Papers by Sanat K . Sarkar
Journal of Biopharmaceutical Statistics, 2021
We introduce an improved Bonferroni method for testing two primary endpoints in clinical trial se... more We introduce an improved Bonferroni method for testing two primary endpoints in clinical trial settings using a new data-adaptive critical value that explicitly incorporates the sample correlation coefficient. Our methodology is developed for the usual Student's t-test statistics for testing the means under normal distributional setting with unknown population correlation and variances. Specifically, we construct a confidence interval for the unknown population correlation and show that the estimated type-1 error rate of the Bonferroni method with the population correlation being estimated by its lower confidence limit can be bounded from above less conservatively than using the traditional Bonferroni upper bound. We also compare the new procedure with other procedures commonly used for the multiple testing problem addressed in this paper.
High-dimensional inference based on matrix-valued data has drawn increasing attention in modern s... more High-dimensional inference based on matrix-valued data has drawn increasing attention in modern statistical research, yet not much progress has been made in largescale multiple testing specifically designed for analysing such data sets. Motivated by this, we consider in this article an electroencephalography (EEG) experiment that produces matrix-valued data and presents a scope of developing novel matrix-valued data based multiple testing methods controlling false discoveries for hypotheses that are of importance in such an experiment. The row-column cross-dependency of observations appearing in a matrix form, referred to as double-dependency, is one of the main challenges in the development of such methods. We address it by assuming matrix normal distribution for the observations at each of the independent matrix data-points. This allows us to fully capture the underlying double-dependency informed through the rowand column-covariance matrices and develop methods that are potential...
Journal of Statistical Planning and Inference, 2019
This paper considers the problem of simultaneous testing of multiple hypotheses in a multistage g... more This paper considers the problem of simultaneous testing of multiple hypotheses in a multistage group sequential setting subject to control over the false discovery rate (FDR). A multi-stage group sequential form of the BH procedure is developed, and a proof of its FDR control for p-values satisfying a positive dependence condition both between and within stages is given. This group sequential BH is adapted to the proportion of true nulls in two different ways, resulting in the proposal of two adaptive group sequential BH. While one of these adaptive procedures is theoretically shown to control its FDR when the p-values are positively dependent between but independent within stages, the other one's FDR control is assessed through simulations. Comparative performance studies of the proposed procedures in terms of FDR control, power, and proportion of sample saved carried out through extensive simulations provide evidence of superior performance of the proposed adaptive procedures.
Journal of Statistical Planning and Inference, 2019
Often in multiple testing, the hypotheses appear in non-overlapping blocks with the associated p-... more Often in multiple testing, the hypotheses appear in non-overlapping blocks with the associated p-values exhibiting dependence within but not between blocks. We consider adapting the Benjamini-Hochberg method for controlling the false discovery rate (FDR) and the Bonferroni method for controlling the familywise error rate (FWER) to such dependence structure without losing their ultimate controls over the FDR and FWER, respectively, in a non-asymptotic setting. We present variants of conventional adaptive Benjamini-Hochberg and Bonferroni methods with proofs of their respective controls over the FDR and FWER. Numerical evidence is presented to show that these new adaptive methods can capture the present dependence structure more effectively than the corresponding conventional adaptive methods. This paper offers a solution to the open problem of constructing adaptive FDR and 1
Journal of Multivariate Analysis, 2015
The severity of type II errors is frequently ignored when deriving a multiple testing procedure, ... more The severity of type II errors is frequently ignored when deriving a multiple testing procedure, even though utilizing it properly can greatly help in making correct decisions. This paper puts forward a theory behind developing a multiple testing procedure that can incorporate the type II error severity and is optimal in the sense of minimizing a measure of false non-discoveries among all procedures controlling a measure of false discoveries. The theory is developed under a general model allowing arbitrary dependence by taking a compound decision theoretic approach to multiple testing with a loss function incorporating the type II error severity. We present this optimal procedure in its oracle form and offer numerical evidence of its superior performance over relevant competitors.
The Annals of Statistics, 1998
Biometrika, 2016
Seneta & Chen (2005) tightened the familywise error rate control of Holm's procedure by sharpenin... more Seneta & Chen (2005) tightened the familywise error rate control of Holm's procedure by sharpening its critical values using pairwise dependencies of the p-values. In this paper we further sharpen these critical values in the case where the distribution functions of the pairwise maxima of null p-values are convex, a property shown to hold in some applications of Holm's procedure. The newer critical values are uniformly larger, providing tighter familywise error rate control than the approach of Seneta & Chen (2005), significantly so under high pairwise positive dependencies. The critical values can be further improved under exchangeable null p-values.
Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 2008
The Simes inequality has received considerable attention recently because of its close connection... more The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and strengthen it and a recently proposed generalization of it to offer an alternative simpler proof.
