• Alfred DeMaris
• Steven H. Selman
Chapter

## Abstract

In this chapter we will learn about several additional advanced multivariate statistical techniques that are finding increasing application in medical research. Multiple imputation is a technique that allows us to “fill in” missing data. Often data on the study endpoint or the explanatory variables are missing for subjects in a study. If these subjects are therefore excluded from analysis, not only do we waste the data that they have provided, but their exclusion also introduces selection bias into the analyses. Multiple imputation allows us to fill in, or impute, the missing data with an estimate of what the data would have been had they been present. Once the data have been imputed, they can be used in any of the types of analyses that are discussed in this primer. Poisson regression and its close relative negative binomial regression are the appropriate models to employ when the study endpoint is a count of the number of events that have occurred to the subject in a given time period. Because counts must be represented by integer values and cannot be negative, we cannot use linear regression for this analysis, for reasons explained below. Propensity-score analysis is a statistical tool that allows us to mimic random assignment to “treatment categories,” even though our data are from an observational study. Although we can control statistically for potentially confounding variables in an observational study, a problem arises if these covariates are imbalanced across groups. That is, the different treatment groups of interest have very different distributions on the covariates. Propensity-score analysis is designed to balance measured covariates across treatment groups in order to more effectively simulate random assignment to treatment. Growth-curve modeling is useful whenever people are studied over time and interest centers on the pattern of change in a quantitative study endpoint over that time period. Because people contribute multiple time points’ worth of measurements to the analysis, linear regression is inadequate to model the complex error term required in these studies. Growth-curve models elegantly incorporate the additional complexity into their structure. Finally, we will consider the dilemma we began with in Chap. 1 involving latent selection factors. What happens if there are one or more unmeasured covariates that might be driving our results? Fixed-effects regression modeling is one technique that, under the right conditions, eliminates the threat from confounds that have not been measured. Several examples from the medical literature will help to illustrate the use of these important techniques.

### Keywords

Placebo Nickel Depression Covariance Income

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