As I said, my name is Colin Rogerson. I'm an intensivist at Indiana University, right at Hospital for Children. We've just had a huge deluge of respiratory physiology for the last couple hours. Now we're going to get into why all of us really went into critical care medicine for the statistics. So statistics is challenging because you can't really draw on your last three plus years of clinical experience to answer the questions. No one had a baby with HSV and tried to calculate the PPV of their test to decide a cycle of your treatment. So it's really just about learning the statistics, learning the equations, studying them before the test. And most of these, again, if you know the equations and you understand the statistics, are pretty straightforward questions to get the points on. So here's the content outline. There's a ton of stuff there. We're not going to be able to cover all that in 20 minutes, the full slides should have things about all of it. But I'll try and hit the highest yield points and the highest yield questions. I took this exam about four years ago, so hopefully we can go over the things that you are most likely to see on the test. So we'll start off with the simple basics, so types of variables. Most of us are pretty familiar with these, but they do find ways to ask you questions about these on the exam. So binary is your first one. It's going to be 0 or 1. Did they get intubated, yes or no? Did they die, mortality, yes or no? We know in the ICU, maybe we try and make mortality not quite a 0 or 1, but that is what it is on the test. Nominal, so this is going to be your unordered categorical variables. And so things to think about with these are variables that the order of the sequence doesn't matter. So this would be like primary diagnostic category, cardiac, respiratory, neurologic. Ordered categorical, these are going to be your pain scales, where they're not exactly continuous, but there is an order to them that makes a difference in how they're represented. And last is your continuous variables, where they'll all be numeric, sometimes with a decimal, sometimes without. So things to think about here would be like a lot of your vital signs, heart rate, respiratory rates are continuous variables. And then time to event is a little bit of a unique example of a continuous variable. But these questions are pretty straightforward, but they can show up on the exam. Other things that, again, you've probably seen for years and years now. So the normal distribution, I'm sure you're pretty familiar with it, but they do find ways to bring this up on the exam. So things to know is that it is symmetric, meaning that the mean, median, and mode should all be very close together. And then if you take standard deviations, one standard deviation plus or minus, the mean should capture about 68% of the observation seen in a normal distribution. Two standard deviations is 95, and three is 99.6. And this is in contrast to a skewed distribution. Things to remember, the skewed sidedness depends on where the tail is. So this is a right skewed distribution. And if the tail was on the left side, it would be a left skewed distribution. And how this changes compared to the normal distribution is that it is asymmetric. And the tail, or the skewness, will pull the mean that direction. So in a right skewed distribution, the mean will be towards the right, will be bigger than the median and the mode. And if you have a skewed distribution that's not normal, you cannot use, again, this is more straightforward for the test statistics than actual statistics, you will often fail to meet the assumptions of the normal distribution, have to use nonparametric tests as opposed to parametric tests. Precision versus accuracy, again, just concepts that you kind of have to memorize. I think the most helpful thing is just the images on the right. So you would like a test to be both precise and accurate. Accurate meaning that it will give you the correct measurement. So for example, a lot of times they use thermometers as a test, and so if you have an accurate thermometer and someone is 102 degrees Fahrenheit, they would like that thermometer to measure 102 consistently. And precision would be that whatever measurement it gets, it gets a very close measurement to the same one every time you do it. So top left is accurate and precise. Top right is accurate but not precise, meaning that you get different measurements every time. But if you took the average of all the measurements, it would be the actual true temperature. Bottom left would be precise but not accurate, meaning the measurements are close together. But if you take the average, it's not what the actual temperature would be. And bottom right is neither accurate nor precise. All right, moving on to risk and odds. So risk is probability is chance. And so all of it is the number of times something happens divided by the number of times it could have happened. Odds is slightly different because odds is the number of times something happens over the number of times it didn't happen. So for an example, if you take a standard deck of playing cards that has 52 cards in the deck and four suits, there are 13 cards in each suit. And if you wanted to calculate the risk and the odds of drawing a diamond suit from a random card in the deck, the risk of the probability would be 13 diamond cards in the deck. There's 52 cards in the deck, so 0.25 or 1 out of 4 risk or probability of drawing a diamond. Odds, you change the denominator. So you subtract from 52, 13, which would be the number of times that it did happen or could happen. And so you'd get 13 divided by 39, which is 0.33. And this is important for how things are measured in studies, especially with logistic regression, which