation of osmolarity for an ionic solution

calculating osmolarity of a non ionic solution

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I hope this unit has provided clarity on the concepts involved in calculating osmolarity. These concepts are often taught in silos of chemistry, physics and physiology. Tying them together leads to true understanding rather than memorization.

If you’ve found this unit helpful I would love to hear from you. Leave a comment or question below!

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

Alligation Calculations Made Easy using Intuitive Equations

Alligation is a mathematical technique used to determine the quantity of 2 concentrations needed to create a desired concentration. The desired concentration will have a value somewhere in the range of the 2 starting concentrations.

There are 2 ways to perform alligation calculations:

Alligation Tables
Intuitive Calculation

This unit focuses on the use of intuitive equations. Take a look at both strategies, decide which one works best for your style of learning.

Problem with Alligation Tables

In the unit on alligation tables there are step-by-step instructions that show how the complex mathematical concept is distilled into a standardized orientation of concentrations on a grid.

Image showing the sequences required for alligation calculations using alligation tables

That unit also discusses the disadvantages of using alligation tables.

Most notably, the heavy reliance on memorization of where each value has to be placed on the grid.

Once you have the correct orientation you must subtract diagonally, add vertically then work horizontally.

Any misstep and your calculation will be incorrect.

This much memorization isn’t an issue if you are studying for an exam in the near future or if you use alligation tables all the time. With consistent use it becomes second nature.

If alligation is not part of your usual practice you need a more intuitive way to perform alligation calculations so that you are prepared whenever the need arises. For those purposes I recommend alligation by intuitive equations. Performing alligation a skill that is not used often but when it is needed it is of critical importance. If you work with neonatal or pediatric patients, you should have a strong understanding of alligation.

Even if you are just studying for an exam, I will always advocate for approaches that rely on deriving answers from foundational concepts rather than memorization. There is no need to memorize every new concept. That will not serve you. You will not retain the skill of alligation for much longer than the duration an exam.

Terminology

Alligation calculations can be broken down into three concentrations. Two starting concentrations and one desired concentration. There are also 3 quantities. A desired quantity of a desired concentration and the quantity needed of each of the initial products. These 6 elements of alligation are presented below along with the symbols that will used to represent them throughout this unit.

Intuitive Calculation

The desired concentration will have a value between those of the 2 starting concentrations:

C₁ > C₃ > C₂

The desired quantity will be the sum of the quantities needed for each of the starting concentrations:

Q₁ + Q₂ = Q₃

This above equation is based on the fundamental property of mass.

Mass is Fundamental

Consider 3 jars of beads. The first jar contains 8 red beads, the second contains 5 blue beds, the 3rd jar is empty. If we add the contents of the first 2 jars into the 3rd, we would have a jar of 13 beads.

These beads represent the fundamental property of mass.

Image showing the significant role hat mass plays in alligation equations.

Mass a measure of the amount of matter in an object or substance. Mass is fundamental. Is does not depend on nor is it influences by any other properties. The only way to change mass is to add or remove from it. You can change weight without any change to the structure of the substance by changing the pull of gravity, therefore weight is not fundamental. No matter where an object is, its mass is the same.

This means that when 2 masses are added together the resultant mass will always be the sum of the individual masses. How does this relate to alligation?

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Concentration|Volume|Mass

Concentration is the mass per unit of quantity of a substance. If we multiple concentration by a given quantity we are left with the fundamental property of mass. Remember mass cannot change.

If mass ₁ + mass ₂ = mass ₃ is also means that:

This is the basis of our alligation equation: the mass of the 2 solutions combined must equal the mass of the final combined solution.

Alligation Equation

Let’s put this equation to the test with some example calculations.

Example Calculations

We will use the same examples from the unit Alligation Tables to show that we can derive the same answer without the use of alligation tables.

We can arrive at the same values by leveraging the fundamental property of mass that tells us total mass must equal the sum of the masses. Since concentration multiplied by volume will give us mass, we equate the sum of the products of our given concentrations and volumes to derive a given volume of our desired concentration.

Personally, this is my preferred method of alligation. It is more intuitive. It avoids having to memorize the various orientations required for alligation tables. We all learn different so check out the unit on Alligation Tables for an alternative method for alligation to find your preference!

GlobalRph provides an alligation calculator but this is best used as a double check for your own calculations. No calculator will relieve you of liability in medical compounding so I highly recommend understanding how to calculate versus the “plug and chug” use of calculators.

If this unit has been helpful I would love to hear from you! Leave a question or comment below.

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

How to Perform Alligation Calculations: Grid Method

When faced with complex dosing problems, understanding alligation calculations can be crucial for determining the right proportions of solutions in pharmaceutical preparations.

Clinical scenario:

The neonatologist orders D12% for a 2 day old neonate. What would you do? Chat GPT or Google? On a 2 day old? Even the most trusted clinical calculators have the disclaimer that results they generate must be re-checked and should not be used alone to guide patient care, nor should they substitute for clinical judgment. In good faith we should have at least some understanding of how to perform alligation calculations.

Alligation is one of those calculation techniques you won’t use often but when it is needed it’s non negotiable.

There are 2 ways to perform alligation:

Alligation Grids
Alligation Equations

This unit focuses on the use of alligation grids. Alligation via intuitive equations is covered in another unit. Take a look at both strategies, decide which one works best for your style of learning.

What is Alligation?

Illustration showing the overall concept of alligation as using 2 different concentrations to generate a 3d concentration with some value in between.

Clinical Application

As we’ve seen alligation is useful in specific patient populations where standard concentrations of fluids are not ideal, like NICU.

It is also useful when there are drug shortages. For instance there have been times when we are not able to get bags of 3% saline for acute hyponatremia but we have vials of concentrated saline (23.4%). We can use alligation to compound lower concentration from the higher concentration.

An understanding of alligation is also needed when compounding custom TPNs.

Terminology

As always terminology is important. It allows us to all to be oriented in the same direction as we work through concepts.

In alligation we are working with 3 concentrations:

higher concentration
lower concentration
desired concentration

We are also working with 3 quantities:

quantity of higher concentration
quantity of lower concentration
desired quantity

The quantity will usually be expressed as a volume or weight.

Alligation Tic-Tac-Toe

An alligation table is a well coordinated version of tic-tac-toe. The grid for alligation is in fact the very way you would set up tic-tac-toe. Alligation grids work by condensing a complex mathematical concept into a standardized table.

Image of an alligation grid showing the position of your starting concentrations and desired concentrations.

