Regression Models as a Tool in Medical Research

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**THE BASICS
Why Use Regression Models?** Why using simple regression
models?

Why using multiple regression models?

Some basic notation

Fitting a single line model

Taking uncertainty into account

A two lines model

How to perform these steps with Stata

Exercise

Exercise

Exercise

Adjusting for imbalances

Exercise Physical activity in school children

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

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

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

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

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

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

Some Useful Technicalities

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 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

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

Selection in dependence on the outcome

Sampling in dependence on covariate values

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?

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 skewed covariates

To categorize or not to categorize

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

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

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 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

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

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

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

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

Alternatives to Regression Modeling

Measures of association: Correlation coefficients

Measures of association: The odds ratio

Propensity scores

Classification and regression trees

Generalized linear models

Regression models for count data

Regression models for ordinal outcome data

Quantile regression and robust regression

ANOVA and regression

Logistic regression for the analysis of matched case control studies

Adjusting for baseline values in randomized clinical trials

Assessing 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 risks

Using the Cox model to analyze multi state models

How good are predictions?

Explained variation

Goodness of fit

Model stability

The usefulness of a model

Computing regression parameters in the classical multiple regression model

Estimation of the standard error

Construction of confidence intervals and p-values

Maximizing the likelihood of a logistic regression model

Estimating the standard error of the ML estimates

Testing composite hypotheses

Robust estimation of standard errors in the presence of clustering

Standard errors for risk scores

The delta rule

Werner Vach is a professor of medical informatics and clinical epidemiology at the University of Freiburg. Dr. Vach has co-authored more than 150 publications in medical journals. His research encompasses biostatistics methodology in the areas of incomplete covariate data, prognostic studies, diagnostic studies, and agreement studies.

"The book can be recommended as a useful overview of practical
aspects of regression modeling, very suitable for medical
researchers who want to apply statistical methods or do apply them
already now. It is also very suitable for students of statistics
and their teachers."

-*ISCB News*, 59, June 2015

"With its focus on conceptual understanding and practical
applications, this book is highly recommended to medical and other
health science researchers who desire to improve their
understanding of regression analysis for a better understanding of
medical literature, for the adequate presentation of their own
regression outcomes, or for improved interpretation of their
results for publications and presentations. ... Additionally, this
book can serve as supplemental reading for an applied graduate
level course on general regression models."

-Journal of Agricultural, Biological, and Environmental Statistics
"The book can be a very helpful contribution especially for
researchers in medical sciences when performing their statistical
analyses and trying to interpret the results obtained. ... This
book provides plenty of practical knowledge about these basic
models and also some of their extensions that is often not easy to
find from statistical textbooks or from software manuals. The basic
methods are well explained and illustrated by numerous practical
examples, mainly using simulated datasets."

-Tapio Nummi, International Statistical Review

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