Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics
Selvakkadunko Selvaratnam1, Yanqing Yi2, Alwell Oyet3
1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada.
Biometrical Journal. Biometrische Zeitschrift
|December 12, 2018
Summary
Personalized medicine uses biomarkers to improve patient well-being and trial efficiency. Covariate-adjusted response-adaptive (CARA) designs enhance statistical inference and patient outcomes in clinical trials.
Area of Science:
- Biostatistics
- Clinical Trial Design
- Personalized Medicine
Background:
- Growing interest in personalized medicine driven by biomarker discovery and patient heterogeneity.
- Biomarkers serve as covariates to improve clinical trial ethics and statistical inference efficiency.
- Covariate-adjusted response-adaptive (CARA) designs leverage covariate information for enhanced randomization.
Purpose of the Study:
- Establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators in generalized linear models (GLM) for adaptive designs.
- Analyze the performance of response-adaptive (RA), CARA, and completely randomized (CR) designs.
- Evaluate the ethical desirability and statistical efficiency of different adaptive designs.
Main Methods:
- Mathematical proofs establishing consistency and asymptotic normality of ML estimators for GLMs under adaptive designs.
- Simulation studies comparing RA, CARA, and CR designs using a logit model with categorical covariates.
- Application to a clinical trial dataset for stroke prevention in atrial fibrillation (SPAF).
Main Results:
- ML estimators for GLMs in adaptive designs are proven to be consistent and asymptotically multivariate Gaussian.
- Response-adaptive (RA) designs demonstrate ethically desirable outcomes and higher statistical efficiency than CARA designs when no treatment-by-covariate interaction exists.
- Covariate-adjusted response-adaptive (CARA) designs are more ethical than RA designs when significant treatment-by-covariate interactions are present.
Conclusions:
- Adaptive designs, particularly RA and CARA, offer improvements in patient well-being and statistical efficiency in clinical trials.
- The choice between RA and CARA designs depends on the presence and significance of treatment-by-covariate interactions.
- This research provides theoretical and empirical support for the use of adaptive designs in personalized medicine.
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