Cox proportional hazards regression in small studies of predictive biomarkers

Predictive biomarkers are essential for personalized medicine since they select the best treatment for a specific patient. However, of all biomarkers that are evaluated, only few are eventually used in clinical practice. Many promising biomarkers may be erroneously abandoned because they are investigated in small studies using standard statistical techniques which can cause small sample bias or lack of power. The standard technique for failure time endpoints is Cox proportional hazards regression with a multiplicative interaction term between binary variables of biomarker and treatment. Properties of this model in small studies have not been evaluated so far, therefore we performed a simulation study to understand its small sample behavior. As a remedy, we applied a Firth correction to the score function of the Cox model and obtained confidence intervals (CI) using a profile likelihood (PL) approach. These methods are generally recommended for small studies of different design. Our results show that a Cox model estimates the biomarker-treatment interaction term and the treatment effect in one of the biomarker subgroups with bias, and overestimates their standard errors. Bias is however reduced and power is increased with Firth correction and PL CIs. Hence, the modified Cox model and PL CI should be used instead of a standard Cox model with Wald based CI in small studies of predictive biomarkers.