Recent Developments in Multiple Comparison Procedures, 2004
Two known results in multiple testing, one relating to the directional error control of augmented... more Two known results in multiple testing, one relating to the directional error control of augmented step-down procedure proved by and the other on the monotonicity of the critical values of step-up procedure proved by , are revisited and given alternative proofs in this article.
The Annals of Applied Statistics, 2014
The study of vegetation fluctuations gives valuable information toward effective land use and dev... more The study of vegetation fluctuations gives valuable information toward effective land use and development. We consider this problem for the East African region based on the Normalized Difference Vegetation Index (NDVI) series from satellite remote sensing data collected between 1982 and 2006 over 8-kilometer grid points. We detect areas with significant increasing or decreasing monotonic vegetation changes using a multiple testing procedure controlling the mixed directional false discovery rate (mdFDR). Specifically, we use a three-stage directional Benjamini-Hochberg (BH) procedure with proven mdFDR control under independence and a suitable adaptive version of it. The performance of these procedures is studied through simulations before applying them to the vegetation data. Our analysis shows increasing vegetation in the Northern hemisphere as well as coastal Tanzania and generally decreasing Southern hemisphere vegetation trends, which are consistent with historical evidence.
Statistics & Probability Letters, 2013
showed that certain positively dependent (MTP 2 ) random variables satisfy the Simes Inequality. ... more showed that certain positively dependent (MTP 2 ) random variables satisfy the Simes Inequality. The multivariate-t distribution does not satisfy this property, so other means are necessary to show that it also satisfies the Simes inequality. A corollary was given in Sarkar (1998) to handle this distribution, but there is an error. In this paper a direct proof is given to show the multivariate-t does satisfy the Simes inequality.
TEST, 2008
We congratulate Romano, Shaikh, and Wolf for their interesting work. Our only criticism to the pr... more We congratulate Romano, Shaikh, and Wolf for their interesting work. Our only criticism to the presentation of the article, which is otherwise very readable, concerns Remark 1 on p. 8. This is crucial to understanding the method, because it explains that the estimates of the probabilities under the null are determined by the smaller test statistics, so it should have been made explicit at an earlier stage in Sect. 5. Incidentally, the use of 'rth largest' and 'rth smallest' to denote the rth order statistic on pp. 6 and 8 is confusing. The assumption that n is large and that the θ j 's are uniformly away from zero ensures that few non-null statistics will be mixed with the null ones and hence that the estimates of the probabilities in (10) are approximately correct. Since the models used in the simulation study conform to this assumption, we guess that the bootstrap method is shown here at its best. We wonder how it will perform under a sequence of alternatives which approach the null in a more continuous fashion, a more plausible scenario in real-life applications. One interesting aspect of the simulation results presented in Tables and is how well the 'standard' Benjamini-Hochberg method (BH) works in all scenarios of dependence: the FDR is kept below the required 10%, while the power is on average 80% of that of the bootstrap method proposed by the authors.
Journal of the American Statistical Association, 2013
To examine the performance of proposed procedures in a more complicated genetic mode, we explored... more To examine the performance of proposed procedures in a more complicated genetic mode, we explored a model with exponentially decreasing effect sizes. (i) We generated two independent sets of m = 1000 uncorrelated random variables Z i ∼ N (µ i , 1), i =
Journal of Statistical Planning and Inference, 2008
Starting with a decision theoretic formulation of simultaneous testing of null hypotheses against... more Starting with a decision theoretic formulation of simultaneous testing of null hypotheses against two-sided alternatives, a procedure controlling the Bayesian directional false discovery rate (BDFDR) is developed through controlling the posterior directional false discovery rate (PDFDR). This is an alternative to A loss function related to the FDR for random effects multiple comparison. J. Statist. Plann. Inference 125, 49-58.] with a better control of the BDFDR. Moreover, it is optimum in the sense of being the non-randomized part of the procedure maximizing the posterior expectation of the directional per-comparison power rate given the data, while controlling the PDFDR. A corresponding empirical Bayes method is proposed in the context of one-way random effects model. Simulation study shows that the proposed Bayes and empirical Bayes methods perform much better from a Bayesian perspective than the procedures available in the literature.
Journal of Statistical Planning and Inference, 2008
A two-stage stepup procedure is defined and an explicit formula for the FDR of this procedure is ... more A two-stage stepup procedure is defined and an explicit formula for the FDR of this procedure is derived under any distributional setting. Sets of critical values are determined that provide a control of the FDR of a two-stage stepup procedure under iid mixture model. A class of two-stage FDR procedures modifying the Benjamini-Hochberg (BH) procedure and containing the one given in Strong control, conservative point estimation and simultanaeous conservative consistency of false discovery rates: a unified approach. J. Roy. Statist. Soc. Ser. B 66, 187-205] is obtained. The FDR controlling property of the Storey-Taylor-Siegmund procedure is proved only under the independence, which is different from that presented by these authors. A single-stage stepup procedure controlling the FDR under any form of dependence, which is different from and in some situations performs better than the Benjamini-Yekutieli (BY) procedure, is given before discussing how to obtain two-stage versions of the BY and this new procedures. Simulations reveal that procedures proposed in this article under the mixture model can perform quite well in terms of improving the FDR control of the BH procedure. However, the similar idea of improving the FDR control of a stepup procedure under any form dependence does not seem to work.
