Semiparametric estimation exploiting covariate independence in two-phase randomized trials.
Recent results for case-control sampling suggest when the covariate distribution is constrained by gene-environment independence, semiparametric estimation exploiting such independence yields a great deal of efficiency gain. We consider the efficient estimation of the treatment-biomarker interaction in two-phase sampling nested within randomized clinical trials, incorporating the independence between a randomized treatment and the baseline markers. We develop a Newton-Raphson algorithm based on the profile likelihood to compute the semiparametric maximum likelihood estimate (SPMLE). Our algorithm accommodates both continuous phase-one outcomes and continuous phase-two biomarkers. The profile information matrix is computed explicitly via numerical differentiation. In certain situations where computing the SPMLE is slow, we propose a maximum estimated likelihood estimator (MELE), which is also capable of incorporating the covariate independence. This estimated likelihood approach uses a one-step empirical covariate distribution, thus is straightforward to maximize. It offers a closed-form variance estimate with limited increase in variance relative to the fully efficient SPMLE. Our results suggest exploiting the covariate independence in two-phase sampling increases the efficiency substantially, particularly for estimating treatment-biomarker interactions.
Dai
James Y
JY
Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, Seattle, Washington 98109, USA. ydai@fhcrc.org
LeBlanc
Michael
M
Kooperberg
Charles
C
D000465:Algorithms; D015415:Biomarkers; D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D006801:Humans; D008962:Models, Theoretical; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D016896:Treatment Outcome
D015415:Biomarkers