Jyoti N. Zalkikar

A Likelihood Ratio Test Based Method for Signal Detection With Application to FDA’s Drug Safety Data

Several statistical methods that are available in the literature to analyze postmarket safety databases, such as the U.S. Federal Drug Administration’s (FDA) adverse event reporting system (AERS), for identifying drug-event combinations with disproportionately high frequencies, are subject to high false discovery rates. Here, we propose a likelihood ratio test (LRT) based method and show, via an extensive simulation study, that the proposed method while retaining good power and sensitivity for identifying signals, controls both the Type I error and false discovery rates. The application of the LRT method to the AERS database is illustrated using two datasets; a small dataset consisting of suicidal behavior and mood change-related AE cases for the drug Montelukast, and a large dataset consisting of all possible AE cases reported to FDA during 2004–2008 for the drug Heparin. This article has supplementary material online.

Bayes estimation for the Pareto failure-model using Gibbs sampling

Bayes estimation of the parameters and the reliability function based on type-1 and type-2 censored samples from a Pareto failure model is considered. The analysis is extended to situations wherein the exact survival times are not available but only the number of deaths in prescribed time intervals is recorded. Bayes calculations can be implemented easily by means of the Gibbs Sampler.

A Bayesian Approach for Benefit-Risk Assessment

An important aspect of the drug evaluation process is to have an integrated benefit-risk assessment to determine, using some quantitative measures, whether the benefit outweighs the risk for the target population. Chuang-Stein et al. proposed a five-category random variable along with three global measures of benefit-risk assessment. Assuming the cell probabilities follow a multinomial distribution, we propose a Bayesian approach for the longitudinal assessment of benefit-risk using these three global measures and a new measure. A Dirichlet distribution is used as the natural conjugate prior for multinomial cell probabilities, and the posterior distributions of cell-probabilities are recursively derived as the data from multiple visits become available. In a more generalized approach, a power prior is used through the likelihood function to discount the information from previous visits, and, again, the posterior distributions of the cell-probabilities at multiple visits are derived. The estimates of the posterior means and credible intervals for the four global measures are derived, and the decision rules based on the credible intervals are applied for the assessment of the four global measures. Using two simulated datasets generated under two different scenarios—one where benefit outweighs risk and the other where benefit does not outweigh risk—the performances of the four measures are evaluated using a Markov chain Monte Carlo (MCMC) technique. We illustrate of the methodology using clinical trial data.

Hierarchical Bayes estimation for the exponential-multinomial model in reliability and competing risks

The exponential-multinomial distribution arises from: (1) observing the system failure of a series system with p components having independent exponential lifetimes, or (2) a competing-risks model with p sources of failure, as well as (3) the Marshall-Olkin multivariate exponential distribution under a series sampling scheme. Hierarchical Bayes (HB) estimators of the component sub-survival function and the system reliability are obtained using the Gibbs sampler. A large-sample approximation of the posterior pdf is used to derive the HB estimators of the parameters of the model with respect to the quadratic loss function. The exact risk of the HE estimator is obtained and is compared with those corresponding to some other estimators such as Bayes, maximum likelihood, and minimum variance unbiased estimators.

Bayes and empirical bayes estimation of the probability that z > x + y

Let X, Y and Z be independent random variables with common unknown distribution F. Using the Dirichlet process prior for F and squared erro loss function, the Bayes and empirical Bayes estimators of the parameters λ(F). the probability that Z > X + Y, are derived. The limiting Bayes estimator of λ(F) under some conditions on the parameter of the process is shown to be asymptotically normal. The aysmptotic optimality of the empirical Bayes estimator of λ(F) is established. When X, Y and Z have support on the positive real line, these results are derived for randomly right censored data. This problem relates to testing whether than used discussed by Hollander and Proshcan (1972) and Chen, Hollander and Langberg (1983).

Testing whether F is “more IFRA than is G”

Abstract For testing the null hypothesis that two life distributions F and G are equal versus the alternative hypothesis that F is more increasing failure rate average than is G, a class of tests is proposed. The properties of tests in this class such as unbiasedness, consistency and asymptotic normality are established. Monte Carlo estimates of power are obtained for small sample sizes. The asymptotic relative efficiency of tests in the class with respect to Hollander, Park and Proschans (1986) test is shown to be reasonably high.

A new measure of ifra-ness and its application to two sample test

A continuous life distribution function f with f(x)=0 for x ≶ is said to be increasing failure rate average (IFRA) if and only if and all x For testing the null hypothesis that f is an exponentia distribution versus the alternative hypothesis that f is a nonexponential IFRA distribution DESHPANDE [BIometrika 70 (1983): 514:518] proposed a class of testing which depends on b the choice of b has been crucial since than In this paper we propose a new measure of IFRA ness that is independent of b and we use it to test whether one destribution is more IFRA than other. The Properties of the test such as unbiasedness, consistency and asymptotic normality are dscussed.Monte Carolo estimates of power are obtained for small sample sizes. Large sample performance is measured in terms of Asymptotic relative efficiency with respect to Tiwri and ZALKIAr,s (1988) test.

Empirical Bayes Estimation of Certain Estimable Parameters of Degree Two

Using empirical Bayes framework of Korwar and Hollander (1976), a sequence of empirical Bayes estimators is defined for estimating certain estimable parameters of degree two. Asymptotic optimality of the sequence relative to Ferguson Dirichlet process prior is established. Exact risk expressiona are derived.

A class of Large Sample Tests for Bivariate Exponentiality Versus Bifra and Bnbu (to, to) Alternatives

Two related problems are considered here. First, a class of tosts is proposed for testing bivariate exponentiality (BVE) against the class of bivariate increasing failure rate average (IFRA) distributions. Secondly, we propose a test of BVE versus bivariate new better than used of ago (to to)),a new class of bivariate distributions introduced here. The PITMAN asymptotic relative efficiencies of these tests with respect to BASU and EBRAHIMIs (1984) bivariate new better than used (BNBU) test, compared