Outcome-dependent sampling design and inference for Cox’s proportional hazards Model

• Proposing the outcome-dependent sampling design for the survival time subjecting to right censor.
• To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation.
• A criteria that can be used to optimally implement the ODS design in practice is proposed and studied.

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies. The proposed design and inference procedure is shown to be statistically more powerful than existing alternative designs with the same sample sizes. We illustrate the proposed method with an existing real data from the Cancer Incidence and Mortality of Uranium Miners Study.