The higher concentration goes to the upper left
The lower concentration goes to the bottom left
The desired concentration goes to the middle of the grid

Your desired concentration will be some value between your initial higher concentration and lower concentration. Once you’ve organized your concentrations on the grid, the next step is a series of diagonal differences.

Diagonal Differences

Calculate the change in concentration (Δ) that will result from each starting concentration to create the desired concentration.

Δ₁ = C₁ – C₃

The difference between the higher concentration and desired concentration

Place Δ₁ in the bottom right, diagonal to C₁

Δ₂ = C₃ – C₂

The difference between the desired concentration and the lower concentration

Place Δ₂ in the top right, diagonal to C₂

Image showing diagonal differences on an alligation grid

Vertical Sum

You’ve organized your grid, calculated differences diagonally, now we add vertically. The sum of Δ₁ and Δ₂ is the combined quantity (parts) that will result from the combination of the 2 starting solutions.

We will place these 4 components on one grid to determine the quantity of 2 concentrations that must be mixed to obtain a desired concentration (alligation)

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Image showing the vertical sum calculated from the alligation grid

Starting concentration: C₁ and C₂
Desired concentration: C₃
Difference in concentration: Δ₁ and Δ₂
Sum of parts: ∑ Δ

Horizontal Quantities

Once we have those 6 values placed on the grid we calculate the quantities needed of each concentration horizontally.

The quantity of higher concentration solution required to achieve desired concentration is the ratio of:

the difference between the desired concentration and lower concentration (Δ₂) and the sum of parts (∑ Δ)

Note that we are using the diagonal difference of the lower concentration to calculate the quantity of the higher concentration.

The quantity of lower concentration solution required to achieve desired concentration is the ratio of:

the difference between the higher concentration and desired concentration (Δ₁) and the sum of parts (∑ Δ).

Again, note that we are using the diagonal difference of the higher concentration to calculate the quantity of the lower concentration.

You can then convert these ratios to the desired unit of measurement, usually volume or weight, to calculate the amount of each solution needed. Let’s look at some example calculations.

Alligation Calculations

Disadvantages of Alligation Grid

As you have seen alligation grids require some memorization. You must orient the 3 concentrations and the differences in concentrations correctly on the grid for it to work. You must subtract diagonally, add vertically then work horizontally. Any misstep and your calculation will be incorrect.

This may be a non-issue if you are studying for a test next week but when you are actually working and haven’t used alligation in weeks, months or even years, it will be hard to remember what goes where.

There is a more intuitive way to solve alligation problems. This method is covered here. If alligation grids work for you, great! If not, consider alligation equations.

GlobalRph offers an alligation calculator. As always no calculator will assume your responsibilities in patient dosing. It is always a good idea to understand what you are plugging into calculators and why.

I hope this unit has provided more context to the usual plug and chug explanation of alligation grids. It will always be easier to retain information when it is connected to already established concepts rather than just memorization. Take the time to walk through the steps diligently and build your confidence in alligation calculations.

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

How to Calculate Milliequivalents in 3 Easy Steps

Why is calculation of milliequivalents so difficult? Dare I say, it is often taught in a way that does not foster understanding.

If you are just memorizing equations and canceling out units to calculate milliequivalents we are going to change that. That strategy may be sufficient to pass an exam but isn’t very useful beyond that.

The problem with understanding milliequivalents is that most explanations start with an assumption that key foundational concepts are already established. If they are not then you will have alot of difficulty understanding what numbers are being used in calculating milliequivalents. Calculating milliequivalents is actually quite simple if you understand what you are doing and why.

We are going to make no assumptions of baseline knowledge so that you are left with the whole picture of milliequivalents.

Let’s take care of a few definitions. Terminology is always important. It ensures that we are all on the same page as we move through these concepts.

The Periodic Table

Understanding milliequivalents requires understanding of the organization of the periodic table. The periodic table is organized into groups (columns) and periods (rows).

Every element in the periodic table has a distinct weight in grams. This is the molar mass or mass number. The mass number increases in increments of 1 across the periodic table.

Every element in the periodic table also an atomic number. The atomic number tells us the number of electrons in the element/atom. The elements all share the same basic structure: a nucleus at the center surrounded by “shells” of electrons.

Ptable.com is the best interactive periodic table. In addition to the Mass and atomic number, it includes the number of atoms per shell for each atom.

Each shell can hold a maximum number of electrons: 2, 8, 8 on the 1st, 2nd and 3rd shell respectively. An atom is considered stable (having low reactivity) when the shells have the maximum number of electrons.

The electrons on the outermost shell are called valence electrons.

These are the highest energy electrons that interact in a chemical reaction in an attempt to form a stable atom.

Valency (which is different from valence electrons) is the number of electrons the outer shell needs to gain or lose to form a stable atom.

Image showing the structure of the electrons around the nucleus of an atom. This is needed to determine valency for milliequivalent calculations.

I cannot emphasize enough how important the concept of valency is to understanding milliequivalents and a bunch of other concepts in pharmacology. It is why I created the unit How to Reading Valence. If any of what you just read is confusing, I highly encourage you to read that unit.

What is a Mole?

A mole is a unit of measurement. We use mole when we need to represent a very large number of particles.

1 mole represents the quantity of a substance that contains 6.002 x10²³ particles. This is known as Avogadro’s number. Think about this number (600,200,000,000,000,000,000,000). That’s lot of particles! That’s too big a number to be used in calculations so we use a mole as a surrogate marker for an Avogadro’s number of particles.

Properties of a Mole

Using carbon and oxygen as examples, let us look at the properties of 1 mole of an element.

For individual elements the weight of one mole is simply the mass number/atomic mass. When atoms react to form a stable molecule, like carbon dioxide (CO₂) the weight of 1 mole of the molecule is the sum of the mass numbers of the atoms in the molecule. The weight of one mole of carbon dioxide (CO₂) is 12 + 16 +16 = 44g

Each atom varies in mass and valency (reactivity). Therefore atoms contribute differently in reactions to form stable molecules. We need a way to compare them with and against each other in a way that accounts for those differences. We do this by calculating the equivalent weight.

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Calculating Equivalent Weight

Equivalent weight is a way to standardize moles. While the value of mole and molar mass is sufficient when describing individual elements we need a away to account for the differences in mass and valence when they interact with each other. These differences will affect their contribution or behavior in reactions.

You can think of it as averaging the weight of the particle to its reactivity so that we can make a proportional comparison across the elements.

The ratio of an element’s mass number to valence provides the equivalent weight.

Image showing the equation for calculating equivalent weight.