uses odds as opposed to risk. So getting into what you could be asked about this on the test, these are some of the equations that, again, you'll have to know, because if you know them, they're very straightforward and easy points to get on the test. So relative risk, which is the risk in one group in a study compared to the risk in another group in the study. And so typically, we put the treatment group on top over the control group on the bottom. And you're looking at the probability of the primary outcome, which is often but not always mortality. In the example we use here, it is mortality. So we're going to look at the ARDSNet tidal volume trial from the year 2000. The treatment group was the one that got 6 cc's per kilo of tidal volume. And the control group was about 12 cc's per kilo of tidal volume. And they looked at the outcome of mortality. And as you can see, the treatment group had a mortality of 31%. The control group had a mortality of 39.8%. So the relative risk is the division product of those two, which is 0.78. If the relative risk or risk ratio was 1, there would be no difference. If it's lower, that means your treatment improved, had a lower chance of the outcome of interest than in the control group. And so once you have a risk ratio, you can translate this to an absolute risk reduction. And so this is simply just looking at the risk of the primary outcome and the difference in that between the groups. So you take the higher risk, 39.8% mortality in the control group minus 31.0% mortality in the treatment group, and you get 8.8% absolute risk reduction. And then you can use this value to calculate the number needed to treat. So you take 100 divided by your absolute risk reduction. And in this example, you get 11.4, which interpreting this means that if you were to treat 11.4 or 12 patients with the lower tidal volume as compared to the higher tidal volume, you would save one life. All right, moving on to the other popular table, which is the 2 by 2 table of sensitivity, specificity, positive predictive value, negative predictive value, which you've probably seen on every board and shelf exam that you've taken in some regard. It's going to be back again on this exam. And it's really just knowing how to build the table and how to calculate the things that it could potentially ask you about. So the complete table is there in the top right with the diseased and healthy. So your gold standard or true diagnosis in the top. And then the test value is positive or negative on the left. And then you have your summative values on the right and the bottom. So measures that are intrinsic to the test that you're using are going to be your sensitivity and your specificity. So your sensitivity is the chance of a patient with the disease testing positive for the disease. And the specificity is the chance that a patient that does not have the disease tests positive or negative for that disease. And the equations, again, are written up there just using the two by two table. So you take the table element that you're interested in divided by the sum of either the column or the row or the column for sensitivity and specificity. Then moving on to positive negative predictive values, you'll go horizontal as opposed to vertical. So the positive predictive value, what's the probability that a patient that has a positive test for the disease actually has the disease? And negative predictive value, what is the probability that a patient that tests negative for the disease actually does not have the disease? The other question that they really like to ask in these types of tests is what disease prevalence has to do with these values. Remember that sensitivity and specificity are intrinsic to the test, not the population. So those do not change depending on the prevalence. But the positive and negative predictive values do depend on the disease prevalence in the population that you're studying. And so if you have a very rare disease, the positive predictive value will go down because the disease is very rare. But if you have a very high prevalence disease, we're going weird again. So to finish my thought, if you have a higher prevalence, then your positive predictive value will be higher. Anything I need to do? All right, I'll keep going. So regression terminology, things to know, so the dependent variable is going to be the variable typically on the left side of the equation, the one that you're trying to predict, the outcome variable that you're interested in. So it could be mortality, could be ventilator-free days. It's the y variable in the equation. And the independent variable is going to be all the other variables that you add into the model, so your covariates or your explanatory variables or your predictors. And these can be a mixture of continuous, categorical, whatever you'd like to include. And again, this is one example of a regression equation. But typically, you'll have your outcome variable as your y on the left, and then your explanatory variables as your x's with beta coefficients on the right side. So type of regression, it depends mostly on your outcome variable that you're interested in. So logistic regression is used to predict or to model categorical outcomes, usually binary in nature. So if you're going to predict mortality, if you're going to predict intubation, those types of things are binary outcomes. And so you'd use logistic regression, which again, like we talked about, relies on odds. Linear regression is for continuous variables or continuous outcomes, like if you were going to predict an oxygenation index or a respiratory rate or a heart rate or something like that, you would use a linear regression or a variable of linear regression. And then if you're going to predict a time