Treatment design selection effects on parameter estimation in dynamic logistic models for longitudinal binary data

In a longitudinal set-up, to examine the effects of certain fixed covariates on the repeated binary responses, there exists an approach to model the binary probabilities through a dynamic logistic relationship. In some practical situations such as in longitudinal clinical studies, it may happen that some of the covariates such as treatments are selected randomly following an adaptive design, whereas the rest of the covariates may be fixed by nature. The purpose of this study is to examine the effects of the design weights selection on the parameter estimation including the treatment effects, after taking the longitudinal correlations of the repeated binary responses into account.     

A RANDOMIZED LONGITUDINAL PLAY-THE-WINNER DESIGN FOR REPEATED BINARY DATA

In some clinical trials with two treatment arms, the patients enter the study at different times and are then allocated to one of two treatment groups. It is important for ethical reasons that there is greater probability of allocating a patient to the group that has displayed more favourable responses up to the patient's entry time. There are many adaptive designs in the literature to meet this ethical constraint, but most have a single binary response. Often the binary response is longitudinal in nature, being observed repeatedly over different monitoring times. This paper develops a randomized longitudinal play‐the‐winner design for such binary responses which meets the ethical constraint. Some performance characteristics of this design have been studied. It has been implemented in a trial of pulsed electro‐magnetic field therapy with rheumatoid arthritis patients.     

Optimal allocation of subjects in a matched pair cluster-randomized trial with fixed number of heterogeneous clusters

In cluster-randomized trials, investigators randomize clusters of individuals such as households, medical practices, schools or classrooms despite the unit of interest are the individuals. It results in the loss of efficiency in terms of the estimation of the unknown parameters as well as the power of the test for testing the treatment effects. To recoup this efficiency loss, some studies pair similar clusters and randomize treatment within pairs. However, the clusters within a treatment arm might be heterogeneous in nature. In this article, we propose a locally optimal design that accounts the clusters heterogeneity and optimally allocates the subjects within each cluster. To address the dependency of design on the unknown parameters, we also discuss Bayesian optimal designs. Performances of proposed designs are investigated numerically through some data examples.     

On efficient inferences in familial-longitudinal binary models with two variance components

When a generalized linear mixed model (GLMM) with multiple (two or more) sources of random effects is considered, the inferences may vary depending on the nature of the random effects. For example, the inference in GLMMs with two independent random effects with two distinct components of dispersion will be different from the inference in GLMMs with two random effects in a two factor factorial design set-up. In this paper, we consider a familial-longitudinal model for repeated binary data where the binary response of an individual member of a family at a given time point is assumed to be influenced by the past responses of the member as well as two but independent sources of random family effects. For the estimation of the parameters of the proposed model, we discuss the well-known maximum-likelihood (ML) method as well as a generalized quasi-likelihood (GQL) approach. The main objective of the paper is to examine the relative asymptotic efficiency performance of the ML and GQL estimators for the regression effects, dynamic (longitudinal) dependence and variance parameters of the random family effects from two sources.     

Empirical Likelihood Inference for the Rao‐Hartley‐Cochran Sampling Design

The Hartley‐Rao‐Cochran sampling design is an unequal probability sampling design which can be used to select samples from finite populations. We propose to adjust the empirical likelihood approach for the Hartley‐Rao‐Cochran sampling design. The approach proposed intrinsically incorporates sampling weights, auxiliary information and allows for large sampling fractions. It can be used to construct confidence intervals. In a simulation study, we show that the coverage may be better for the empirical likelihood confidence interval than for standard confidence intervals based on variance estimates. The approach proposed is simple to implement and less computer intensive than bootstrap. The confidence interval proposed does not rely on re‐sampling, linearization, variance estimation, design‐effects or joint inclusion probabilities.     

