Tolerance and confidence limits for classes of distributions based on failure rate

Tolerance and confidence limits for classes of distributions based on failure rate

Estimation of Conditional Power for Cluster-Randomized Trials with Interval-Censored Endpoints

Cluster-randomized trials (CRTs) of infectious disease preventions often yield correlated, interval-censored data: dependencies may exist between observations from the same cluster, and event occurrence may be assessed only at intermittent clinic visits. This data structure must be accounted for when conducting interim monitoring and futility assessment for CRTs. In this article, we propose a flexible framework for conditional power estimation when outcomes are correlated and interval-censored. Under the assumption that the survival times follow a shared frailty model, we first characterize the correspondence between the marginal and cluster-conditional survival functions, and then use this relationship to semiparametrically estimate the cluster-specific survival distributions from the available interim data. We incorporate assumptions about changes to the event process over the remainder of the trial---as well as estimates of the dependency among observations in the same cluster---to extend these survival curves through the end of the study. Based on these projected survival functions we generate correlated interval-censored observations, and then calculate the conditional power as the proportion of times (across multiple full-data generation steps) that the null hypothesis of no treatment effect is rejected. We evaluate the performance of the proposed method through extensive simulation studies, and illustrate its use on a large cluster-randomized HIV prevention trial

A partial ordering of rank densities

AbstractA function f(π) on the set of permutations of {1, 2, …, n} is called arrangement increasing (AI) if it increases each time we transpose a pair of coordinates in descending order, i < j and πi > πj, putting them in ascending order. We define and develop a partial ordering ≤AI on densities of rank vectors in terms of expectations of AI functions. Specially, one density g is defined to be AI-larger than another density f(f≤AI g) if the expectation under g of any AI function is at least as large as its expectation under f. We show that the uniform density is the AI-smallest AI density, and this leads to power results for tests of agreement of two rank vectors. The extreme points of the convex set of AI densities are determined, from which additional results concerning the minimum power of rank tests are shown to follow. We also give applications to ranking and selection problems

A Generalization of the Exponential-Poisson Distribution

The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new distribution can be decreasing or increasing. The failure rate can also be upside-down bathtub shaped. A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival and failure rate functions; we also obtain the density of the $i$th order statistic. We derive the $r$th raw moment of the new distribution and also the moments of order statistics. Moreover, we discuss estimation by maximum likelihood and obtain an expression for Fisher's information matrix. Furthermore, expressions for the R\'enyi and Shannon entropies are given and estimation of the stress-strength parameter is discussed. Applications using two real data sets are presented

Statistical Estimation Procedures for the ''burn-in'' Process

Statistical estimation procedures for identifying and eliminating poor quality or defective item

Recommendations on multiple testing adjustment in multi-arm trials with a shared control group

Multi-arm clinical trials assessing multiple experimental treatments against a shared control group can offer efficiency advantages over independent trials through assessing an increased number of hypotheses. Published opinion is divided on the requirement for multiple testing adjustment to control the family-wise type-I error rate (FWER). The probability of a false positive error in multi-arm trials compared to equivalent independent trials is affected by the correlation between comparisons due to sharing control data. We demonstrate that this correlation in fact leads to a reduction in the FWER, therefore FWER adjustment is not recommended solely due to sharing control data. In contrast, the correlation increases the probability of multiple false positive outcomes across the hypotheses, although standard FWER adjustment methods do not control for this. A stringent critical value adjustment is proposed to maintain equivalent evidence of superiority in two correlated comparisons to that obtained within independent trials. FWER adjustment is only required if there is an increased chance of making a single claim of effectiveness by testing multiple hypotheses, not due to sharing control data. For competing experimental therapies, the correlation between comparisons can be advantageous as it eliminates bias due to the experimental therapies being compared to different control populations

On the Decreasing Failure Rate property for general counting process. Results based on conditional interarrival times

In the present paper we consider general counting processes stopped at a random time $T$, independent of the process. Provided that $T$ has the decreasing failure rate (DFR) property, we give sufficient conditions on the arrival times so that the number of events occurring before $T$ preserves the DFR property of $T$. These conditions involve the study of the conditional interarrival times. As a main application, we prove the DFR property in a context of maintenance models in reliability, by the consideration of Kijima type I virtual age models under quite general assumptions