THE BASICS Why Use Regression Models? Why using simple regression models? Why using multiple regression models? Some basic notation An Introductory Example A single line model Fitting a single line model Taking uncertainty into account A two lines model How to perform these steps with Stata Exercise 5-HIAA and serotonin Exercise Haemoglobin Exercise Scaling of variables The Classical Multiple Regression Model Adjusted Effects Adjusting for confounding Adjusting for imbalances Exercise Physical activity in school children Inference for the Classical Multiple Regression Model The traditional and the modern way of inference How to perform the modern way of inference with Stata How valid and good are least squares estimates? A note on the use and interpretation of p-values in regression analyses Logistic Regression The definition of the logistic regression model Analyzing a dose response experiment by logistic regression How to fit a dose response model with Stata Estimating odds ratios and adjusted odds ratios using logistic regression How to compute (adjusted) odds ratios using logistic regression in Stata Exercise Allergy in children More on logit scale and odds scale Inference for the Logistic Regression Model The maximum likelihood principle Properties of the ML estimates for logistic regression Inference for a single regression parameter How to perform Wald tests and likelihood ratio tests in Stata Categorical Covariates Incorporating categorical covariates in a regression model Some technicalities in using categorical covariates Testing the effect of a categorical covariate The handling of categorical covariates in Stata Presenting results of a regression analysis involving categorical covariates in a table Exercise Physical occupation and back pain Exercise Odds ratios and categorical covariates Handling Ordered Categories: A First Lesson in Regression Modeling Strategies The Cox Proportional Hazard Model Modeling the risk of dying Modeling the risk of dying in continuous time Using the Cox proportional hazards model to quantify the difference in survival between groups How to fit a Cox proportional hazards model with Stata Exercise Prognostic factors in breast cancer patients ¿ Part 1 Common Pitfalls in Using Regression Models Association vs. causation Difference between subjects vs. difference within subjects Real world models vs. statistical models Relevance vs. significance Exercise Prognostic factors in breast cancer patients ¿ Part 2 ADVANCED TOPICS AND TECHNIQUES Some Useful Technicalities Illustrating models by using model based predictions How to work with predictions in Stata Residuals and the standard deviation of the error term Working with residuals and the RMSE in Stata Linear and nonlinear functions of regression parameters Transformations of regression parameters Centering of covariate values Exercise Paternal smoking vs. maternal smoking Comparing Regression Coefficients Comparing regression coefficients among continuous covariates Comparing regression coefficients among binary covariates Measuring the impact of changing covariate values Translating regression coefficients How to compare regression coefficients in Stata Exercise Health in young people Power and Sample Size The power of a regression analysis Determinants of power in regression models with a single covariate Determinants of power in regression models with several covariates Power and sample size calculations when a sample from the covariate distribution is given Power and sample size calculations given a sample from the covariate distribution with Stata The choice of the values of the regression parameters in a simulation study Simulating a covariate distribution Simulating a covariate distribution with Stata Choosing the parameters to simulate a covariate distribution Necessary sample sizes to justify asymptotic methods Exercise Power considerations for a study on neck pain Exercise Choosing between two outcomes The Selection of the Sample Selection in dependence on the covariates Selection in dependence on the outcome Sampling in dependence on covariate values The Selection of Covariates Fitting regression models with correlated covariates The "Adjustment vs. power" dilemma The "Adjustment makes effects small" dilemma Adjusting for mediators Adjusting for confounding - A useful academic game Adjusting for correlated confounders Including predictive covariates Automatic variable selection How to choose relevant sets of covariates Preparing the selection of covariates: Analyzing the association among covariates Preparing the selection of covariates: Univariate analyses? Exercise Vocabulary size in young children ¿ Part 1 Preprocessing of the covariate space How to preprocess the covariate space with Stata Exercise Vocabulary size in young children ¿ Part 2 What is a confounder? Modeling Nonlinear Effects Quadratic regression Polynomial regression Splines Fractional Polynomials Gain in power by modeling nonlinear effects? Demonstrating the effect of a covariate Demonstrating a nonlinear effect Describing the shape of a nonlinear effect Detecting nonlinearity by analysis of residuals Judging of nonlinearity may require adjustment How to model nonlinear effects in Stata The impact of ignoring nonlinearity Modeling the nonlinear effect of confounders Nonlinear models Exercise Serum markers for AMI Transformation of Covariates Transformations to obtain a linear relationship Transformation of skewed covariates To categorize or not to categorize Effect Modification and Interactions Modeling effect modification Adjusted effect modifications Interactions Modeling effect modifications in several covariates The effect of a covariate in the presence of interactions Interactions as deviations from additivity Scales and interactions Ceiling effects and interactions Hunting for interactions How to analyze effect modification and interactions with Stata Exercise Treatment interactions in a randomized clinical trial for the treatment of malignant glioma Applying Regression Models to Clustered Data Why clustered data can invalidate inference Robust standard errors Improving the efficiency Within and between cluster effects Some unusual but useful usages of robust standard errors in clustered data How to take clustering into account in Stata Applying Regression Models to Longitudinal Data Analyzing time trends in the outcome Analyzing time trends in the effect of covariates Analyzing the effect of covariates Analyzing individual variation in time trends Analyzing summary measures Analyzing the effect of change How to perform regression modeling of longitudinal data in Stata Exercise Increase of body fat in adolescents The Impact of Measurement Error The impact of systematic and random measurement error The impact of misclassification The impact of measurement error in confounders The impact of differential misclassification and measurement error Studying the measurement error Exercise Measurement error and interactions The Impact of Incomplete Covariate Data Missing value mechanisms Properties of a complete case analysis Bias due to using ad hoc methods Advanced techniques to handle incomplete covariate data Handling of partially defined covariates RISK SCORES AND PREDICTORS Risk Scores What is a risk score? Judging the usefulness of a risk score The precision of risk score values The overall precision of a risk score Using Stata¿s predict command to compute risk scores Categorization of risk scores Exercise Computing risk scores for breast cancer patients Construction of Predictors From risk scores to predictors Predictions and prediction intervals for a continuous outcome Predictions for a binary outcome Construction of predictions for time to event data How to construct predictions with Stata The overall precision of a predictor Evaluating the Predictive Performance The predictive performance of an existing predictor How to assess the predictive performance of an existing predictor in Stata Estimating the predictive performance of a new predictor How to assess the predictive performance via cross validation in Stata Exercise Assessing the predictive performance of a prognostic score in breast cancer patients Outlook: Construction of Parsimonious Predictors MISCELLANEOUS Alternatives to Regression Modeling Stratification Measures of association: Correlation coefficients Measures of association: The odds ratio Propensity scores Classification and regression trees Specific Regression Models Probit regression for binary outcomes Generalized linear models Regression models f.