Estimating Baseline Survival Function in the Proportional Hazards Model Under Monotone Hazards

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• Estimating survival functions is crucial in biomedical studies, especially with time-varying patient risk.
• Challenges arise from left-truncated (delayed entry) and right-censored (incomplete follow-up) data.
• Existing methods for the Cox proportional hazards (PH) model struggle with these data complexities.

Purpose of the Study:

• To develop a robust estimator for the baseline survival function in the presence of left-truncation and right-censoring.
• To propose a covariate-adjusted monotone maximum likelihood estimator (MLE) under the Cox PH model.
• To generalize existing univariate and right-censored-only monotone estimators.

Main Methods:

• Developed a Breslow-type estimator incorporating Cox regression coefficients.
• Integrated these coefficients into Tsai's monotone MLE framework.
• Established theoretical strong consistency and derived asymptotic distribution for the new estimator.

Main Results:

• The proposed covariate-adjusted monotone MLE demonstrated numerical stability, even with sparse early-time data.
• Simulations showed nearly unbiased survival estimates in small samples.
• Consistent efficiency gains were observed due to baseline covariate adjustment.

Conclusions:

• The new estimator effectively handles left-truncated and right-censored data under a monotone hazard assumption.
• It offers improved accuracy and efficiency compared to existing methods.
• The approach is validated through theoretical analysis and empirical simulations, with an illustration on the Channing House data.