Rahul Bhattacharya

• Ph.D(Statistics)
• Professor at University of Calcutta

An alternative definition of the stress-strength reliability function is developed for the discrete stress-strength reliability models by taking into consideration the presence of ties. A unique template is also developed to evaluate any definition of stress-strength reliability function from a practical viewpoint. The proposed and existing definit...

A new non asymptotic upper bound for the tail probability of a non negative random variable is developed as an alternative to that given by the Markov Inequality. The new bound is derived under the sole assumption of the existence of the first order moment. A thorough comparative investigation of the theoretical properties of the derived bound is e...

Multi-treatment two stage adaptive design for survival responses is generally developed under different assumptions. In this work, we explore the performance of such a design when the assumptions are violated. As a choice of design, we consider a specific design of Bhattacharya and Shome (2019), which uses random censoring, exponential response, Ko...

In the context of clinical trials, a multi-treatment two-stage adaptive randomization procedure is developed for survival responses with copula-based nonrandom censoring. Because no such allocation design is available for survival responses with nonrandom censoring, this is probably the first work in this direction. After allocating the first-stage...

A modified definition of the stress-strength reliability function is proposed for discrete family of distributions. The newly introduced definition is utilized to derive expressions of the reliability function as well as its Uniformly Minimum Variance Unbiased Estimator (UMVUE) and unbiased estimator of the variance of the UMVUE for different membe...

This work focuses on the nonparametric procedures which are devised as an alternative to analyse the repeated measurements arising in the basic two-treatment, two-period crossover design for continuous responses. Comparing direct effect difference of two treatments is not enough to check for the interchangeability of the treatments in a crossover s...

Background India is going through the maintenance phase of VL elimination programme which may be threatened by the persistence of hidden parasite pools among asymptomatic leishmanial infection (ALI) and PKDL. The present work was designed to determine the burden of VL, PKDL, and ALI and to assess the role of treatment of ALI in maintaining post-eli...

Assuming binary treatment outcomes, a covariate adjusted response adaptive (CARA) design is developed for multi-arm clinical trials assuming the presence of treatment-covariate interaction. The proposed allocation skews the allocation dynamically according to the performance of the treatments and the covariate profile of any incoming subject. Relev...

In this paper, stein-type two-stage sampling procedure is carried out for fixed accuracy confidence interval estimation of the common variance (σ2) parameter corresponding to multivariate normal distribution with autoregressive covariance structure of order 1. Related asymptotics are obtained and simulation results are presented.

The Uniformly Minimum Variance Unbiased (UMVU) and the Maximum Likelihood (ML) estimations of R = P(X ≤ Y) and the associated variance are considered for independent discrete random variables X and Y. Assuming a discrete uniform distribution for X and the distribution of Y as a member of the discrete one parameter exponential family of distribution...

Covariate adjusted response adaptive designs are developed with ordinal categorical responses for phase III clinical trial involving multiple treatments. Stochastic ordering principle is used to order the treatments according to effectiveness and consequently allocation functions are developed by combining the cumulative odds ratios suitably. The p...

The effectiveness of the Pulsed Electromagnetic Field (PEMF) Therapy is investigated statistically considering a real clinical trial in the treatment of Osteoarthritis (OA) patients with longitudinal monitoring. Relevant statistical modelling followed by an appropriate analysis for ordinal longitudinal data is carried out to evaluate the usefulness...

Compromising ethics and precision in the context of a multiarmed clinical trial, an optimal order adjusted response adaptive design is proposed for survival outcomes subject to independent random censoring. The operating characteristics of the proposed design and the follow-up inference are studied both theoretically as well as empirically and are...

In clinical trials, fixed randomizations in a prefixed proportion (e.g. 1:1 or 2:1 for two treatment trials) may be adopted to allocate the entering patients among the competing treatments. However, such an allocation procedure ignores the knowledge obtained from the accrued information on the performance of the treatments until that point. However...