Small area estimation of mean price of habitation transaction using time-series and cross-sectional area-level models

In this paper, a new small domain estimator for area-level data is proposed. The proposed estimator is driven by a real problem of estimating the mean price of habitation transaction at a regional level in a European country, using data collected from a longitudinal survey conducted by a national statistical office. At the desired level of inference, it is not possible to provide accurate direct estimates because the sample sizes in these domains are very small. An area-level model with a heterogeneous covariance structure of random effects assists the proposed combined estimator. This model is an extension of a model due to Fay and Herriot [5], but it integrates information across domains and over several periods of time. In addition, a modified method of estimation of variance components for time-series and cross-sectional area-level models is proposed by including the design weights. A Monte Carlo simulation, based on real data, is conducted to investigate the performance of the proposed estimators in comparison with other estimators frequently used in small area estimation problems. In particular, we compare the performance of these estimators with the estimator based on the Rao–Yu model [23]. The simulation study also accesses the performance of the modified variance component estimators in comparison with the traditional ANOVA method. Simulation results show that the estimators proposed perform better than the other estimators in terms of both precision and bias.     

Multiple-objective response-adaptive repeated measurement designs for clinical trials

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achieve a specific goal. Response-adaptive designs for clinical trials are usually constructed to achieve a single objective. In this paper, we develop a new adaptive allocation rule to improve current strategies for building response-adaptive designs to construct multiple-objective repeated measurement designs. This new rule is designed to increase estimation precision and treatment benefit by assigning more patients to a better treatment sequence. We demonstrate that designs constructed under the new proposed allocation rule can be nearly as efficient as fixed optimal designs in terms of the mean squared error, while leading to improved patient care.     

Inference in Semi‐Parametric Dynamic Models for Repeated Count Data

This paper deals with a longitudinal semi‐parametric regression model in a generalised linear model setup for repeated count data collected from a large number of independent individuals. To accommodate the longitudinal correlations, we consider a dynamic model for repeated counts which has decaying auto‐correlations as the time lag increases between the repeated responses. The semi‐parametric regression function involved in the model contains a specified regression function in some suitable time‐dependent covariates and a non‐parametric function in some other time‐dependent covariates. As far as the inference is concerned, because the non‐parametric function is of secondary interest, we estimate this function consistently using the independence assumption‐based well‐known quasi‐likelihood approach. Next, the proposed longitudinal correlation structure and the estimate of the non‐parametric function are used to develop a semi‐parametric generalised quasi‐likelihood approach for consistent and efficient estimation of the regression effects in the parametric regression function. The finite sample performance of the proposed estimation approach is examined through an intensive simulation study based on both large and small samples. Both balanced and unbalanced cluster sizes are incorporated in the simulation study. The asymptotic performances of the estimators are given. The estimation methodology is illustrated by reanalysing the well‐known health care utilisation data consisting of counts of yearly visits to a physician by 180 individuals for four years and several important primary and secondary covariates.     

Latent class models for longitudinal studies of the elderly with data missing at random

The elderly population in the USA is expected to double in size by the year 2025, making longitudinal health studies of this population of increasing importance. The degree of loss to follow-up in studies of the elderly, which is often because elderly people cannot remain in the study, enter a nursing home or die, make longitudinal studies of this population problematic. We propose a latent class model for analysing multiple longitudinal binary health outcomes with multiple-cause non-response when the data are missing at random and a non-likelihood-based analysis is performed. We extend the estimating equations approach of Robins and co-workers to latent class models by reweighting the multiple binary longitudinal outcomes by the inverse probability of being observed. This results in consistent parameter estimates when the probability of non-response depends on observed outcomes and covariates (missing at random) assuming that the model for non-response is correctly specified. We extend the non-response model so that institutionalization, death and missingness due to failure to locate, refusal or incomplete data each have their own set of non-response probabilities. Robust variance estimates are derived which account for the use of a possibly misspecified covariance matrix, estimation of missing data weights and estimation of latent class measurement parameters. This approach is then applied to a study of lower body function among a subsample of the elderly participating in the 6-year Longitudinal Study of Aging.     

