Regression Analysis

Besides stratified analysis, regression analysisRegression analysis is a way to control for confounding in the analysis of a study’s data. The way we use regression analysis to control for confounding is by including confounders as independent variables in the regression equation. This has an advantage over stratified analysis in control of continuous confounders. In regression analysis, there is no residual confounding if the model is correct. For occurrence data that are not a function of time, we use logistic regression analysisRegression analysis. With logistic regression analysis we transform the dependent variable so that reflects the log odds of the event represented by the dependent variable. In doing this, we create a sigmoid curveSigmoid curve for the relationship between the probability of the dependent variable event and independent variables. This keeps estimates of the probability in the range from zero to one. Since the dependent variable uses the log odds transformationTransformation, we most often interpret the results of logistic regression analysisRegression analysis as odds ratios. If we take a regression coefficient as the exponent of the base of the natural log scale (e), we get an odds ratioOdds ratio for a one-unit change in the value of the corresponding independent variable. There are three kinds of independent variables we use in regression analysisRegression analysis. First, we use continuous independent variables to represent continuous data. Second, we use indicator variables to represent categorical data. Generally, an indicator variable is equal to one if the person is in the category and zero otherwise. If the categorical data has more than two categories, more than one indicator variable is needed. Third, we use interaction variables to represent relationships between variables. Interaction variables are created by multiplying an indicator variable by another variable. When the occurrence data is a function of time, we use Cox Proportional Hazards regressionCox Proportional Hazards regression. In this regression analysisRegression analysis, the dependent variable is used as the natural log of the incidence. This makes the regression coefficients incidence ratios for a one-unit difference in the value of the independent variable when you make them exponents of e. A feature of Cox Proportional Hazards regression is that the intercept (a) is no longer a constant, but rather a function of time. This is how the regression analysis takes the influence of time into account.