Uniformly minimum variance unbiased (UMVU) estimators of reliability function (both stress–strength and mission time) and the associated variance are derived for a class of generalization of Lindley distribution. The application of the results is further validated by a real data study. AMS 2020 subject classification: 62N05 62F10

This work deals with nonparametric test procedures for comparing effects of two treatments in two period parallel group design, where each subject receives the same treatment over the two periods. The procedures are based on consistent estimators of relative treatment effects in each period and that of covariate adjusted effects with responses in p...

Explicit expression of the Stress - Strength reliability function, R=P(X≤Y) is derived, when the stress (X) and strength (Y) distributions are different members of the Power series family of distributions. Minimum Variance Unbiased (MVU) estimator of R, variance of the MVU estimator together with its MVU estimator are derived for Power series famil...

Weighing the cumulative odds ratios suitably, a two treatment response adaptive design for phase III clinical trial is proposed for ordinal categorical responses. Properties of the proposed design are investigated theoretically as well as empirically. Applicability of the design is further verified using a data pertaining to a real clinical trial w...

A two stage randomized design is developed for two treatment clinical trials in which response variables are exponential and the observations are censored by using failure censoring and time censoring in the first and second stages respectively. The censoring time for the second stage is determined from the outcomes of the first stage. An applicati...

A multi-treatment response adaptive procedure is developed considering “comparison with the best” philosophy of multiple comparison procedures for clinical trials with ordinal categorical responses, when there is no shared control. For each response category, we arbitrarily create two outcome groups; one by combining the categories more favorable t...

A multi-arm response-adaptive allocation design is developed for circular treatment outcomes. Several exact and asymptotic properties of the design are studied. Stage-wise treatment selection procedures based on the proposed response-adaptive design are also suggested to exclude the worse performing treatment(s) at earlier stages. Detailed simulati...

A class of adaptive designs is formulated in two stages for clinical trials to favour the better performing treatment for further allocation in an efficient way. The first stage of the allocation consists in randomizing subjects to each treatment arm with equal probability and performing a test of equality of treatment effects. The resulting p valu...

An adaptive two stage allocation design is developed for survival responses subject to independent informative censoring. Asymptotic p value of a score test related to a hypothesis of treatment effectiveness is used to set the assignment probability of the second stage. Several characteristics of the design and the follow-up inference are studied,...

An optimal target proportion is derived balancing between the needs of clinician and statistician considering a general criterion and binary treatment outcome. A response-adaptive procedure based on this optimal proportion is developed and the associated limiting results are derived. In addition, the proposed procedure is compared with the existing...

A multi-treatment two stage adaptive allocation design is developed for survival responses. Assuming noninformative random censoring, asymptotic p values of relevant tests of equality of treatment effects are used to derive the assignment probability of incoming second stage subjects. Several ethical and inferential criteria of the design are studi...

A two treatment response adaptive design is developed for phase III clinical trials with ordinal categorical treatment outcome using Goodman-Kruskal measure of association. Properties of the proposed design are studied both empirically and theoretically and the acceptability is further illustrated using two real data-sets; one from a clinical trial...

A class of covariate-adjusted response-adaptive randomization procedures is developed for binary treatment outcomes in a phase III clinical trial set up involving multiple treatments. The target allocation is developed by combining the ethical aspects with statistical precision under the existence of treatment covariate interaction. Relevant measur...

Simultaneous estimation of several normal means is considered under simple order restriction. Maximum likelihood estimators of normal means are derived under such order restriction and compared empirically with the existing estimators using Pitman closeness as well as mean square type precision criteria.

Tests for the equality of treatment effects are developed for a two-stage sampling design with failure censoring in each stage. Depending on the results in the first stage, adaptive failure censoring is adopted in the second stage. Assuming exponential responses, tests for comparing the response distributions are obtained and some related small sam...

A number of allocation designs are developed for continuous and binary treatment outcomes to assign a higher number of subjects to the treatment doing better in course of the trial. However, if the response is circular in nature, the definition of a better treatment differs from that under the linear response and hence the already developed designs...

