Regression Analysis Explained: Confounders & Clinical Meaning

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Well, welcome to this lecture where I'm going to be covering the very basics of regression analysis.
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And this is part of our series on summary statistics, specifically in the area of inferential statistics.
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Hey guys, I'm Dr.
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Bustaye, your faculty and host on This Is Why, a show that helps healthcare professionals transform their medical knowledge from what to why.
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Because when you know why you do what you do in the proper context of the evidence, it changes the how.
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And that changes everything about how we approach everyday decisions and the patients that are depending on us.
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Okay.
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In this particular topic, if you need a full access to the playlist and all the topics that go around it in the area of descriptive and inferential statistics, okay, check out that summary statistics playlist andor collection over on YouTube or over at the website thisiswhy.
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Okay.
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This stuff is relevant not only for board exams, but for those of you learning andor developing clinic uh clinical research protocols that are going to go through the IRB.
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You want to set it up right at the beginning, right?
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Especially if you're going for funding.
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But you also need this for real-world practice if you're reading papers.
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Okay.
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Now, this particular topic follows other inferential statistics, things like p-value, the effect sides, that's like odds ratios, risk ratio, relative risk, hazards ratios, and those things.
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And again, those are in that overall series.
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So I'm just trying to help you stay oriented.
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So as we go through the topics, we're in the biostatistics series, and there's three parts.
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Okay.
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Part one is before the study starts, that statistical analysis plan.
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Part two is the part that happens when you get the completion of the study.
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And then part three is really a separate discussion on its own.
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But when we talk about evaluation of studies, uh, it has to do with diagnostic tests.
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All right, so remember, before the study starts, so if you're in that research development stage and this topic is applicable to you, right?
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That's when you're doing the statistical analysis plan.
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You're coming up with your hypothesis.
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You're establishing what type of data is it nominal, ordinal, continuous?
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What type of study groups do you have?
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Are you going to use parametric, non-parametric statistical analysis?
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And then do you need to do an alpha uh analysis and to set that and do a power analysis to determine your sample size?
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Whereas part two, which is where we're at, again, just to keep you oriented, there's descriptive statistics that describe our data that we collected, how it is interacts with each other, how far away from it it is, what kind of data does it generate, mean, median, modes, those kind of things, right?
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Interquartile ranges and things like that.
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And then there's that inferential statistics.
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And we're on this topic regression analysis, where we really start to think about how variables and confounders that exist in patients are interacting and influencing one another.
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Okay.
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Now, um, so when we start thinking about that in regression analysis, we need to think about the application.
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Okay, as a clinician or as a researcher, the so what who cares?
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So let's take, for example, a scenario like we have a 55-year-old patient with known chest pain, okay, and you you say, okay, well, what factors independently are going to predict the risk of myocardial infarction?
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And how do we adjust then for going to look at other variables?
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How do we adjust for things that we know can influence and are associated with that outcome?
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Things like age, smoking, diabetes, and the list goes on, right?
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You can do BMIs, waist circumference, things like that.
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All of those things start to interact with each other because when you do a study and at the end of it you get a result, what you're hoping to be able to help the clinician, right?
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Bringing new information to the front lines is this intervention that we were looking at the result of the outcome?
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Or were there other things that could be influencing that outcome?
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And did we control for them?
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And do we even know what they are?
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They also help us when we're thinking about risk stratification tools.
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We think about those patients who have risk factors for a disease.
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All of these things become important in developing risk calculators, guideline committees use them for establishing recommendations.
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Okay.
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And almost every observational study that you read will do that.
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For example, things like the Framingham, ASVC, uh ASCVD scores, things like, and confounders adjustments that are occurred in those observational studies.
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That's how we developed those tools.
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Without them, we would not be able to stratify and understand those risk factors that play the predominant role on that outcome that we're worried about.
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And so when you think about regression analysis, it's a mathematical model, an equation that predicts the influence of one variable, an association, on another variable, especially as it changes potentially.
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All right?
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And you're gonna hear from me a lot of words that sound a little confusing.
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I'm just gonna say that up front.
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It's difficult to sometimes, if you don't do this on a regular basis, or if you're not a biostatistician, which I'm not, and other people are not, while I've had training in evidence-based healthcare, doesn't mean I know everything, but it can be confusing the terminology.
