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Marginal regression for binary longitudinal data in adaptive clinical trials. (English) Zbl 1090.62130

An adaptive clinical trial research is considered in which the treatment of the \(i\)-th patient is selected dependent on the results (responses) of the \(1,\dots, i-1\) patients. It is assumed that the data on each patient are longitudinal, i.e., for the \(i\)-th patient the binary responses \(y_{it}\) and covariates \(x_{it}\) are observed at the time points \(t=i,i+1,\dots, i+T-1\). Two types of treatments are considered. The simple longitudinal randomised play-winner rule is proposed for the selection of treatments. The limit behaviour of probabilities to select a specified treatment is studied. The weighted generalized quasi-likelihood approach is used for the estimation of the treatment and covariates effects. A confidence interval for the treatment effect is constructed. Results of simulations are presented.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62N02 Estimation in survival analysis and censored data
62L05 Sequential statistical design
62K99 Design of statistical experiments
62J12 Generalized linear models (logistic models)
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