We know that our mass number is the larger number in the periodic table. We know how to calculate valency from the periodic table. If you are still unsure of how to calculate valency please review the unit How to Read Valence.

Let us calculate the equivalent weight of carbon and oxygen.

Example calculations of equivalent weight.

These calculations are the equivalent weight of 1 mole of oxygen and 1 mole of carbon respectively.

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Calculating Equivalents

Once you know the weight of one equivalent (equivalent weight) we can calculate the number of equivalents in any given quantity of a substance.

The number of equivalents is the ratio of your given quantity in grams to the equivalent weight.

Equivalents to Milliequivalents

Equivalent is usually expressed as milliequivalent simply to provide a number than is easier to read. Milliequivalent is: number of equivalents x 1000

Considering all of we have discussed there are 3 broad steps to calculating milliequivalents:

determine the equivalent weight using mass number and valency
use equivalent weight to calculate number of equivalents
convert equivalents to milliequivalents

illustration of steps required to calculate number of milliequivalents.

Let’s look at a few example calculations for milliequivalents.

Milliequivalent Calculations

Second example calculation of milliequivalents

Example calculations of milliequivalents

If we understand what we are doing, we can tackle any variation of calculating milliequivalent. It allows us to advance the concept of milliequivalents to other calculations like osmolarity and other fluid calculations.

If you have found the unit helpful, I would love to hear from you. Leave your questions or comments below!

Subscribe to get the latest study unit in your inbox.

The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

How to Read Valence in 4 Easy Steps

Reading valence on the periodic table is often relegated to soon forgotten introductory chemistry. However it is applicable to more complex concepts in pharmacology calculations like milliequivalent and osmolarity.

Unfortunately concepts are usually taught in silos. Being able to integrate concepts is necessary for advanced application rather than short term memorization. The goal is to create a solid foundation of valency that will be the basis for future topics.

Overview of the Periodic Table

The periodic table is organized into rows called “periods” (across) and columns called “groups” (down).

Within the periodic table there are several classes of elements that “behave” similarly. For the purpose of this unit, which is calculating valence, we will focus only on the sections of the periodic table that obeys the rules of valency.

Image showing the basics of how we read the periodic table for valence calculations

Ptable provides an excellent, interactive periodic table.

For each element, the periodic table provides an atomic number and an atomic mass (mass number).

The atomic number is the number above the element. It increases in increments of 1 across the periodic table from left to right.

The atomic number tells us the total number of electrons in the atom. Carbon has an atomic number of 6, there are 6 electrons in a carbon atom.

The basic structure of the atom is a nucleus at the center surrounded by electrons. Electrons on each atom are arranged in several “shells” around the nucleus of the atom.

Structure of an Atom

The innermost shell on a stable can hold 2 electrons, the second shell can hold 8 electrons and the outermost shell can hold a maximum of 8 electrons. When the shells are occupied with the maximum number of electrons, this creates a stable atom. Stable atoms have low reactivity.

Illustration of how electrons are arranged in an atom including the valence electrons

When the outermost shell is not maximized, those electrons are the most reactive. They are high energy electrons that undergo reactions in a attempt to achieve a stable atom or create a stable molecule. These high energy, outermost electrons are called the valence electrons.

Valence electrons react by either donating, accepting or sharing these outer shell electrons to create a stable atom or molecule. The number of electrons donated, accepted or shared (the valence) is the number of bonds that can be formed in a reaction.

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Valence Electrons and Groups

Reading valence on the periodic table centers around the organization of the groups (columns). The group numbers are listed above each column in the periodic table.

Image showing the groups in the periodic table that are needed for valence calculations.

The elements in each group have similarities in the way they will react. This is because the elements in each group have the same number of energetic electrons in the outermost shell. They have the same number of valence electrons.

Groups 3-12 on the periodic table (the middle stripped square) has a more nuanced calculation of valence that is beyond the scope of the unit and my level of understanding honestly.

Valence Electrons and Valency

The number of valence electrons does NOT indicate the valency

This is a common misconception. Valence electrons refer to the number of electrons on the outermost shell.

Valency refers to the number of electrons the atom must gain, loss or share to form a stable atom.

Understanding this difference in terminology is key to making sense of valency calculations

How to Read Valency in 4 Steps

Find the atomic number: total number of electrons in atom
Assign the total number of electrons to each shell up to the maximum quantities of each: 2,8,8 (1st, 2nd, 3rd respectively)
Determine the number of electrons in the outermost shell (valence electrons)
Determine the number of electrons to gain, lose or share (the valency) to get an outer shell with the maximum number of electrons: 2,8,8 (1st, 2nd, 3rd respectively)

Less than 4 valence electrons: you will lose

Greater than 5 valence electrons: you will gain

4 electrons: you will share electrons

5 valence electrons: you can gain or lose

Exceptions

Hydrogen follows all the rules except gain/lose. Hydrogen has only 1 valence electron. While all other elements with less than 5 electrons will lose electrons to create a stable atom, hydrogen must gain to form a stable 1st outer shell of 2 electrons. It cannot lose the only electron it has!

Group 14 can neither gain nor lose electrons it will only share its 4 valence electrons to form a stable atom.

Group 15 is a point of transition in the periodic table in terms of valence. In group 15 the elements all have 5 valence electrons. They can gain OR lose their outermost electrons to achieve a stable outer shell of 8 electrons. They can gain 3 electrons OR lose 5 electrons to create a stable atom. Because of this the elements in group 15 can have a valence of 3 or 5.

Valency Calculations

(Swipe): The tables above provide a breakdown of the valency of elements in each group of the periodic table. This allows you to visualize the relationship between all the factors at play: atomic number, valence electrons and valency.

Notice that valency correlates only to the number of electrons needed to create a stable atom.
Notice that the valency correlates to the charge on the atom.
Notice that the number of valence electrons does NOT equal valency.

All the values provided in these tables are derived using the 4 simple steps discussed above and summarized below:

The atomic number tells us the total number of electrons in the atom. Assign the electrons to their respective shells: 2,8,8 (1st, 2nd, 3rd respectively). Figure out the number of electrons on the outermost shell. This is your number of valence electrons. The valency is then simply the number of electrons it will take to maximize the electrons in the outer shell to form a stable atom.

I hope this unit will clear up the confusion about how we determine the valency. In future units you will see how a solid understanding of valency will allow you to track along with more complicated topics.

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

Read an ABG in 4 Simple Steps

Arterial Blood Gas

Terminology

Arterial blood gas (ABGs) are drawn from arterial blood and measures the concentration of concentration of oxygen and carbon dioxide in the blood among other things.