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You're gonna hear things like linear regression or simple regressions analysis, multiple regression, multivariable logistic regression analysis, things like that, those words start to run together.
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But what we're really trying to figure out here is we're trying to provide a mathematical model and sort of an objective indicator of a what degree of statistical control can we have on a confounder.
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Helps us to isolate those independent effects of a predictor while also holding other variables in the background constant because they exist.
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And we remember, even thinking about baseline characteristics on a clinical trial, you randomize people and you write up these tables and you describe them.
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And why are we doing that?
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Because we're trying to show people, the reader, that we considered these variables about the patient.
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And here's what they look like between the groups.
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Now, this is where things like wordings of terminology like associations, correlations, predictability start to get also again fuzzy.
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So if you think about the differences between correlation and regression, correlation is measuring the association only, whereas regression is looking at the association as well, but it provides a model for direction, the magnitude, and it helps in the prediction while also controlling for other variables.
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And that is the difference between just doing a correlation analysis, which I discuss in another lecture.
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If you need to go and review that, okay.
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Regression analysis is providing an additional perspective while holding other variables accountable.
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Okay, so now this is where we start to dive in first to the linear regression.
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Okay, there is simple and then there's multiple linear regression.
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Okay, those are two separate things, and I'll cover multiple here in a minute.
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It's also different from multivariable logistic regression analysis.
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It's how we hold the variables and the endpoints and how we look at the data and the angles that we're doing.
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That's what makes them different.
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And so I just try to help us all stay on the same page, especially if this is the first time you've interacted with this topic, okay, and you're trying to learn it or figure out how it applies to your potential paper, or if you're reading a study and you're trying to understand what they did.
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Okay.
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So simple linear, okay, that's about one independent variable and its influence on a continuous dependent variable, all right?
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And so you get this, you can create a line, right?
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And there's an equation for this that I'll show you here in a minute.
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We're not going to spend a lot of time.
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I'm not going to do any math here, not going to try to overwhelm you, but I'm going to show you the equation for those of you that are interested in that.
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But an example is does the age of the patient predict the systolic blood pressure?
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Now think about systolic blood pressure is a continuous data endpoint.
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Continuous being it can go on to infinity, and the magnitude of difference between each level of the blood pressure is the same.
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Again, I do a lecture on the type of data and how you treat it.
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Is it nominal, ordinal, or continuous?
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So if you don't understand the word continuous dependent variable, and in the context of systolic blood pressure, you should pause and go watch the lecture that I do on the type of data that we're dealing with.
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Okay, and that's also the end point of a study.
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It's not just applicable to regression analysis.
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Okay.
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So that's an example.
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Independent variable associated in its impact on in its relationship with a dependent continuous variable.
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Multiple linear regression obviously is beyond just simple.
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So there's multiple variables, right?
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So you have a relationship between greater than one independent variable and one continuous variable.
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And again, looking at that, going back and building on the age and blood pressure example.
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Does the patient's age predict the systolic blood pressure after adjusting for their BMI, smoking, and exercise status and behaviors?
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You see where the multiple is now being integrated, and you're trying to look at the impact and control for things and try to understand the influence of the association of one variable's impact on another, especially when they're changing.
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And so, for example, if you want to think about how would I apply this, what would it look like in real-world clinical practice when you, and this is an example, of course, it's not from some you know real day.
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I'm just showing you what it feels like, what it looks like.
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And that would be for every one year increase in the age of the patient, the systolic blood pressure increases by X amount of millimeters of mercury pressure while holding other variables constant.
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Like we know they're there, but we're gonna hold them constant because we want to understand the impact of age.
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And we know that's true, isn't it?
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As we age, our blood pressure increases.
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Why?
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Because the vascularity of the system builds up plaques, it gets hardened, it becomes less compliant, less elastic.
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And so the pressures that have to be generated to keep forward flow have to go up.
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And so when you look at patients in their 20s and 30s, they look different than in their 50s, 60s, and 70s as it relates to who has hypertension and how many meds are you on.
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So that statement makes sense to us, but we get that understanding because of things like this, and we can quantify it, we can measure it out mathematically, and that's where this formula really comes in, okay?
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And you fill in these components and you look, and we'll talk about error and again a little bit when we talk about residuals and things like that, but you want to understand and be aware of these formulas, not so much that I'm gonna again spend time doing it.