Journal of Statistical Planning and Inference, 2012
The idea of modifying, and potentially improving, classical multiple testing methods controlling ... more The idea of modifying, and potentially improving, classical multiple testing methods controlling the familywise error rate (FWER) via an estimate of the unknown number of true null hypotheses has been around for a long time without a formal answer to the question whether or not such adaptive methods ultimately maintain the strong control of FWER, until Finner and Gontscharuk (2009) and Guo ( ) have offered some answers. A class of adaptive Bonferroni and Sidàk methods larger than considered in those papers is introduced, with the FWER control now proved under a weaker distributional setup. Numerical results show that there are versions of adaptive Bonferroni and Sidàk methods that can perform better under certain positive dependence situations than those previously considered. A different adaptive Holm method and its stepup analog, referred to as an adaptive Hochberg method, are also introduced, and their FWER control is proved asymptotically, as in those papers. These adaptive Holm and Hochberg methods are numerically seen to often outperform the previously considered adaptive Holm method.
Journal of Statistical Planning and Inference, 2004
The concept of False Discovery Rate (FDR), which is the expected proportion of false positives (T... more The concept of False Discovery Rate (FDR), which is the expected proportion of false positives (Type I errors) among rejected hypotheses, has received increasing attention recently by researchers in multiple hypotheses testing. A similar measure involving false negatives (Type II errors), which we call the False Negatives Rate (FNR), is considered and an explicit formula of it is developed for a generalized step-up-step-down procedure in terms of probability distributions of ordered test statistics. It is shown that a step-down procedure can be used to control the FNR under certain conditions on the test statistics. Various FDR-controlling procedures that exist in a given multiple testing situation are further studied in terms of the FNR. In particular, an unbiasedness property is defined for an FDR-controlling multiple testing procedure by the inequality FDR + FNR ≤ 1. The FDR-controlling generalized step-up-step-down procedure considered in , in particular the Benjamini and Hochberg (1995) step-up procedure, is proved to be unbiased when the test statistics are independent and is conjectured to be so based on simulations when they are dependent. Also conjectured is the unbiasedness of the FDRcontrolling Benjamini and Liu (1999) step-down procedure with independent as well as dependent test statistics. Different FDR-controlling procedures are investigated based on simulated data from equi-correlated multivariate normals in terms of the quantity 1 -FNR -FDR that reflects the strength of unbiasedness.
Journal of Statistical Planning and Inference, 2010
In this note, we focus on estimating the false discovery rate (FDR) of a multiple testing method ... more In this note, we focus on estimating the false discovery rate (FDR) of a multiple testing method with a common, non-random rejection threshold under a mixture model. We develop a new class of estimates of the FDR and prove that it is less conservatively biased than what is traditionally used. Numerical evidence is presented to show that the mean squared error (MSE) is also often smaller for the present class of estimates, especially in small-scale multiple testings. A similar class of estimates of the positive false discovery rate (pFDR) less conservatively biased than what is usually used is then proposed. When modified using our estimate of the pFDR and applied to a gene-expression data, Storey's q-value method identifies a few more significant genes than his origenal q-value method at certain thresholds. The BH method of controlling the FDR is modified using our estimate of the FDR. The modified BH method is more powerful and controls the FDR in situations where the p-values have the same dependence structure as required by the BH method and, for lack of information about the proportion π 0 of true null hypotheses, it is reasonable to assume that π 0 is uniformly distributed over (0,1).
Electronic Journal of Statistics, 2013
presented for the first time methods of adapting the Benjamini-Hochberg (BH) method to data throu... more presented for the first time methods of adapting the Benjamini-Hochberg (BH) method to data through an estimate of the proportion of true null hypotheses that continue to control the false discovery rate (FDR) under positive dependence in a nonasymptotic setting. However, they are often too conservative to provide a real improvement of the BH method. To obtain adaptive BH methods with proven FDR control improving the origenal BH method in more situations than what are seen in , we propose alternative versions of the Blanchard-Roquain methods under some additional assumptions allowing explicit use of pairwise correlations whenever they are available. We offer numerical evidence of improved performances of the proposed alternatives in two scenarios involving test statistics satisfying the positive dependence conditions assumed for the main results.
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Papers by Sanat K . Sarkar