Optimal designs for full and partial likelihood information — With application to survival models

• We derive a general optimal design framework for partial likelihood estimation.
• Our theory facilitates finding optimal designs for Cox’s proportional hazard model.
• We show that certain c-optimal designs are highly efficient.
• We suggest a simple but efficient alternative to the optimal designs.
• These designs should appeal to practitioners.

Time-to-event data are often modelled through Cox’s proportional hazards model for which inference is based on the partial likelihood function. We derive a general expression for the asymptotic covariance matrix of Cox’s partial likelihood estimator for the covariate coefficients. Our approach is illustrated through an application to the special case of only one covariate, for which we construct minimum variance designs for different censoring mechanisms and both binary and interval design spaces. We compare these designs with the corresponding ones found using the full likelihood approach and demonstrate that the latter designs are highly efficient also for partial likelihood estimation.