Regression Analysis Chapter 29 29 1 Regression Modeling

Regression Analysis Chapter 29

29. 1 Regression Modeling • Regression models seek to understand the relationship between one or more independent variables (or predictor variable) and one dependent variable (or outcome variable).

Figure 29 -1

29. 2 Simple Linear Regression • A linear regression model is used when the outcome variable is a ratio or interval variable. • Simple linear regression models examine whethere is a linear relationship between one predictor variable and the outcome variable.

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29. 3 Simple Logistic Regression • Logistic regression models (sometimes called logit regression models) are used when the outcome variable is a dichotomous variable. • Logistic regression models predict the probabilities of the outcome occurring. • Logistic regression is commonly used in casecontrol studies, for which the outcome variable is usually case status, with case 1 and control 0. • Predictor variables for a logistic regression model can be categorical (when the categories are coded with numbers) or continuous.

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29. 4 Confounding and Effect Modification • A confounder may make the association between an exposure variable and an outcome variable appear more or less significant than it truly is. • An effect modifier is a third variable that often defines groups of individuals who might experience different biological responses to various exposures. • To be a confounder or effect modifier, the third variable must be independently associated with both an exposure (or predictor) variable and an outcome variable.

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29. 5 Multivariable Comparisons of Means • One-way ANOVA (analysis of variance) is used to compare the mean values of a continuous variable among independent groups of people. • Two-way ANOVA compares the mean values of a continuous variable across two factors. • Analysis of covariance (ANCOVA) can be used to control for confounding variables when comparing the means of two or more groups.

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29. 6 Dummy Variables • A set of dummy variables can be created to convert categorical responses to a series of dichotomous (0/1) variables that can all be included in the same regression model. • If the original categorical variable has “n” possible responses, then “n– 1” dummy variables are required to capture all the responses to the original question.

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29. 7 Multiple Regression • A variety of analytic approaches can be used to test relationships among three or more variables while adjusting for possible confounders, including both linear and logistic regression models. • Multiple linear regression models examine the effects of several predictor variables on the value of one continuous outcome variable. • Multiple logistic regression models examine the effects of several predictor variables on the value of one dichotomous outcome variable.

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Figure 29 -8 Example of a Multiple Linear Regression Model with Two Continuous Variables

Figure 29 -9 Example of a Multiple Linear Regression Model with One Continuous and One Categorical Variable with No Interaction

Figure 29 -10 Example of a Multiple Linear Regression Model with One Continuous and One Categorical Variable with Interaction

Figure 29 -11 Example of a Multiple Logistic Regression Model

29. 8 Causal Analysis • Although multiple regression models cannot prove that an exposure caused an outcome, they can provide insights into causality. • The results of regression models can be used as part of qualitative considerations of causality derived from the Bradford Hill criteria and other more recent adaptations.

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29. 9 Survival Analysis (1 of 2) • Survival analysis examines the distribution of the durations of time that individuals in a study population experience from an initial time point (such as the date of enrollment in a study or the date of diagnosis of a particular condition) until some well-defined event, which can be death, discharge from a hospital, or some other outcome.

29. 9 Survival Analysis (2 of 2) Common measures of survival include: • median survival time; • cumulative survival at set times after enrollment or diagnosis; • life tables that record conditional and cumulative probabilities of survival; • Kaplan-Meier plots that display cumulative survival rates in a study population; • log-rank tests that determine whether survival rates are longer in one population than another; and • Cox proportional hazards regression, which estimates a hazard ratio that compares durations of time to an event (such as death) in two populations.

Figure 29 -13 Example of a Kaplan-Meier Plot

29. 10 Cautions • Advanced statistical tests should be used only when they are necessary for the research question.