Robust models in probability sampling

In the estimation of a population mean or total from a random sample, certain methods based on linear models are known to be automatically design consistent, regardless of how well the underlying model describes the population. A sufficient condition is identified for this type of robustness to model failure; the condition, which we call 'internal bias calibration', relates to the combination of a model and the method used to fit it. Included among the internally bias-calibrated models, in addition to the aforementioned linear models, are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting. Other models can often be made robust by using a suboptimal fitting method. Thus the class of model-based, but design consistent, analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts. Particular applications discussed are the estimation of the size of a population subdomain, as arises in tax auditing for example, and the estimation of a bootstrap tail probability.     

Minimax designs for 2k factorial experiments for generalized linear models

ABSTRACT

Formulas for A- and C-optimal allocations for binary factorial experiments in the context of generalized linear models are derived. Since the optimal allocations depend on GLM weights, which often are unknown, a minimax strategy is considered. This is shown to be simple to apply to factorial experiments. Efficiency is used to evaluate the resulting design. In some cases, the minimax design equals the optimal design. For other cases no general conclusion can be drawn. An example of a two-factor logit model suggests that the minimax design performs well, and often better than a uniform allocation.     

A Bayesian shared parameter model for joint modeling of longitudinal continuous and binary outcomes

Joint modeling of associated mixed biomarkers in longitudinal studies leads to a better clinical decision by improving the efficiency of parameter estimates. In many clinical studies, the observed time for two biomarkers may not be equivalent and one of the longitudinal responses may have recorded in a longer time than the other one. In addition, the response variables may have different missing patterns. In this paper, we propose a new joint model of associated continuous and binary responses by accounting different missing patterns for two longitudinal outcomes. A conditional model for joint modeling of the two responses is used and two shared random effects models are considered for intermittent missingness of two responses. A Bayesian approach using Markov Chain Monte Carlo (MCMC) is adopted for parameter estimation and model implementation. The validation and performance of the proposed model are investigated using some simulation studies. The proposed model is also applied for analyzing a real data set of bariatric surgery.     

On the grouped selection and model complexity of the adaptive elastic net

Lasso proved to be an extremely successful technique for simultaneous estimation and variable selection. However lasso has two major drawbacks. First, it does not enforce any grouping effect and secondly in some situation lasso solutions are inconsistent for variable selection. To overcome this inconsistency adaptive lasso is proposed where adaptive weights are used for penalizing different coefficients. Recently a doubly regularized technique namely elastic net is proposed which encourages grouping effect i.e. either selection or omission of the correlated variables together. However elastic net is also inconsistent. In this paper we study adaptive elastic net which does not have this drawback. In this article we specially focus on the grouped selection property of adaptive elastic net along with its model selection complexity. We also shed some light on the bias-variance tradeoff of different regularization methods including adaptive elastic net. An efficient algorithm was proposed in the line of LARS-EN, which is then illustrated with simulated as well as real life data examples.     

Bayesian response adaptive randomization using longitudinal outcomes

The response adaptive randomization (RAR) method is used to increase the number of patients assigned to more efficacious treatment arms in clinical trials. In many trials evaluating longitudinal patient outcomes, RAR methods based only on the final measurement may not benefit significantly from RAR because of its delayed initiation. We propose a Bayesian RAR method to improve RAR performance by accounting for longitudinal patient outcomes (longitudinal RAR). We use a Bayesian linear mixed effects model to analyze longitudinal continuous patient outcomes for calculating a patient allocation probability. In addition, we aim to mitigate the loss of statistical power because of large patient allocation imbalances by embedding adjusters into the patient allocation probability calculation. Using extensive simulation we compared the operating characteristics of our proposed longitudinal RAR method with those of the RAR method based only on the final measurement and with an equal randomization method. Simulation results showed that our proposed longitudinal RAR method assigned more patients to the presumably superior treatment arm compared with the other two methods. In addition, the embedded adjuster effectively worked to prevent extreme patient allocation imbalances. However, our proposed method may not function adequately when the treatment effect difference is moderate or less, and still needs to be modified to deal with unexpectedly large departures from the presumed longitudinal data model. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian estimation with integrated nested Laplace approximation for binary logit mixed models

