Logical and statistical fallacies in the use of Cox regression models

Time-dependent covariates are an essential data analysis tool for modeling the effect of a study factor whose value changes during follow-up. However, survival analysis models can yield conclusions that are contrary to the truth if such time-dependent factors are not defined and used carefully. We outline some of the biases that can occur when time-dependent covariates are used improperly in a Cox regression model. For example, we discuss why one should almost never use a covariate that has been averaged over a patient's entire follow-up time as a baseline covariate. Instead, the baseline value should be used as a covariate, or the cumulative average up to each point in time should be used as a time-dependent covariate. We also document why one should use time-dependent covariates with great caution in analyses when the evaluation of a baseline factor is the primary objective. Several simulated examples are given to illustrate the direction and magnitude of the biases that can result from not adhering to some basic assumptions that underlie all survival analysis methodologies.