to an event, that's when you'd use Cox regression. Other point would be, so incidence and prevalence, you could potentially get asked about. The way I remember this best is the epidemiologist's bathtub. So for example, let's use BPD. Prevalence would be at a single point in time, how many kids in a geographic area have BPD? Incidence is how many new ones are coming in over a period of time. So incidence can't be a flat number. It has to be a rate. So 500 cases per year or something like that is what's coming into the prevalence. And then the ways to decrease the prevalence is either recovery, BPD gets better, or death. Measures of correlation. So again, correlation is a measurement of how associated two variables are. Typically, it's one of the explanatory variables on the x-axis and the outcome on the y-axis. A positive correlation means that as your explanatory variable increases, your outcome also increases. Negative correlation is the opposite. Both are correlated. And correlation always goes from negative 1 to positive 1. So positive 1 would be they're perfectly correlated. Negative 1 is they're perfectly negatively correlated. And 0 is they're not correlated at all. It would be just a scatter of values. Pearson's correlation is the parametric version. And it will give you an r value. So r is your correlation that goes from negative 1 to positive 1. And if you square that, you get your r squared value. And what that measures is the percent of the variability in the outcome that can be explained by your x variable, your explanatory variable. Next up, looking at different kinds of studies. They do have questions about study design. And we'll want to know some of the specifics about what these are testing or how to set these up. So for example, your experimental study is going to be a randomized controlled trial. For the exam, this is your gold standard clinical trial to provide causal effect, to say that this treatment directly affects this outcome. Other important thing is that really why it's the gold standard is because all the unmeasured confounders are, in theory, equally distributed between the groups due to the randomization process. Observational studies are not randomized. And these are the three main ones that they ask you about, so your cohort, your case control, and your cross-sectional. There's a lot of grayness between these in actual research. But for purposes of the test, they try to make it very straightforward. So for the cross-sectional, it's usually going to be a single snapshot in time, usually a survey, to say how many patients in this state have bronchopulmonary dysplasia. And then you do a survey, and you get the prevalence. And that's a cross-sectional study. So a case control study is going to focus on the disease of interest. So for example, let's use HPV-associated cervical cancer. So a case control study would be, I'm going to find a group of cases that all have cervical cancer. I'm going to find a matching control. And then we're going to look backwards in time to find who had HPV and if the rate is the same or different between the groups. So case control focuses on the disease. And it's good for rare diseases because you build cases based on the disease. Cohort is different because you're focused more on the exposure and not the disease. So for that example, you would find a cohort of patients that all were exposed to HPV. And then you would look either forward or backwards in time to find who ended up getting cervical cancer. So best way to remember these for the test, case control, you focus on the outcome, the disease you're interested in. Cohort, you're focused on the exposure that you think is related to the disease. Final couple of points, so type 1 and type 2 errors. So type 1 error is measured by your alpha value. It's the probability of incorrectly rejecting the null hypothesis and concluding that there's a statistically significant difference between two groups, your treatment and your control group. So we measure this by an alpha level, which we equate to a p-value. And what that p-value is measuring is the probability that the results that show a difference between these groups is just due to chance alone. And we arbitrarily have set that at 0.05 in most studies. That's type 1 error. Type 2 error is your beta value. And type 2 error is the probability of failing to reject a null hypothesis, saying that there is no difference between the groups when there actually is a difference between the groups. So we usually change the beta value into a power, which is 1 minus the beta. And we generally say about 80%, sometimes 90%, is the risk that we're willing to accept of failing to reject the null hypothesis if there's actually a difference. Other thing to note is that as sample size increases, you get more power in a study. So if you want 90% power, you'll need a bigger sample size. 80% power will be a lower sample size. So if you have a hard time remembering the difference between these two and which one's which, you can use this, which always helped me. Type 1 error, concluding that this man is pregnant. Type 2 error, concluding that this third trimester woman is not pregnant. So conclusions, there's a lot of statistics that you have to know for the test. There's a lot of equations you just have to memorize and write down. And you know how to use the 2 by 2 table. You have to know how to do absolute risk reduction, number needed to treat those types of things. But again, if you learn them the week before the test, they're pretty easy to get. There's a lot more things in the full slide packet than this. But I think these are the most high yield things. So thank you.

critical care medicine

statistics

exam preparation

sensitivity and specificity

study designs