Description
Taylor & Francis Ltd Regression Models As A Tool In Medical Research 2012 Edition by Werner Vach
While regression models have become standard tools in medical research, understanding how to properly apply the models and interpret the results is often challenging for beginners. Regression Models as a Tool in Medical Research presents the fundamental concepts and important aspects of regression models most commonly used in medical research, including the classical regression model for continuous outcomes, the logistic regression model for binary outcomes, and the Cox proportional hazards model for survival data. The text emphasizes adequate use, correct interpretation of results, appropriate presentation of results, and avoidance of potential pitfalls. After reviewing popular models and basic methods, the book focuses on advanced topics and techniques. It considers the comparison of regression coefficients, the selection of covariates, the modeling of nonlinear and nonadditive effects, and the analysis of clustered and longitudinal data, highlighting the impact of selection mechanisms, measurement error, and incomplete covariate data. The text then covers the use of regression models to construct risk scores and predictors. It also gives an overview of more specific regression models and their applications as well as alternatives to regression modeling. The mathematical details underlying the estimation and inference techniques are provided in the appendices. THE BASICS Why Use Regression Models? Why using simple regression models? Why using multiple regression models? Some basic notation An Introductory ExampleA 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 ModelAdjusted Effects Adjusting for confounding Adjusting for imbalances Exercise Physical activity in school children Inference for the Classical Multiple Regression ModelThe 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 analysesLogistic RegressionThe 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 StataExercise Allergy in children More on logit scale and odds scaleInference for the Logistic Regression ModelThe 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 StataCategorical CovariatesIncorporating 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 covariatesHandling Ordered Categories: A First Lesson in Regression Modeling StrategiesThe Cox Proportional Hazard ModelModeling 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 1Common Pitfalls in Using Regression ModelsAssociation vs. causation Difference between subjects vs. difference within subjectsReal world models vs. statistical models Relevance vs. significance Exercise Prognostic factors in breast cancer patients - Part 2ADVANCED TOPICS AND TECHNIQUESSome Useful TechnicalitiesIllustrating 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 smokingComparing Regression CoefficientsComparing regression coefficients among continuous covariates Comparing regression coefficients among binary covariatesMeasuring the impact of changing covariate values Translating regression coefficients How to compare regression coefficients in Stata Exercise Health in young peoplePower and Sample SizeThe 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 outcomesThe Selection of the SampleSelection in dependence on the covariates Selection in dependence on the outcome Sampling in dependence on covariate valuesThe Selection of CovariatesFitting regression models with correlated covariates The "Adjustment vs. power" dilemma The "Adjustment makes effects small" dilemmaAdjusting for mediators Adjusting for confounding - A useful academic game Adjusting for correlated confounders Including predictive covariatesAutomatic 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 EffectsQuadratic 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 confoundersNonlinear models Exercise Serum markers for AMITransformation of CovariatesTransformations to obtain a linear relationship Transformation of skewed covariates To categorize or not to categorizeEffect Modification and InteractionsModeling 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 interactionsCeiling 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 gliomaApplying Regression Models to Clustered DataWhy 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 StataApplying Regression Models to Longitudinal DataAnalyzing 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 adolescentsThe Impact of Measurement ErrorThe 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 interactionsThe Impact of Incomplete Covariate DataMissing 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 covariatesRISK SCORES AND PREDICTORSRisk ScoresWhat is a risk score? Judging the usefulness of a risk scoreThe 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 patientsConstruction of PredictorsFrom 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 predictorEvaluating the Predictive PerformanceThe 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 patientsOutlook: Construction of Parsimonious PredictorsMISCELLANEOUSAlternatives to Regression ModelingStratification Measures of association: Correlation coefficients Measures of association: The odds ratio Propensity scores Classification and regression treesSpecific Regression ModelsProbit regression for binary outcomes Generalized linear models Regression models for count data Regression models for ordinal outcome data Quantile regression and robust regression ANOVA and regressionSpecific Usages of Regression ModelsLogistic regression for the analysis of case control studiesLogistic regression for the analysis of matched case control studies Adjusting for baseline values in randomized clinical trialsAssessing predictive factors Incorporating time varying covariates in a Cox model Time dependent effects in a Cox model Using the Cox model in the presence of competing risksUsing the Cox model to analyze multi state modelsWhat Is a Good Model?Does the model fit the data? How good are predictions? Explained variation Goodness of fit Model stability The usefulness of a modelFinal Remarks on the Role of Prespecified Models and Model DevelopmentMATHEMATICAL DETAILSMathematics behind the Classical Linear Regression Model Computing regression parameters in simple linear regression Computing regression parameters in the classical multiple regression model Estimation of the standard errorConstruction of confidence intervals and p-values Mathematics behind the Logistic Regression Model The least squares principle as a maximum likelihood principle Maximizing the likelihood of a logistic regression model Estimating the standard error of the ML estimates Testing composite hypotheses The Modern Way of Inference Robust estimation of standard errors Robust estimation of standard errors in the presence of clustering Mathematics for Risk Scores and Predictors Computing individual survival probabilities after fitting a Cox model Standard errors for risk scores The delta ruleBibliography Indexshow more