Everything we will discuss is centered around the goal of maintaining a normal blood pH. The general term used for pathologies surrounding blood pH is acid-base disorders.

When are ABGs Used

illustration showing the systems typically involved when ABGs have abnormal values: the lungs, circulatory and metabolic systems.

ABGs are drawn when there is concern regarding the pulmonary system, circulatory system or metabolic processes.

These systems affect the major organs of the body and are necessary for maintaining homeostasis and the pH of blood.

They are codependent, and as we will see, they are so intertwined that they compensate for each other when one is dysregulated.

When coordination becomes so dysregulated that they can no longer compensate for each other we see critical illness. ABGs are usually needed in patients who are severely ill.

What do ABGs Measure

An ABG panel will report:

image showing the main components of an ABG report. oxygen, carbon dioxide, bicarbonate and pH.

pH: the degree of acidity or alkalinity

PCO₂: partial pressure of carbon dioxide i.e. the dissolved carbon dioxide in the blood

PO₂: partial pressure of oxygen i.e. the dissolved oxygen in the blood

HCO₃^–: dissolved bicarbonate in the blood

SaO₂: oxygen saturation. The percent of hemoglobin carrying oxygen

There are more components to the ABG panel but the concentration of oxygen, carbon dioxide and bicarbonate primarily affects the pH of blood and will be the focus of this unit.

Acid-Base Disorders:

There are 2 broad categories of acid-base disorders:

Metabolic Disorders

Respiratory Disorders

Each of these can result in either acidosis (low pH) of alkalosis (high pH)

illustration showing the clinical scenarios for acid base disorders.
Metabolic acidosis, metabolic alkalosis, respiratory acidosis, respiratory alkalosis.

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Primary Problem & Compensation

Illustration of the kidneys and lungs working together to maintain blood pH via the metabolic and respiratory system.

The respiratory and metabolic system work together to maintain pH of blood. They compensate for each other. When the primary cause of abnormal pH is because of respiratory issues, the metabolic system will try to compensate to restore pH. In this case the respiratory system is the primary problem and the metabolic system compensates.

Likewise, if dysfunction in the metabolic system is causing acidosis or alkalosis, the respiratory system will respond trying to correct pH. In this case the metabolic system is the primary problem and the respiratory system compensates.

Metabolic

Acid-Base Disorders

image showing that the kidneys regulate the uptake and excretion of bicarbonate to maintain blood pH

Metabolic acid-base disorders are oriented about the bicarbonate level. Bicarbonate is basic (alkalotic).

Metabolic acidosis will therefore result when bicarbonate levels are low. Metabolic alkalosis will result when bicarbonate levels are high.

Metabolic acid-base homeostasis is maintained largely by the kidneys. The kidneys are able to regulate the release or uptake of bicarbonate to maintain pH.

The respiratory response will compensate for pH imbalance that is caused by metabolic dysregulation. Respiratory response is fairly rapid, achieved by adjusting the rate of breathing (hyperventilation/hypoventilation).

Respiratory

Acid-Base Disorders

Respiratory acid-base disorders are oriented about the partial pressure of carbon dioxide.

Carbon dioxide is weak acid. Respiratory acidosis will therefore result when CO₂levels are high. Respiratory alkalosis will occur when CO₂ levels are low.

Respiratory acid-base homeostasis is maintained largely by the rate of breathing (respiratory rate).

Slowing down the rate of exhalation will keep more carbon dioxide which will increase acidity (low pH). Increasing the rate of exhalation will clear carbon dioxide from the blood decreasing acidity (increase pH).

Image showing the lungs regulating the levels of carbon dioxide in the blood to maintain plasma pH

Metabolic responses will compensate for pH imbalances caused by respiratory dysregulation. This is a slow response, it can takes hours or days for the kidneys to detect and adjust bicarbonate levels.

Blood pH Equation

Bicarbonate and carbon dioxide make up the main pH buffering system in the body. Plasma is 92% water therefore these molecules exist in plasma in solution creating a codependent balance between acids and bases.

This balance is represented by the equation below:

Image showing the blood main buffering system. It is dependent on carbon dioxide and bicarbonate.

Note that carbon dioxide and bicarbonate are on opposite sides of the equilibrium equation. To maintain equilibrium, if one increases in concentration, the other must decrease and vice versa. This is the basis of the tandem relationship of the kidneys and lungs in acid base disorders.

Image showing the lungs and kidneys as the primary organs that maintain the blood's pH

Normal ABG Values

As discussed above an ABG reports many values but we will focus on the three that are used to determine acid-base disturbances.

Chart showing the components and normal lab values on an ABG report.

Mental hacks to remember these values:

Notice that the pCO₂ range has the same value as the decimal points as the pH values (35 and 45)
(Bi) means 2. Your value range for (bi)carbonate includes all twos and 6 (22-26).

Read an ABG in 4 Simple Steps

When we read an ABG we want to determine the cause of an acid-base disorder. This is referred to as the primary problem. We can read an ABG in simple in 4 steps:

Image showing the 4 steps needed to read an ABG report

Is the pH: acidic or alkalotic?
Is the pCO₂ acidic or alkalotic?
Is the HCO₃ acidic or alkalotic?
Whichever (pCO₂/HCO₃) can be described the same as pH is the primary problem.

Illustration showing how pH, bicarbonate and carbon dioxide varies with acidosis versus alkalosis

Primary problem is respiratory if pH and pCO₂can be described the same (acidic/basic)

Primary problem is metabolic if pH and HCO3- can be described the same (acidic/basic)

Clinical Scenarios

Because respiratory will compensate for metabolic and vice versa there are really only 4 basic clinical scenarios that can result.

HCO₃ represents metabolic, pCO₂represents respiratory.

If pH is acidic, one value will also be acidic (primary problem) the other will be alkalotic (trying to compensate).

If pH is basic, one value will also be basic (primary problem) the other will be acidic (trying to compensate).

MedCalc offers an ABG analyzer. As always, I will caution you that no calculator assumes your liability in patient care. It is always best that you understand that values you are entering and how to interpret the results.

Example Calculations

These concepts are the foundation of acid-base base disorders. Can it get more complicated? Absolutely!

Compensation by either system is not complete, so it does not “solve” the primary problem. Secondary problems can also coexist with primary problems. We can have mixed acid-base disorders. ABGs can also present differently if the disturbance is acute versus chronic. You will have difficulty understanding these more advanced concepts of acid-base disorders if you do not get a good grasp on the concepts in this unit.

