In setting up your model, include those variables, in addition to the risk factor or group assignment, that have been theorized or shown in prior research to be confounders or those that empirically are associated with the risk factor and the outcome in bivariate analysis.

Exclude variables that are on the intervening pathway between the risk factor and outcome, those that are extraneous because they are not on the causal pathway, redundant variables, and variables with a lot of missing data.

Sample size calculation for multivariable analysis is complicated but statistical programs exist to help you to calculate it. Missing data on independent variables can compromise your multivariable analysis. Several methods exist to compensate for missing independent data including deleting cases, using indicator variables to represent missing data and estimating the value of missing cases. Methods also exist for estimating missing outcome data using other data you have about the subject and multiple imputation.

Multivariable analysis is used for four major types of studies: observational studies of etiology, randomized and nonrandomized intervention studies, studies of diagnosis, and studies of prognosis.

For observational studies, whether etiologic or intervention, the most important reason to do multivariable analysis is to eliminate confounding, since in observational studies the groups are not randomly assigned. With randomized studies, multiple analysis is used to adjust for baseline differences that occurred by chance, to identify other independent predictors of outcome besides the randomized group, and x.

With studies of diagnosis, multivariable analysis is used to identify the best combination of diagnostic information to determine whether a person has a particular disease. Multivariable analysis can also be used to predict the prognosis of a group of patients with a particular set of known prognostic factors.

This chapter describes how to model multiple discrete quantities as discrete random variables within the same probability space and manipulate them using their joint pmf. We explain how to estimate the joint pmf from data, and use it to model precipitation in Oregon. Then, we introduce marginal distributions, which describe the individual behavior of each variable in a model, and conditional distributions, which describe the behavior of a variable when other variables are fixed. Next, we generalize the concepts of independence and conditional independence to random variables. In addition, we discuss the problem of causal inference, which seeks to identify causal relationships between variables. We then turn our attention to a fundamental challenge: It is impossible to completely characterize the dependence between all variables in a model, unless they are very few. This phenomenon, known as the curse of dimensionality, is the reason why independence assumptions are needed to make probabilistic models tractable. We conclude the chapter by describing two popular models based on such assumptions: Naive Bayes and Markov chains.