Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well-being of patients (ethics) and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates that can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate-adjusted response-adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well-being of participating patients as well as increase the efficiency of statistical inference at the end of a clinical trial. In this paper, we establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators of generalized linear models (GLM) for a general class of adaptive designs. We prove that the ML estimators are consistent and asymptotically follow a multivariate Gaussian distribution. The efficiency of the estimators and the performance of response-adaptive (RA), CARA, and completely randomized (CR) designs are examined based on the well-being of patients under a logit model with categorical covariates. Results from our simulation studies and application to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF) show that RA designs lead to ethically desirable outcomes as well as higher statistical efficiency compared to CARA designs if there is no treatment by covariate interaction in an ideal model. CARA designs were however more ethical than RA designs when there was significant interaction. K E Y W O R D Sadaptive designs, clinical trials, consistency, generalized linear models, maximum likelihood estimation 630
Response‐adaptive designs are important alternatives to equal allocation in clinical trials because equal treatment allocation has been found to have ethical issues. In this article we discuss the implementation of response‐adaptive designs in multi‐centre clinical trials. We develop a generalized linear mixed model (GLMM) for analyzing data obtained from multi‐centre clinical trials and use the maximum likelihood (ML) approach to estimate the model parameters. We apply influence function techniques to derive the asymptotic properties of our estimators. The advantage of using the influence function approach is that it leads to a closed form expression for the asymptotic covariance of the estimated parameters. To our knowledge such a closed form expression does not currently exist in the literature. The performance of the ML estimator under various response‐adaptive designs is examined through simulation studies. We use our simulation studies to compare the asymptotic covariance matrix, based on the influence function to that based on the inverse of the Hessian matrix obtained from the likelihood function of the observations. The techniques are applied to real data obtained from a multi‐centre clinical trial designed to compare two cream preparations (active drug/control) for treating an infection. The Canadian Journal of Statistics 45: 310–325; 2017 © 2017 Statistical Society of Canada
We construct robust designs for nonlinear quantile regression, in the presence of both a possibly misspecified nonlinear quantile function and heteroscedasticity of an unknown form. The asymptotic mean-squared error of the quantile estimate is evaluated and maximized over a neighbourhood of the fitted quantile regression model. This maximum depends on the scale function and on the design. We entertain two methods to find designs that minimize the maximum loss. The first is local – we minimize for given values of the parameters and the scale function, using a sequential approach, whereby each new design point minimizes the subsequent loss, given the current design. The second is adaptive – at each stage, the maximized loss is evaluated at quantile estimates of the parameters, and a kernel estimate of scale, and then the next design point is obtained as in the sequential method. In the context of a Michaelis–Menten response model for an estrogen/hormone study, and a variety of scale functions, we demonstrate that the adaptive approach performs as well, in large study sizes, as if the parameter values and scale function were known beforehand and the sequential method applied. When the sequential method uses an incorrectly specified scale function, the adaptive method yields an, often substantial, improvement. The performance of the adaptive designs for smaller study sizes is assessed and seen to still be very favourable, especially so since the prior information required to design sequentially is rarely available.
In clinical trials, efficient statistical inference is critical to the well-being of future patients. We therefore construct Wald-type tests for the hypothesis of treatment-by-covariate interaction when treatments are assigned to patients by an adaptive design and the true model is a generalized linear model. Our measure of efficiency is the power of the test while ethics of a trial or well-being of participating patients is measured by the success rate of treatments. We demonstrate that the power of the test depends on the target allocation proportion, the bias of the randomization procedure from the target, and the variability induced by the randomization process (design variability) for adaptive designs. We prove that these quantities influence the power when the trial involves two treatments and a single covariate. We also show that, in this case, as design variability decreases the power increases. Due to the complexity of the problem, we demonstrate by simulation that this result still holds when more than one covariate is present in the model. In simulation studies, we compare the measures of efficiency and ethics under response-adaptive (RA), covariate-adjusted responseadaptive (CARA), and completely randomized (CR) designs. The methods are applied to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF). Journal of Statistical Research 2022, Vol. 56, No. 1, pp. 11-36
We discuss the construction of designs for estimation of nonparametric regression models with autocorrelated errors when the mean response is to be approximated by a finite order linear combination of dilated and translated versions of the Daubechies wavelet bases with four vanishing moments. We assume that the parameters of the resulting model will be estimated by weighted least squares (WLS) or by generalized least squares (GLS). The bias induced by the unused components of the wavelet bases, in the linear approximation, then inflates the natural variation of the WLS and GLS estimates. We therefore construct our designs by minimizing the maximum value of the average mean squared error (AMSE). Such designs are said to be robust in the minimax sense. Our illustrative examples are constructed by using the simulated annealing algorithm to select an optimal [Formula: see text]-point design, which are integers, from a grid of possible values of the explanatory or design variable [Formula: see text]. We found that the integer-valued designs we constructed based on GLS estimation, have smaller minimum loss when compared to the designs for WLS or ordinary least squares (OLS) estimation, except when the correlation parameter [Formula: see text] approaches 1.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.