Optimal designs for discrete-time survival models with random effects

Xiao-Dong Zhou (), Yun-Juan Wang () and Rong-Xian Yue ()
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Xiao-Dong Zhou: Shanghai University of International Business and Economics
Yun-Juan Wang: Shanghai Lixin University Accounting and Finance
Rong-Xian Yue: Shanghai Normal University

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2021, vol. 27, issue 2, No 5, 300-332

Abstract: Abstract This paper considers the optimal design for the frailty model with discrete-time survival endpoints in longitudinal studies. We introduce the random effects into the discrete hazard models to account for the heterogeneity between experimental subjects, which causes the observations of the same subject at the sequential time points being correlated. We propose a general design method to collect the survival endpoints as inexpensively and efficiently as possible. A cost-based generalized D ( $$D_s$$ D s )-optimal design criterion is proposed to derive the optimal designs for estimating the fixed effects with cost constraint. Different computation strategies based on grid search or particle swarm optimization (PSO) algorithm are provided to obtain generalized D ( $$D_s$$ D s )-optimal designs. The equivalence theorem for the cost-based D ( $$D_s$$ D s )-optimal design criterion is given to verify the optimality of the designs. Our numerical results indicate that the presence of the random effects has a great influence on the optimal designs. Some useful suggestions are also put forward for future designing longitudinal studies.

Keywords: Optimal designs; Discrete-time survival model; Random effects; Equivalence theorem; Particle swarm optimization (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10985-020-09512-2

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