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Now, there's mnemonics that can guide us to understanding, especially when you're reading a paper where linear regression results are being presented.
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You you want to know as a reader, is it are they trustworthy?
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As a writer, author, researcher, you want to make sure you address things, especially if you're gonna try to get it published.
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Hopefully, a a good peer review peer reviewer will apply these principles and ask these questions and look for these things.
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But a good clinician who understands this and is trying to build maybe something else needs to understand what some of these things mean.
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So when we think about there's a mnemonic called line, L-I-N-E, and it and it works for linear regressions, both simple and then multiple, as some things that you also can add on and assumptions.
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But linear linearity, right, that's the relationship in a straight line.
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So remember earlier you saw the X and the Y and the variables, independent variable and a continuous dependent variable.
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We talked about that.
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And that's the true average of change in y being constant per unit change in X.
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And I gave you kind of an example, and that's a kind of a check scatter plot look.
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That there's independence of observations.
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Okay, so each data point is unique.
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There's no clustering, there's no repeated measures on the same patient.
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Okay.
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Now, when we start to think about, especially multiple uh linear regression, this is the normality of the residuals, okay, not the raw variables themselves.
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And this is really about errors, the interval between the space and result from the observed raw variables from the predicted models, okay?
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And if it should follow a Bell curve around zero, not the raw data, but the errors, okay.
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And then there's something called for E, L-I-N-E, equal or constant variance of the residuals.
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Okay.
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Now, when you have multicollinearity, okay, these are when predictors are not highly correlated to one another.
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Okay, you want this variable inflation factor or VIF to be low.
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Okay, we do not want it to be high.
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And so low, and they should kind of guide you to that, especially when they're really trying to define these variables, that that's what their VIF is, less you usually less than 5 to 10, especially important in that multiple linear regression analysis.
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And the spread of those residuals should be roughly the same no matter what the predictor value is.
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Okay, so there's no funnel, there's no cone shaped in the residual plot.
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Okay.
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Now, context of line, the mnemonic L-I-N-E, okay, assumes things that the linear regression follows in ordinary least squares, OLS.
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Okay, so it's both simple, that applies for both simple and multiple.
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Whereas multivariable regression analysis, which we're starting to transition to here, uses maximum likelihood estimations, not the OLS.
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Okay, it doesn't require the normality of the residuals.
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Okay.
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Um, instead, logistical analysis has its own set of core assumptions.
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All right.
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So that that was primarily obviously linear, simple and multiple linear regression.
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Uh, I'm not gonna say it's straightforward and crystal clear, easy.
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It's not.
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You have to dive into this stuff and apply it, see it used.
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But again, going back, we're trying to think of the big picture.
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What are these confounders, background variables doing to influence each other at some level?
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What is the association of the change in one variable and its impact on another?
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So when we think about multivariable logistic regression, this is when we use, and the outcome, the endpoint, is binary.
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Think of nominal data, yes or no.
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An event happened or it did not.
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Okay.
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Now the goal here is to identify when variables independently predict the probability of that outcome.
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Okay, and a reason that a variable may not remain significant is that there's no true relationship, or that it's highly correlated with another variable already in that model, and that's that multicollinearity.
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Okay.
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We don't remember, we don't want that to be typically that VIF variable inflation factor to be high.
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Insufficient statistical power.
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And so when we think about what does it look like, because you're gonna see these in a lot of papers, it'll say the adjusted odds ratio of this example is 2.8, okay, and you see that 95% confidence interval is between 1.5 and 5.3, right?
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So that you would say that there's about a three times greater odds or higher odds of an outcome after adjusting for confounders.
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Okay, so that but the one of the key things in here is this addition of adjusted odds ratio.
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Okay, and so that becomes very important.
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Now we will use things because you'll see like survival analysis, which is a kind of a Cox proportional hazards regression.
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Okay, this is a time to an event data versus a continuous linear and binary logistic, right?
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So if the logistic regression answers, did the patient die?
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Well, that's a yes or a no, isn't it?
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And Cox regression says, yeah, did the patient die, but how long did it take for that to happen?
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Okay, and that's where you see uh survival curves that are based on a time, time to a an event.
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Okay, so it's another part of that regression.
