Efficient Estimation of Semiparametric Transformation Models for Two-Phase Cohort Studies

Area of Science:

• Biostatistics
• Epidemiology
• Health Research Methodology

Background:

• Two-phase cohort designs (e.g., case-cohort, nested case-control) are efficient for collecting data on expensive covariates.
• These designs involve sequential data collection, with initial inexpensive covariate data informing the selection for expensive covariate measurements.
• Controlling for confounding and evaluating interactions using both inexpensive and expensive covariates is crucial in these designs.

Purpose of the Study:

• To develop efficient estimation methods for semiparametric transformation models in two-phase cohort designs.
• To accommodate both discrete and continuous covariates, allowing for correlation between inexpensive and expensive covariates.
• To provide robust statistical tools for analyzing complex epidemiological and clinical data.

Main Methods:

• Utilized a modified nonparametric likelihood function maximization approach.
• Employed a generalized expectation-maximization algorithm for estimation.
• Developed estimators that are consistent, asymptotically normal, and asymptotically efficient with easily estimated variances.

Main Results:

• The proposed estimation method is efficient for semiparametric transformation models under two-phase cohort designs.
• The estimators demonstrate desirable statistical properties: consistency, asymptotic normality, and asymptotic efficiency.
• Simulation studies confirmed the accuracy of asymptotic approximations in practical scenarios.

Conclusions:

• The developed methods provide a statistically sound and efficient approach for analyzing data from two-phase cohort studies.
• The methodology effectively handles correlated inexpensive and expensive covariates, enhancing the analysis of confounding and interactions.
• The approach is validated by empirical data from Wilms' tumor studies and the Atherosclerosis Risk in Communities (ARIC) study.