Case-only analysis in small studies of predictive biomarkers

Characteristics of tumors and patients can be used as predictive biomarkers to guide treatment choice. Although many potential biomarkers are evaluated each year, only few will eventually be used since evidence is usually based on small studies leading to inconclusive results. Such data are often analyzed with Cox proportional hazards regression using a multiplicative interaction term between biomarker and treatment, with insufficient power and possibly biased results. Instead of analyzing patients who do (cases) and do not experience (non-cases) the survival event of interest, case-only analysis with logistic regression has been proposed, however with unknown small sample properties. We evaluated the performance of case-only analysis with bias-eliminating Firth correction and confidence intervals obtained with a profile likelihood method in a simulation study tailored to breast cancer. Our results show that this approach is generally inferior to the full cohort analysis but has acceptable properties when the marker is protective or null among patients treated with the standard treatment, the event rate is low (e.g., a rare event and a protective marker) and treatment assignment is independent of the marker level (e.g., in randomized studies). In such situations, the case-only design offers substantial cost savings. However, the model is sensitive to these assumptions.