Model building strategy for logistic regression: purposeful selection

Abstract

Logistic regression is one of the most commonly used models to account for confounders in medical literature. The article introduces how to perform purposeful selection model building strategy with R. I stress on the use of likelihood ratio test to see whether deleting a variable will have significant impact on model fit. A deleted variable should also be checked for whether it is an important adjustment of remaining covariates. Interaction should be checked to disentangle complex relationship between covariates and their synergistic effect on response variable. Model should be checked for the goodness-of-fit (GOF). In other words, how the fitted model reflects the real data. Hosmer-Lemeshow GOF test is the most widely used for logistic regression model.

Keywords: Hosmer-Lemeshow; Logistic regression; R; interaction; linearity; purposeful selection.

Zhongheng Zhang, MMed.

Figure 1

Smoothed scatter plots showing the relationship between variable of interest with mortality outcome in logit scale.

Figure 2

Effect of hb on the probability of mortality, stratified by different age groups.

Figure 3

The plot of jittered outcome (alive=1; die=2) versus estimated probability of death from fitted model.

Figure 4

Histogram of estimated probability of death, stratified by observed outcome.

Figure 5

The receiver operating characteristic curve (ROC) reflecting the discrimination power of the model.