In multilevel models for binary responses, estimation is computationally challenging due to the need to evaluate intractable integrals. In this paper, we investigate the performance of integrated nested Laplace approximation (INLA), a fast deterministic method for Bayesian inference. In particular, we conduct an extensive simulation study to compare the results obtained with INLA to the results obtained with a traditional stochastic method for Bayesian inference (MCMC Gibbs sampling), and with maximum likelihood through adaptive quadrature. Particular attention is devoted to the case of small number of clusters. The specification of the prior distribution for the cluster variance plays a crucial role and it turns out to be more relevant than the choice of the estimation method. The simulations show that INLA has an excellent performance as it achieves good accuracy (similar to MCMC) with reduced computational times (similar to adaptive quadrature).     

Inference in Targeted Group‐Sequential Covariate‐Adjusted Randomized Clinical Trials

This article is devoted to the construction and asymptotic study of adaptive, group‐sequential, covariate‐adjusted randomized clinical trials analysed through the prism of the semiparametric methodology of targeted maximum likelihood estimation. We show how to build, as the data accrue group‐sequentially, a sampling design that targets a user‐supplied optimal covariate‐adjusted design. We also show how to carry out sound statistical inference based on such an adaptive sampling scheme (therefore extending some results known in the independent and identically distributed setting only so far), and how group‐sequential testing applies on top of it. The procedure is robust (i.e. consistent even if the working model is mis‐specified). A simulation study confirms the theoretical results and validates the conjecture that the procedure may also be efficient.     

Inferences in dynamic logit models in semi-parametric setup for repeated binary data

Binary dynamic fixed and mixed logit models are extensively studied in the literature. These models are developed to examine the effects of certain fixed covariates through a parametric regression function as a part of the models. However, there are situations where one may like to consider more covariates in the model but their direct effect is not of interest. In this paper we propose a generalization of the existing binary dynamic logit (BDL) models to the semi-parametric longitudinal setup to address this issue of additional covariates. The regression function involved in such a semi-parametric BDL model contains (i) a parametric linear regression function in some primary covariates, and (ii) a non-parametric function in certain secondary covariates. We use a simple semi-parametric conditional quasi-likelihood approach for consistent estimation of the non-parametric function, and a semi-parametric likelihood approach for the joint estimation of the main regression and dynamic dependence parameters of the model. The finite sample performance of the estimation approaches is examined through a simulation study. The asymptotic properties of the estimators are also discussed. The proposed model and the estimation approaches are illustrated by reanalysing a longitudinal infectious disease data.     

Unconditional empirical likelihood approach for analytic use of public survey data

Modeling survey data often requires having the knowledge of design and weighting variables. With public-use survey data, some of these variables may not be available for confidentiality reasons. The proposed approach can be used in this situation, as long as calibrated weights and variables specifying the strata and primary sampling units are available. It gives consistent point estimation and a pivotal statistics for testing and confidence intervals. The proposed approach does not rely on with-replacement sampling, single-stage, negligible sampling fractions, or noninformative sampling. Adjustments based on design effects, eigenvalues, joint-inclusion probabilities or bootstrap, are not needed. The inclusion probabilities and auxiliary variables do not have to be known. Multistage designs with unequal selection of primary sampling units are considered. Nonresponse can be easily accommodated if the calibrated weights include reweighting adjustment for nonresponse. We use an unconditional approach, where the variables and sample are random variables. The design can be informative.     

Bias due to Ignoring the Sample Design in Case–Control Studies

Case–control studies allow efficient estimation of the associations of covariates with a binary response in settings where the probability of a positive response is small. It is well known that covariate–response associations can be consistently estimated using a logistic model by acting as if the case–control (retrospective) data were prospective, and that this result does not hold for other binary regression models. However, in practice an investigator may be interested in fitting a non–logistic link binary regression model and this paper examines the magnitude of the bias resulting from ignoring the case–control sample design with such models. The paper presents an approximation to the magnitude of this bias in terms of the sampling rates of cases and controls, as well as simulation results that show that the bias can be substantial.