Research and Publications

Abstract

This paper considers a location test in a single sample setting without any assumption about the symmetry of the continuous distribution. Two adaptive test procedures are suggested — one is a probabilistic approach while the other is a deterministic approach. The deterministic approach is based on calculating a measure of symmetry and using it as a basis for choosing between the sign test and the Wilcoxon signed rank test. The probabilistic approach is also a combination of the sign test and the Wilcoxon signed rank test according to evidence of asymmetry provided by the P-value from the triples test for symmetry given in Randles et al. [R.H. Randles, M.A. Fligner, G.E. Policello, D.A. Wolfe, An asymptotically distribution-free test for symmetry versus asymmetry, Journal of the American Statistical Association 75 (1980) 168–172]. A simulation study shows that the proposed deterministic approach using a simple measure of symmetry is as good as Lemmer [H.H. Lemmer, Adaptive tests for the median, IEEE Transactions on Reliability 42 (1993) 442–448] in terms of power and attainment of the nominal size. The probabilistic approach has been shown to be superior to the other existing competitors.

Abstract

The present paper considers two-sample tests for scale problem under symmetry without any assumption regarding the equality of medians. Two adaptive procedures are proposed—one is probabilistic while the other is deterministic. The proposed probabilistic approach is shown, by simulation studies, to maintain its significance level for various symmetric distributions and is found to be superior to the other existing competitors in terms of both robustness of size and power. Both the adaptive procedures are illustrated by using a real data. Some relevant asymptotic properties are also discussed.

Abstract

Some adaptive test procedures are developed for the generalized Behrens-Fisher problem. The one having a deterministic approach is based on calculating a measure of symmetry from each sample and using them as a basis for choosing between the modifiedWilcoxon-Mann-Whitney test (Fligner and Policello, 1981) and the modified Mood’s median test (Fligner and Rust, 1982). The other one is a probabilistic approach which also uses a combination of the modified Wilcoxon-Mann-Whitney test and the modified Mood’s

median test according to an evidence of asymmetry provided by the p-value from the triples test for symmetry given in Randles, Fligner, Policello, and Wolfe (1980). This probabilistic approach is further modified by using a suitable function of the p-value from the triples test. A simulation study reveals that the modified procedure performs reasonably well in terms of power and attainment of the nominal size. 

Abstract

We consider a test based on a possible modification of the inverse binomial sampling procedure which has the same size and power as the binomial UMPU test. The proposed procedure leads to a considerable saving in trial size as compared to the fixed trial size binomial two-sided test procedure. We carry out a simulation study to evaluate the performance of the proposed methodology and compare it with a natural competitor. 

Abstract

The present paper considers a generalization of the Behrens-Fisher problem without assuming that the underlying distribution functions are continuous so that the proposed procedure is also applicable to count or ordered categorical data. The proposed test is based on a generalization of the Wilcoxon-Mann-Whitney statistic where the data correspond to sequentially observed responses from patients allocated at random to two treatments in two stages. At stage 1, patients are allocated completely at random between two treatments. At the end of stage 1, the accumulated responses corresponding to the treatments are compared. At stage 2, the patients are assigned to the treatments in such a way that the more promising treatment receives more patients. Simulation comparisons of the proposed procedure with some natural competitors show a considerably larger number of allocations to the better treatment and a smaller average sample number with a little loss in power. 

Abstract

Matched case-control paired data are commonly used to study the association between a disease and an exposure of interest. This work provides a consistent test for this association with respect to the conditional odds ratio (), which is a measure of association that is also valid in prospective studies. We formulate the test from the maximum likelihood (ML) estimate of  by using data under inverse binomial sampling, in which individuals are selected sequentially to form matched pairs until for the first time one obtains either a prefixed number of index pairs with the case unexposed but the control exposed or with the case exposed but the control unexposed. We discuss the situation of possible early stopping. We compare numerically the performance of our procedure with a competitor proposed by Lui (1996) in terms of type I error rate, power, average sample number (ASN) and the corresponding standard error. Our numerical study shows a gain in sample size without loss in power as compared to the competitor. Finally, we use the data taken from a case-control study on the use of X-rays and the risk of childhood acute myeloid leukemia for illustration. 

Abstract

We develop a test for proportion that modifies the negative binomial UMPU test and leads to gain in sample size without loss in power. We apply the proposed idea to provide a test for association in matched pair study. 

NONPARAMETRIC METHODS FOR ESTIMATING SURVIVAL FUNCTIONS.

Abstract: 

Survival analysis refers to a set of statistical methods for analysing time-to-event data. Here the variable of interest is time until an event occurs. Survival data commonly involves censoring which must be taken into account for drawing valid inferences. Survival analysis is not only applicable to biology and medicine, but it is also useful in various other fields including engineering, economics, among others. The present work discusses the fundamental concepts of survival analysis and reviews some nonparametric statistical methods for analysing survival data. Here we will primarily focus on the Kaplan-Meier product limit method and the actuarial life-table analysis. 

THE SIGN TEST UNDER INVERSE SAMPLING SCHEME

Abstract: 

We consider a modification of the sign test based on the inverse binomial sampling procedure. The test procedure is applicable for both the one-sample location problem and the paired-sample location problem. It has the same size and power as the fixed sample size sign test.  These tests serve as nonparametric alternatives to the one-sample t-test and paired sample t-test. The test procedure based on inverse sampling allows for early stopping if a significant result is obtained or if continuing the trial would not lead to a significant result. The test procedure is illustrated through a real life example. 

CONFIDENCE INTERVAL ASSOCIATED WITH THE BRUNNER-MUNZEL TEST. 

Abstract: 

The present paper considers the problem of interval estimation of the generalized treatment effect in a nonparametric setup without assuming that the underlying distribution functions are continuous. Two confidence intervals are constructed based on the generalization of the Wilcoxon-Mann-Whitney statistic, as in Brunner and Munzel (2000), so that they are also applicable for count or ordered categorical data. The performance of the two confidence intervals are compared in terms of the coverage probabilities and the expected lengths through a simulation study. The confidence intervals are illustrated with the help of a data from a study relating to the effect of an anti-depressant drug on radicular back pain. 

A TEST FOR EQUIVALENCE BETWEEN TWO TREATMENTS BASED ON THE GENERALIZED TREATMENT EFFECT. 

Abstract: 

The present paper considers the problem of testing for equivalence between two treatments without assuming that the underlying distribution functions are continuous. The testing problem is formulated on the basis of the generalized treatment effect as a measure of the difference between two treatment arms in a clinical trial. The proposed test is based on a generalization of the Wilcoxon-Mann-Whitney statistic so that the proposed procedure is also applicable for count or ordered categorical data. The proposed test is applied to a data from a study relating to the effect of an anti-depressant drug on radicular back pain.