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So now as we start to close up on this conversation, there's a few pearls and pitfalls, some degrees of clinical relevance that I just want to make sure that we hit on.
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The first is that regression shows us associations, not causation.
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And it's really about how one variable changes when another one is also potentially changing.
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What impact does it have?
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Okay.
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Multicollinearity, when you have two or more predictors that are highly correlated, that makes unstable estimates and a difficulty in isolating the individual effect of those variables.
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Remember again, we want that VIF to be low.
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Overfitting, you have too many predictors uh that are relative to events, and so you end up creating your the the researcher creates this poor ability to generalize it to new patients.
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Okay?
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So there's a balance because we need to apply data in the context of the patients that we all see every day.
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You need also enough people.
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So there's a sample size rule of thumb, if you will, for logistics.
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You need 10 to 20 events, not patients per se, but events per predictor variable, so that you have enough to get that proper mathematical.
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Objective evaluation.
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Common misuse.
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Treating adjusted OR, odds ratio, as a risk ratio when the outcome is common.
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Okay.
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People use again, this is where terminology gets a little wonky.
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You gotta keep yourself oriented.
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And then there's the real world impact.
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Things that are used in scoring tools, prognostic models, observational studies that adjust for and control for confounders.
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Okay.
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Now remember, a confounder is just this variable.
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You may want to again mathematically remove adjusting age when you're looking at coffee and heart disease.
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So an effect modifier is a biological reality that you need to highlight.
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A drug works wonderful in a female or woman, but poorly in a man.
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So sex modifies the effect.
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Next is when you see an adjusted odds ratio or eight uh hazards ratio in a paper, you need to ask, was it adjusted for properly?
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What were the assumptions and were they checked?
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Is the sample size adequate for the events?
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Okay.
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Regression is again predictability and control plus control of that confounder.
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And you want to choose a model based on the outcome type, remember?
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So this is where your orientation to your data and endpoints goes back to that type of data and understanding it.
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So continuous, you do a linear, straight line, binary, logistic regression, right?
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And that math is done to convert the straight line into probability between zero and one, and so you get this sigmoid effect.
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Okay.
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Lastly, is you always want to interpret in the clinical context and you check those assumptions.
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And that's why those mnemonics and things like that are available to us to try to create that.
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That's why we also have critical appraisal tools to systematically help us to walk through a paper and ask the right questions.
00:24:26.000 --> 00:24:28.640
It's to help us to get to a meaningful endpoint.
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So I I hope at some level the introduction of these terms, while may not be perfectly crystal clear to you, especially if you've never applied them or read about them, begins to lay that foundation along with the other topics in evidence-based medicine and biostatistical analysis.
00:24:47.839 --> 00:24:49.759
It's not easy, it takes time.
00:24:50.000 --> 00:24:55.039
I spent years reading, studying, trying to apply it myself.
00:24:55.279 --> 00:24:56.880
And it just takes that time.
00:24:57.039 --> 00:24:58.480
So don't give up.
00:24:58.799 --> 00:25:14.880
You sometimes have to learn things in the context of the overall big picture, which is why we put together those collections and playlists on individual topic areas, and we do offer you a order to go through if you need that guidance.
00:25:15.119 --> 00:25:27.839
Now, they individually stand as topics on their own, but sometimes people need the continuous discussion and orientation as we move through the topics because it's overwhelming to do it all at once, isn't it?
00:25:28.160 --> 00:25:33.279
And so please check those over out on our YouTube channel, okay, or at thisiswhy.
00:25:34.240 --> 00:25:34.880
But I'm Dr.
00:25:35.039 --> 00:25:39.839
Bustaye, and I thank you so much for joining us and participating and investing in your knowledge.
00:25:39.920 --> 00:25:43.440
I hope that you would subscribe if you're not already a subscriber.
00:25:43.599 --> 00:25:46.799
Follow us, give us a like, provide a comment.
00:25:46.960 --> 00:25:49.119
We that's how we learn from each other.
00:25:49.359 --> 00:25:54.640
If there's a little pearl or thing that you can share with your friends and colleagues, let's do that.
00:25:54.960 --> 00:25:55.279
Okay.
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I know that I've benefited from those over the years, and others want to benefit from it as well.
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So we'll see you next time.
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Take care.