If you found this unit helpful, I would love to hear from you! Leave a question or comment below.

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

Statistics: How to Calculate Odds Ratio in 4 Simple Steps

Odds ratio is measure of probability. It is typically explained together with risk ratio or relative risk. I am opting to address these separately so that we can understand them as distinct assessments of probability.

The concept of statistical risk of more intuitive. Odds requires more orientation. The concept of odds is usually thrown in together with risk because there are common threads in how they are calculated. This type of explanation often results in an understanding of odds that piggybacks off risk instead of understanding odds in its own rights. Our goal is to understand not memorize so we will consider them separately.

Statistics can seem confusing because lecturers often assume that the reader already knows some key foundational concepts. They jump deep into statistics and never explain the simple parts which then makes it possible to follow along with the more complex parts. Let’s start at step 1.

Data Points

Illustration of the 4 types of ratio data

Whether you are calculating odds for your own research or assessing statistics published by another author, the first step is assuring that the correct type of data was used.

Calculation of odds requires the use of ratio data. Ratio data has 4 defining properties: quantitative, continuous, equidistant, have a true zero.

There is a unit on ratio data for the explanation of properties. If the correct type of data is not used, no useful information can be derived.

What are Odds?

Odds are…you’re have a hard time wrapping your head around risks and odds :). Here is a quick way to remember:

The odds of an outcome, the risk of exposure

When we think about odds we are looking at our results from the perspective of the outcome. We consider all the people who have a specified outcome and ask…is there an association between observing the outcome and having a specific exposure.

When we calculate odds we are looking at the presence of outcome and absence of outcome individually i.e. we can calculate the odds of an observed outcome and the odds of not observing the outcome. As you will see, this differs from odds ratio which compares the groups.

Understanding this distinction in terminology and using them consistently will make a huge difference in your ability to track along with statistical concepts.

Illustration of key difference in terminology between odds and odds ratio

Calculating Odds in 3 Steps

Orient your focus to the outcomes
Considering only persons who had the specified outcome
- How many had the exposure? A
- How many did not have the exposure? C
Odds = number exposed/number not exposed = A/C

You would repeat these 3 steps to calculate the odds with those persons who did not have the specified outcome.

Orient your focus to outcomes
Considering only persons who did not have the specified outcome
- How many had the exposure? B
- How many did not have the exposure? D
Odds = number exposed/number not exposed = B/D

For each outcome we are dividing exposed by non-exposed. Any nonzero number divided by itself is 1. Therefore, for each outcome, any deviation from 1 suggests that there is a difference that is associated with the differences in exposure.

Contingency Tables

We can place these values on a contingency table to calculate the odds for each possible outcome.

Illustration showing the odds of each possible outcome.

A: those who had the specified outcome and the specified exposure

B: those who did not have the specified outcome but had the specified exposure

C: those who had the specified outcome but not the exposure

D: Those who did not have the specified outcome but had the exposure

Note that all of these possibilities are first oriented to outcome and then assessed for exposure.

The odds of experiencing an outcome is: A/C

The odds of not experiencing outcome is: B/D

Again, with odds we are oriented to outcome. Looking at only the people who had a specific outcome we compare their exposures to see if there is an association between outcome and exposure.

We will briefly compare this to risk so that you see how they both can be calculated from one contingency based on where you orient your focus.

With risk we are focused on the exposure. Considering all of the persons who were exposed and not exposed individually what is the probability that we will see the specified outcome.

Illustrating that risk focuses on exposure

Same data points: the only thing changed was the focus on exposure versus outcomes.

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Odds Ratio

To calculate odds ratio we compare the odds from the group with the observed outcome and the group without the observed outcome. It is just a way to visualized the magnitude of the difference between the outcome and non-outcome groups.

With the hypothesis that outcome is based on exposure any difference between outcome and non-outcome is because of the difference in exposure. This is key to conceptualizing odds and odds ratio.

Showing the relationship between odds and odds ratio.

(A/C) / (B/D) is equivalent to (A x D)/(B x C)

If the odds are the same in both groups, then the odds ratio will be 1. Any non-zero number divided by itself is one. An odds ratio of one suggests that there is no association between observation of outcome and exposure. This is why 1 is a critical point of assessment with ratios. We will discuss this concept further when we discuss confidence intervals.

Any deviation from one suggests that there is a difference between the groups.

Overview of Calculations

Take the time to understand these steps. They are key to truly understanding the concept of odds. Odds are actually quite simple if you remember 4 things. Odds are:

1. oriented to outcomes

2. odds = exposure per outcome/non exposure per outcome

3. odds ratio = odds outcome/odds no outcome

4. assumes that any difference in outcome is related to difference in exposure

Because odds of outcome is the numerator in the calculation of odds ratio, an odds ratio less than 1 suggests that:

odds of observing an outcome is less
outcome is based on exposure
therefore there is lower odds of observing outcome in the exposed
- there is a lower association of outcome with exposure

An odds ratio is greater than one suggests that:

odds of observing an outcome is greater
outcome is based on exposure
therefore there is a higher odds of observing an outcome in the exposed
- there is a greater association of outcome with exposure

One Step Further

Now that I have explained odds in the simplest form, comparing exposure to non-exposure I am going to stretch the concept to include multiple, differing exposures. All calculations will be the same. The only difference is instead of exposure and non-exposure we would consider exposure^₁ and exposure_².

This would look like a comparing an outcome of heart attack when treated with beta blocker (exposure^₁) compared with a calcium channel blocker (exposure_²).

Lets challenged everything discussed here with some examples:

Example Calculations

These examples are from the CDC. https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section5.html

We will work through them using our strategy and see if we will arrive at the same answer.

Example 1: In an outbreak of tuberculosis among prison inmates in South Carolina in 1999, 28 of 157 inmates residing on the East wing of the dormitory developed tuberculosis, compared with 4 of 137 inmates residing on the West wing.

Calculating the odds:

Outcomes₁: tuberculosis Outcome₂: no tuberculosis
Exposure₁: East wing Exposure₂: West wing
Contingency table oriented to outcomes:

Odds looks at each outcome individually

Any difference in outcomes is theorized to be associated with difference in exposure
Odds ratio compares the odds of the outcomes

Example 2: To study the causes of an outbreak of aflatoxin poisoning in Africa, investigators conducted a case-control study with 40 case-patients and 80 controls. Among the 40 poisoning victims, 32 reported storing their maize inside rather than outside. Among the 80 controls, 20 stored their maize inside. The resulting odds ratio for the association between inside storage of maize and illness is:

Outcome₁: illness Outcome₂: no illness
Exposure₁ inside storage Exposure₂: outside storage
Contingency table oriented to outcomes:

Summary of steps for calculation of odds ratio

My hope is that this breakdown of odds will boost your confidence in understanding statistical data. If you found this helpful I would love to hear from you, leave a comment below!