Proper classification of different astronomical objects are of great importance in order to study the nature of origin of those objects. Although clustering and classification techniques are exploratory in nature, there are model based techniques which use distributional assumptions extensively. Many astronomical data sets related to galaxies, glob...

For testing a simple null hypothesis against a simple alternative using Neyman-Pearson theory, examples of most powerful non-randomized critical regions are constructed, which are overlapping for varying sizes. A likelihood ratio based criterion, characterizing such critical regions, is also provided. A simple method, in addition, is suggested to c...

Response-adaptive designs are important in clinical trials for their ability to skew the allocation towards the better performing treatment. Most of the designs are derived under specific assumptions (e.g. normality, existence of first few moments, etc.) on the response model. But responses may be non-normal and consequently the existence of moment...

An allocation function, invariant under monotonic transformation, is proposed in the context of multi-arm clinical trials for a class of continuous response distributions. The aim is to skew the allocation towards the most promising treatment using the whole information about the response distributions. A response adaptive implementation based on t...

In the context of clinical trials for comparing two treatments, a new class of covariate adjusted response adaptive procedures is developed to achieve a balance between clinical optimality and inferential precision. Assuming normally distributed responses, several exact and asymptotic properties are studied and compared with a reasonable alternativ...

A randomized two treatment allocation design, conducted in two stages, is proposed for a class of continuous response trials. Patients are assigned to each treatment in equal numbers in the first stage and p value of a test of equality of treatment effects based on these data is used to determine the assignment probability of second stage patients....

A class of optimal covariate-adjusted response adaptive procedures is developed for phase III clinical trials when the treatment response is a survival time and there is random censoring. The basic aim is to develop an allocation design by combining the ethical aspects with statistical precision in a reasonable way under the presence of covariate i...

A class of covariate-adjusted adaptive allocation procedures is developed for a general class of responses with an aim to satisfy relevant clinical requirements. Some exact and asymptotic properties of the procedures, proposed and a reasonable competitor, are studied and compared under the presence of treatment-covariate interaction. Copyright © 20...

Traditionally optimal target allocation proportions for response-adaptive designs are derived by completely ignoring the actual adaptive randomization procedure. Considering efficiency of the allocation designs, we derive near efficient target proportions to balance between individual and collective ethics. Performance of the derived allocation tar...

A variety of response-adaptive randomization procedures have been proposed in literature assuming binary outcomes. However, the list is not so long for continuous outcomes though many real clinical trials deal with continuous treatment responses. In this paper, we attempt to explore the available procedures together with a comparison of their perfo...

An urn based covariate adjusted response adaptive allocation design with dichotomous responses is proposed incorporating the ordered nature of the covariate. The allocation procedure is assessed both numerically and theoretically. The performance of the allocation design is also investigated in a relevant hypothetical clinical trial.

Optimal response-adaptive designs have been studied by various authors in the context for allocating patients among two competing treatments in a phase III clinical trial. However, depending on the variabilities of the responses, most of these designs may allocate a smaller number of patients to the better treatment. In the current work, we obtain...

Response-adaptive designs are used in phase III clinical trials to allocate a larger number of patients to the better treatment. Optimal response-adaptive designs have become popular in recent days for this purpose, where the design is derived from some optimal viewpoints, mostly by optimizing some objective function subject to some constraint(s)....

Several response-adaptive designs are available to allocate sequentially entering patients between two competing treatments, so that a larger number of patients are treated by the better treatment. Most of the designs are for binary treatment responses. Among the few available designs for continuous responses, the continuous drop-the-loser (CDL) ru...

Response-adaptive designs have become popular for allocation of the entering patients among two or more competing treatments in a phase III clinical trial. Although there are a lot of designs for binary treatment responses, the number of designs involving covariates is very small. Sometimes the patients give repeated responses. The only available r...

A randomized two-stage adaptive design is proposed and studied for allocation of patients to treatments and comparison in a phase III clinical trial with survival time as treatment responses. We consider the possibility of several covariates in the design and analysis. Several exact and limiting properties of the design and the follow-up inference...

