A weighted casebase framework for outcome-dependent two-phase sampling designs

Outcome-dependent two-phase sampling designs permit cost-effective measurement of expensive covariates in large prospective cohorts. Weighted Cox regression is commonly used for these designs, but applications requiring smooth hazard estimation or direct absolute risk prediction motivate a complementary parametric approach.

We extend the casebase framework, which represents hazard regression as logistic regression on sampled person-moments, by combining the casebase sampling offset with inverse-probability weights for phase-two inclusion. We formulate the estimator as a participant-level M-estimator, establish consistency and asymptotic normality under standard conditions, and develop a computationally efficient dfbeta-based jackknife/sandwich variance estimator. Performance was evaluated against weighted Cox regression in simulations, and implementation was illustrated using a frequency-matched biomarker substudy within the Ontario Health Study.

Weighted casebase and weighted Cox regression had broadly similar coefficient performance across the scenarios studied. Both methods showed small bias and approximately nominal coverage in the binary-covariate and targeted sensitivity scenarios, whereas continuous or highly skewed covariates combined with fixed phase-two sample sizes and large weights produced finite-sample instability for both approaches. In the illustrative application, the two methods showed similar discrimination and weighted Brier score patterns, while the casebase model additionally produced smooth absolute-risk curves.

Weighted casebase regression provides a practical GLM-based approach to smooth parametric or flexible-parametric hazard estimation and direct absolute risk prediction under outcome-dependent two-phase sampling. It is complementary to weighted Cox regression rather than a replacement for it.