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

Statistics: How to Calculate Absolute and Relative Risk

You will often encounter ratio calculations in medical literature. It is a calculation of probability. Ratio calculations include absolute risk, absolute risk reduction, absolute risk increase, number needed to treat and relative risk.

Risk calculations are especially useful in cohort studies and randomized controlled trials where selected patients are observed over period of time to determine if they will experience a particular outcome. In other words, the probability that they will experience a particular outcome. In other words, their risk of experiencing a particular outcome.

illustration showing the relationship between absolute risk and relative risk in a cohort study

The incidence of occurrence in each group is the absolute risk.

Relative risk compares the probability of outcome in one group versus the other.

The ratio of absolute risk between the 2 groups is the relative risk or risk ratio.

illustration showing the relationship between absolute risk and relative risk in a controlled trial

As a practitioner, you may be tasked to perform ratio calculations for your own publications. Most often you will be assessing the ratio calculations of other authors as a way of validating their results. We should make some effort to evaluate literature for use of appropriate data points and the corresponding statistical test. If the data points and/or test are not appropriate no valid information can be derived from a study.

The type of data that is needed for calculation of relative risk is very important. In the unit Statistics: Ratio Data we discussed several important foundational concepts for understanding calculations of risk. I highly recommend reviewing this unit.

Ratio calculations, including relative risk, requires the use of ratio data. Ratio data has 4 properties.

Image showing the different types of ratio data

Ratio data is:

quantitative
continuous
equidistant
has a true zero

The unit on ratio data that explains each of these properties.

Knowing that the appropriate data points were used is the first step in the assessment of ratio calculations.

Once we validate data points as ratio data we can proceed to the calculation of risk.

Contingency Tables

To perform ratio calculations we set up contingency tables. These tables organize the observed and non-observed results for each group of patients in a way that allows us to calculate probability.

We have 2 study groups (exposed/intervention) each with one of 2 possible outcomes or results. These 4 values will be placed in their respective position on the contingency table. We will use the following letters to represent each value.

A: those who had the specified exposure and the specified outcome

B: those who had the specified exposure but no specified outcome

C: those who did not have the specified exposure but has the specified outcome

D: those who did not have the specified exposure and did not have the specified outcome

Using our contingency table with letters (ABCD) to represent the outcome for each of the 4 groups, we will set up the equation for calculating absolute risk.

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Absolute Risk

Absolute risk is the probability of an event occurring within ONE group i.e. either the exposed group or non-exposed group. Terminology will start to become very important here as we differentiate between absolute risk and relative risk. Teasing out these differences will take you far in understanding statistics. With absolute risk we are looking at ONE group at a time.

Let us consider our exposure to be: daily exercise for 1 month and our outcome to be: atleast 1 pound weight lose.

Absolute Risk Scenario 1: Exposed

Of all the people who exercised daily for one month what is the probability that they will lose atleast 1 pound (Group A: exposed + outcome). This is the absolute risk for the exposed group (A+B)

illustration showing contingency tables for absolute risk calculations in exposed patients

Absolute Risk Scenario 2:

Of all the people who did NOT exercise daily for one month what is the probability that they will lose atleast 1 pound (Group C: not exposed + outcome). This is the absolute risk for the non-exposed group (C+D).

illustration showing contingency tables for absolute risk calculations in non exposed patients

Again, when we think about absolute risk, we are considering the probability of a specified outcome in the exposed and non exposed group individually.

Absolute Risk Difference

Once we know the absolute risk for each group there are many other calculations that can be derived from those values.

Absolute risk difference in simply the numerical difference between the absolute risk in each group. This is also sometimes referred to as absolute risk reduction or absolute risk increase (reduction or increase being the two differences that can occur).

From this simple calculation of difference we can derive a very important value: the number needed to treat.

Number Needed to Treat

The number needed to treat (NNT) is the number of persons that need to be exposed in a given time period to see a specified positive outcome or prevent a negative outcome. NNT is calculated as follows.

The number needed to treat give us a sense of the impact an exposure/treatment will have. It is valuable when considering if the cost or complexity of an intervention justifies the outcome we are seeking. It is expressed as the nearest whole number.

Relative Risk

Using the absolute risk values from the exposed group and the non exposed group we are also able to calculate the relative risk. Relative risk is also referred to as risk ratio. The question we are attempting to answer with relative risk: is there a difference in risk between persons exposed and not exposed?

Relative risk compares the risk between the 2 groups. It is the incidence of an event or outcome in the exposed group divided by the incidence in the non-exposed group. Compare this to absolute risk which considers one group at a time. We calculate relative risk by dividing the absolute risk of the treatment group by the absolute risk on the non-exposed group.

When we compare 2 groups using their relative risk we are asking: is the probability of an event occurring greater in the exposed group or the non exposed group?

If the probability of risk is the same in both groups, the absolute risk will be the same for both groups. Any non-zero number divided by itself will have a value of 1. This is why 1 is a critical value in the assessment of ratios. A value of one is the point of significance, it suggests that there is no difference between the exposed and the non exposed groups. Any deviation from one suggests a difference exist between the groups.

Because the absolute risk in the treatment group is the numerator in the calculation of relative risk, a value less than 1 implies there is less risk of outcome in the treatment group. If the relative risk is greater than 1 is implies there is a lower risk out outcome in the non-exposed group.

Calculations

Let us put all of these calculations into an example.

Example calculation of absolute risk, absolute risk difference, number needed to treat and relative risk

Absolute Risk Exposed: There is a 45% chance of outcome being observed in the exposed group
Absolute Risk Non-Exposed: There is a 29% chance of outcome being observed in the non-exposed group
Absolute Risk Difference: There is 16% increase in risk of occurrence in the exposed group
Number Needed to Treat: Atleast 6 patients need to be exposed for an outcome to be observed
Relative Risk: 60% more likely to observe outcome in exposed group relative to non-exposed group.

MedCalc provides a risk calculator. As always, it is best to use these calculators as a tool once you’ve understood the concept.

Illustration showing the sequence of risk calculations

Hopefully this unit has truly helped you to understand the terminology and intention of ratio calculations. I hope that it takes you away from simply memorizing equations to understanding what you are doing and why.