The article deals with an optimal response-adaptive design for allocating patients among two competing treatments in a phase III clinical trial. An optimal response-adaptive target is developed for a general class of response distributions subject to two clinically relevant constraints. Various theoretical and numerical properties of the proposed p...

A randomized two-stage adaptive Bayesian design is proposed and studied for allocation and comparison in a phase III clinical trial with survival time as treatment response. Several exact and limiting properties of the design and the follow-up inference are studied, both numerically and theoretically, and are compared with a single-stage randomized...

Response-adaptive designs are becoming popular in phase III clinical trials. We propose a response-adaptive design for a general class of continuous responses. The design is based on two kernels and does not require the existence of any moment of the response variables, and thus applicable for any type of continuous responses, even if the distribut...

The paper proposes an optimal response-adaptive procedure for a general class of responses using a combination of two clinically relevant optimality criteria. We provide a thorough development for trials involving two treatments and sketch the possible extension for multiple treatments. Some related asymptotic results are worked out. We provide sim...

Most of the available response-adaptive designs in phase III clinical trial set up are not from any optimal consideration. An optimal design for binary responses is given by Rosenberger et al. (2001) and an optimal design for continuous responses is provided by Biswas and Mandal (2004). Recently, Zhang and Rosenberger (2006) [ZR] provided another d...

In the present work we develop a randomized two-treatment adaptive allocation design with covariates ensuring smaller variability of treatment allocations. We study, both numerically and theoretically, several exact and limiting properties of the design and consider an inferential problem following the allocation design. We compare the design with...

In most of the two-treatment clinical trials, patients are randomized to either treatment in a balanced fashion, and at the end of the experiment a decision is made as to which treatment is more effective. But such a strategy of finding the effective treatment by assigning half of the subjects to the inferior treatment lacks ethical imperative. Urn...

In the present work, we formulate a two-treatment single period two-stage adaptive allocation design for achieving larger allocation proportion to the better treatment arm in the course of the trial with increased precision of the parameter estimator. We examine some properties of the proposed rule and compare it with some of the existing allocatio...

In the present work, we develop a two-stage allocation rule for binary response using the log-odds ratio within the Bayesian framework allowing the current allocation to depend on the covariate value of the current subject. We study, both numerically and theoretically, several exact and limiting properties of this design. The applicability of the p...

Optimal response-adaptive designs in phase III clinical trial set up are gaining more interest. Most of the available designs are not based on any optimal consideration. An optimal design for binary responses is given by Rosenberger et al. (2001) and one for continuous responses is provided by Biswas and Mandal (2004). Recently, Zhang and Rosenberg...

Introduction Adaptive Designs for Binary Treatment Responses Adaptive Designs for Binary Treatment Responses Incorporating Covariates Adaptive Designs for Categorical Responses Adaptive Designs for Continuous Responses Optimal Adaptive Designs Delayed Responses in Adaptive Designs Biased Coin Designs Real Adaptive Clinical Trials Data Study for Dif...

An adaptive design is provided for phase III clinical trials where the treatment responses are categorical. The proposed design extends the drop-the-loser rule [A. Ivanova, Metrika 58, No. 1, 1–13 (2003; Zbl 1019.62076)] which is proposed for binary treatment responses only. It is illustrated that the proposed design is an improvement over the exis...

In this paper, given an arbitrary fixed target sample size, we describe a sequential allocation scheme for comparing two competing treatments in clinical trials. The proposed scheme is a compromise between ethical and optimum allocations. Using some specific probability models, we have shown that, for estimating the risk difference (RD) between two...

In the present work, we develop a randomized two-treatment single period response adaptive design by combining two contrasting aspects (i.e., ethics and optimality), where optimality is defined in a meaningful way. We compare this rule with some of the existing rules by computing various performance measures of the rules.

A reliability setting is considered for comparing two competing equipments based on a fixed number of observations. A two stage failure censored design is proposed in which a preassigned number of items are randomised equally at the first stage and the better items are examined exclusively at the end of the second stage. Here at each stage we consi...