A Lindley-binomial model for analyzing the proportions with sparseness and excessive zeros.

Proportional data arise frequently in a wide variety of fields of study. Such data often exhibit extra variation such as over/under dispersion, sparseness and zero inflation. For example, the hepatitis data present both sparseness and zero inflation with 19 contributing non-zero denominators of 5 or less and with 36 having zero seropositive out of 83 annual age groups. The whitefly data consists of 640 observations with 339 zeros (53%), which demonstrates extra zero inflation. The catheter management data involve excessive zeros with over 60% zeros averagely for outcomes of 193 urinary tract infections, 194 outcomes of catheter blockages and 193 outcomes of catheter displacements. However, the existing models cannot always address such features appropriately. In this paper, a new two-parameter probability distribution called Lindley-binomial (LB) distribution is proposed to analyze the proportional data with such features. The probabilistic properties of the distribution such as moment, moment generating function are derived. The Fisher scoring algorithm and EM algorithm are presented for the computation of estimates of parameters in the proposed LB regression model. The issues on goodness of fit for the LB model are discussed. A limited simulation study is also performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates. The proposed model is illustrated through three aforementioned proportional datasets.

Adaptive aggregation for longitudinal quantile regression based on censored history process.

Most of the studies for longitudinal quantile regression are based on the correct specification. Nevertheless, one specific model can hardly perform precisely under different conditions and assessing which conditions are (approximately) satisfied to determine the optimal one is rather difficult. In the case of the mixed effect model, the misspecification of the fixed effect part will cause a lack of predicting accuracy of random effects, and affect the efficiency of the cumulative function estimator. On the other hand, limited research has focused on incorporating multiple candidate procedures in longitudinal data analysis, which is of current emergency. This paper proposes an exponential aggregation weighting algorithm for longitudinal quantile regression. Based on the secondary smoothing loss function, we establish oracle inequalities for aggregated estimator. The proposed method is applied to evaluate the cumulative τth quantile function for additive mixed effect model with right-censored history process, and an aggregation-based best linear prediction for random effects is constructed as well. We show that the asymptotic properties are conveniently imposed owing to the smoothing scheme. Simulation studies are carried out to exhibit the rationality, and our method is illustrated to analyze the data set from a multicenter automatic defibrillator implantation trial.

A multivariate zero-inflated binomial model for the analysis of correlated proportional data.

In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies.

Estimating the quantile medical cost under time-dependent covariates and right censored time-to-event variable based on a state process.

Estimating the medical costs from disease diagnosis to a terminal event is of immense interest to researchers. However, most of existing literature on such research focused on the estimation of cumulative mean function (CMF) for history process. In this paper, the combined scheme of both inverse probability of censoring weighting (IPCW) technique and longitudinal quantile regression model is used to develop a novel procedure to the estimation of cumulative quantile function (CQF) based on history process with time-dependent covariates and right censored time-to-event variable. The consistency of proposed estimator is derived. The extensive simulation study is conducted to investigate the performance of the estimator given in this paper. A medical cost data from a multicenter automatic defibrillator implantation trial (MADIT) is analyzed to illustrate the application of developed method.

Estimating the cumulative mean function for history process with time-dependent covariates and censoring mechanism.

In this paper, an approach to estimating the cumulative mean function for history process with time dependent covariates and right censored time-to-event variable is developed using the combined technique of joint modeling and inverse probability weighting method. The consistency of proposed estimator is derived. Theoretical analysis and simulation studies indicate that the estimator given in this paper is quite recommendable to practical applications because of its simplicity and accuracy. A real data set from a multicenter automatic defibrillator implantation trial is used to illustrate the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.

Modeling sustained treatment effects in tumor xenograft experiments.

In cancer drug development, demonstrated efficacy in tumor xenograft models is an important step toward bringing a promising compound to human use. A key outcome variable is tumor volume measured over a period of time, while mice are treated with certain treatment regimens. A constrained parametric model has been proposed to account for special features, such as intrinsic tumor growth, or tumor volume truncations due to tumor size being either too large or too small to detect. However, since the drug concentration in the blood of a mouse or its tissues may be stabilized at a certain level and maintained during a period of time, the treatment may have sustained effects. This article extends the constrained parametric model to account for the sustained drug effects. The ECM algorithm for incomplete data is applied to estimating the dose-response relationship in the proposed model. The model selection based on likelihood functions is given and a simulation study is conducted to investigate the performance of the proposed estimator. A real xenograft study on the antitumor agent temozolomide combined with irinotecan against the rhabdomyosarcoma is analyzed using the proposed methods.