If you’ve found this information helpful I would love to hear from you! Leave a comment below.

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

Ratio Data: How to Analyze Statistics in Medical Literature

Statistics can seem daunting but they cannot be avoided in medical research. If we don’t understand statistical concepts, like ratio data, we are at the mercy of the author’s conclusions. While there are guidelines and peer review processes that help to maintain the integrity of how studies are conducted or reported, there are gaps.

Perhaps you’ve heard of John Carlisle whose skill in statistical analysis has led to the retraction and correction of hundreds of publications including randomized controlled trials and studies published in the New England Journal of Medicine. The concerns raised were both from mistakes but some were also because of misconduct. You can read more about the work of John Carlisle here. It will undoubtedly impart the importance of having a working knowledge of statistics.

The goal here is not to become a statistician. At the most basic level we should be able to look at the main outcomes of the study and determine if the numbers support the conclusions of the author. Let’s start with understanding ratios.

Statistical Tests

Statistical tests are tools that we use to analyze data and make predictions. They are mathematical formulas that are based on validated assumptions. One of those assumptions is the type of data that is being studied. Statistical tests are like mathematical recipes. The recipe was created to use specific ingredients. If you deviate from that you will not get the mathematical “cake” intended by the test.

One of those mathematical ingredients needed for statistical tests is the type of data.

It is important to understand the difference between the type of data and calculations that use a specific type of data. Some of the terminology is very similar. Taking the time to tease out those small differences will make it easier to actually understand statistical concepts.

Ratio Data vs Ratio Calculations

Image highlighting the important difference between ratio data and ratio calculations.

The term ratio descriptive. It tells you the characteristics of the type of data that was used for the calculation or to obtain a result.

Often, you will hear, “there are 2 kinds of ratio: risk ratio and odds ratio”.

In reality, there is only one type of data set that can be referred to as ratio but there are multiple ratio calculations (risk ratio or odds ratio) that can be derived from ratio data.

It is a small but simple distinction that can resolve a lot of confusion when trying to understand statistics.

Ratio is a type of data. Odds ratio and risk ratio are ratio calculations.

Odds ratio and risk ratio are calculations of probability using ratio data points.

Properties of Ratio Data

When the term ratio is used this automatically implies 4 properties of the data.

Ratios can only be used to describe data that is quantitative, continuous, equidistant order with a true zero.

This is a mouthful but each those components are important. Once we break down what each means, it will be easy to remember.

Illustration showing the 4 type of ratio data

Knowing whether the data used to calculate the probability of risk is ratio (i.e. quantitative, continuous, equidistant order with a true zero) is the very first step is knowing that the correct calculation was done. It is how we know that the right ingredients were used for a particular statistical test.

Illustration explaining the differences between 4 types pf ratio data

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Quantitative Data

Quantitative simply means that the variable has a value or number that can be measured. It is not descriptive like white or black, yes or no. Is it quantitative data? Ask yourself: Can I measure this variable and assign it a numerical value? Ratio data, used in ratio calculations must be quantitative.

Continuous Data

Illustrating the difference between continuous and discrete data

Continuous data means that it can take any value within a range. You could not predict what the value could be because there are an infinite number of options. For example, if I ask you to pick a number from 1-5 that number can be: 1, 4, 1.25, 3.6, 1.678, 0.004, 2.99984.

Considering the opposite of continuous data will help make it clear.

Discrete data is the opposite of continuous data. Discrete data is a finite or countable number of options. For example, if I asked you to choose 1 of 5 people, then that would be discrete because it can only be a whole person, there is no in between, no half person.

In both cases you’re choosing from 1-5 but what you are choosing is what makes it continuous versus discrete. How can you remember what is continuous versus discrete data? Ask yourself: Can I break the variable into smaller units?

Can I breakdown number of people/patients into smaller units? No! Therefore number of people/patients is discrete data.

Can I break down length of time (time to an event like occurrence of a heart attack) down into smaller units? Yes! Did it occur after 2 years or 2 months (i.e. 0.67 years)? If the variable can be a expressed as a decimal or fraction it is continuous data. Ratio data, used in ratio calculations must be continuous.

Equidistance

Equidistant order means that there is a established hierarchy of the data points AND there is an equal distance/measurement as you move along the hierarchy.

Let’s use the same example of 1-5. We all agree that after 1 comes 2, then 3, then 4, then 5. As we move from one to the other the difference is consistently 1. This the basis of measurement tools like rulers.

Let’s consider college degrees as a data point. There is a clear, established hierarchy there. Associate degree, to bachelor’s, to master’s degree, to doctoral degree.

What is the numerical value that can be measured between those degrees? There is none! They are ordered but not equidistant and therefore cannot be ratio data or be used in ratio calculations.

True Zero

If at point 0 of your data, nothing exists then your data set has a true zero. True zero means we can get to a point where nothing would exist i.e. a point of nothing. There are no negative values because there nothing less than zero with ratio data.

Why is it called true zero instead of just zero? Because in some cases, specifically temperature in Celsius, zero degrees does not create a point of nothing. In fact zero Celsius will create something… ice! There must be a complete absence at point zero for it to be considered true zero.

This includes data points like number of patients or objects. We can get down to zero patients but not a negative number of patients.

Weight: at 0 kg, nothing exists. Change is weight can also be zero. Height: at 0 inches, there is nothing. Time: at 0 seconds, no time has past.

Image showing examples of what would be considered true zero in statistical calculations

For whatever variable (X) you are considering ask yourself: if I have zero of X, do I have nothing? If yes, then your data has a true zero. True zero must exist for your data to be considered ratio and used in ratio calculations.

If you are presented with results of a study that utilizes ratio calculations like risk ratio and odds ratio, you can verify that the correct mathematical ingredient (ratio data) has been used. Look at the variable that was used in those calculations and ask yourself: is it quantitative, continuous, equidistant AND has a true zero?

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.

Community Acquired Pneumonia: When to Admit to ICU and How to Treat

In this unit we will discuss the subset of patients with community acquired pneumonia who are at a higher risk for morbidity and mortality. Those patients require a high level of inpatient care and should be admitted directly to intensive care.

In the unit Community Acquired Pneumonia: Inpatient Treatment we introduced the CURB 65 score. This tool assesses the need for hospitalization in patients with pneumonia. A score of 2 or more suggests that the patient needs to be treated in the hospital.

Once we’ve determined the need for hospitalization we use the Severe CAP criteria to determine the level of care needed in the hospital. The Severe CAP criteria is a clinical diagnostic tool used to predict the probability of ICU admission.

Diagram showing the decision pathway for where we treat community acquired pneumonia

For patients who are critically ill, the risk of mortality is higher if they are first placed on the medical floor and then transferred to ICU. Assessing the need for a higher level of care is one of the 3 “where questions” in the treatment of pneumonia.

The severe CAP criteria is divided into major and minor criteria.

Major Criteria

The major criteria are straightforward. If you patient is hypotensive enough to require the use of vasopressors or requires mechanical ventilation due to respiratory failure, the recommendation is that your patient is admitted directly to intensive care.

Minor Criteria

If your patient does not clearly need ICU admission we assess the minor criteria. If there are 3 or more minor criteria, this suggests that your patient is high risk for ICU admission.

The selection of appropriate antibiotics in patients admitted to the ICU for community acquired pneumonia is dependent on specific risk factors.

Illustration showing the history of exposure that must be assess on all patients with CAP

All patients must have a throughout assessment of their medical history to see if they have had:

history of respiratory MRSA infection in the past 12 months
history of pseudomonas infection in the past 12 months
history of recent hospitalization in the past 3 months with use of IV antibiotics

If none of these are present then your patient is considered to have no significant medical history with regards to pneumonia.

These risk factors result in 5 clinical scenarios for your patients with community acquired pneumonia requiring intensive care.

Clinical Scenario 1:

Your patient has no history of MRSA or pseudomonas in the last year and no hospital admission with IV antibiotics in the last 90 days.

Treatment algorithm for empiric treatment of CAP with alternate therapies when there are no risk factors for MRSA and pseudomonas

Fluoroquinolone monotherapy is not recommended for inpatient treatment of CAP.

Clinical Scenario 2:

Your patient has a history of respiratory MRSA in the last 12 months.

Treatment algorithm for empiric treatment of CAP with alternate therapies when there is a history of MRSA

Clinical Scenario 3:

Your patient has a history of respiratory pseudomonas in the last 12 months.

Treatment algorithm for empiric treatment of CAP with alternate therapies when there is a history of pseudomonas

Zosyn will provide the coverage of regimen 1 + pseudomonas coverage. This is the same regimen for a patient non-severe inpatient CAP (general medical)

Clinical Scenario 4:

Your patient has a history of respiratory MRSA and pseudomonas in the last 12 months

Treatment algorithm for empiric treatment of CAP with alternate therapies when there is a history of MRSA and pseudomonas

This is the same regimen for a patient non severe inpatient CAP (general medical) with history of MRSA and pseudomonas.

Clinical Scenario 5:

Your patient has a history of hospitalization with intravenous antibiotics in the last 90 days

vancomycin + piperacillin-tazobactam
Get sputum gram stain and culture
Deescalate to standard regimen (clinical scenario1) is results return negative.

If you compare scenarios 5 in the ICU group and general medicine group we see that in the more critically ill patients we do not wait for culture results to expand coverage for multidrug resistant bacteria. In both cases we obtain cultures, ideally prior to any antibiotic treatment but wait on the results to broaden coverage in non-ICU patients.

It is a good idea to compare each of these 5 clinical scenarios for ICU patients to the corresponding scenarios for non ICU patients. It is more efficient to know one set of regimens and how it changes with a different level of care versus memorizing each as separate topics. You can find the regimens for non medical ICU patients here.

Alternative Antibiotics

When are they needed?

Illustration showing the list of considerations that must be made when choosing an antibiotic

The primary regimen provided in each clinical scenario include antibiotics that are fairly common throughout the United States. A common reason you will have to deviate from this standard regimen is allergy.

Pneumonia guidelines are laced with beta lactams. Unfortunately penicillin is also the most commonly reported drug allergy. Whether these are true anaphylactic responses or simply drug intolerances/unfavorable side effects is another discussion in itself.

Some hospitals preferentially use antibiotics that have lower dosing frequencies or requires less management. Azithromycin, for example, is dosed daily, clarithromycin is dosed twice a day. Vancomycin requires patient specific dosing and fairly frequent monitoring of labs and levels. Linezolid does not.

Certain antibiotics may be restricted to use only by infectious disease doctors due to their cost and spectrum of coverage. Those antibiotics are usually referred to as the “big guns” and are reserved for especially resistant strains of bacteria like extended spectrum beta lactamase resistance or Acinetobacter.

Know what antibiotics are on your hospital’s formulary and which have restricted access.

Sputum Cultures:

When are they needed in CAP?

The ATS/IDSA guidelines state that they are “neither for or against routinely obtaining sputum gram stain and cultures in all adult patients treated in a hospital setting.”

They however specifically recommend sputum gram stain and cultures in severe CAP (ICU admission) and when there are risk factors for MRSA and pseudomonas (history for prior infection in the last 12 months or history intravenous antibiotics in the last 3 months).

Illustration showing the decision algorithm for sputum culture in patients with CAP in the ICU

If there is an actual documented history of MRSA and/or pseudomonas: start empiric antibiotic coverage and deescalate if the sputum results are negative.

If they have no history of respiratory MDR bacteria but are at risk for MRSA and/or pseudomonas due to exposure wait for culture results before extending coverage.

Gram stains usually result in 24 hours, culture results in 24-48 hours.

Blood Cultures:

When are they needed in CAP?

ATS/IDSA guidelines recommended that blood cultures be drawn PRIOR to initiation of antibiotics only in those same patients we just discussed for sputum cultures. Hospitalized patients with:

severe CAP (ICU admission)
history of respiratory MRSA and/or pseudomonas in the past 12 months
recent exposure to MRSA and/or pseudomonas exposure i.e. hospitalization with intravenous antibiotics in the past 3 months

If we’re covering MRSA and/ or pseudomonas for treatment of CAP we need blood and sputum cultures.

Why do we need blood cultures for pneumonia?

Infectious organisms can enter the lower respiratory tract in 1 of 3 ways:

direct inhalation
aspiration from the throat (oropharyngeal)
via the blood from another site of infection (hematogenous transfer)

Duration of Treatment

The ATS/IDSA guidelines are pretty straightforward with regard to the duration of treatment for CAP.

Treatment should be no less than 5 days even if patient is clinically stable before then
If CAP is due to MRSA or pseudomonas then treat for 7 days

IDSA provides a great overview of the clinical pathway for community acquired pneumonia that is a great supplement to what you’ve learned here.

Hopefully the way the guidelines have been deconstructed here will make it easier to apply in your practice. CAP is one of those disease states you will see over and over again. Use the aids and illustrations as a reference and soon it will become second nature.

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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.