Inference on the bivariate L1 median with censored data

Consider two random variables subject to random right censoring, like the time to two different diseases for individuals under study or the survival times of twins. Of interest is the bivariate median of these two random variables. There are various ways that the univariate median has been extended to higher dimensions for completely observed data. We concentrate on the so-called bivariate L1 median and extend this estimator to the censored data situation. The estimator is based on van der Laan (1996)'s estimator of the bivariate distribution of two random variables that are subject to censoring. Asymptotic results for the proposed estimator are established. The obtained results include the asymptotic normality of the estimator, its local power and the construction of a confidence region for the true median. Finally, we consider a data set on kidney dialysis patients and estimate the median time to two different infections for these individuals

Robust correlation analyses: false positive and power validation using a new open source Matlab toolbox

Pearson’s correlation measures the strength of the association between two variables. The technique is, however, restricted to linear associations and is overly sensitive to outliers. Indeed, a single outlier can result in a highly inaccurate summary of the data. Yet, it remains the most commonly used measure of association in psychology research. Here we describe a free Matlab(R) based toolbox (http://sourceforge.net/projects/robustcorrtool/) that computes robust measures of association between two or more random variables: the percentage-bend correlation and skipped-correlations. After illustrating how to use the toolbox, we show that robust methods, where outliers are down weighted or removed and accounted for in significance testing, provide better estimates of the true association with accurate false positive control and without loss of power. The different correlation methods were tested with normal data and normal data contaminated with marginal or bivariate outliers. We report estimates of effect size, false positive rate and power, and advise on which technique to use depending on the data at hand

Authorized Generic Entry prior to Patent Expiry: Reassessing Incentives for Independent Generic Entry

Patent holders frequently attempt to mitigate the loss of monopoly power by authorizing generic entry prior to patent expiry (early entry). Competition in off-patent pharmaceutical markets may be adversely affected if early entry substantially impairs the attractiveness of subsequent market entry. I examine generic entry decisions made in the course of recent patent expiries to quantify the impact of early entry on incentives for generic entry. Using unique micro data and accounting for the endogeneity of early entry, I estimate recursive bivariate probit models of entry. Drug markets' pre-entry revenues largely determine both independent generic entry and early entry decisions. Early entry in turn has no significant impact on the likelihood of generic entry. Original drug producers appear to authorize generic entry prior to loss of exclusivity primarily fueled by rent-seeking rather than strategic entry-deterrence motives

Nonparametric inference procedure for percentiles of the random effects distribution in meta-analysis

To investigate whether treating cancer patients with erythropoiesis-stimulating agents (ESAs) would increase the mortality risk, Bennett et al. [Journal of the American Medical Association 299 (2008) 914--924] conducted a meta-analysis with the data from 52 phase III trials comparing ESAs with placebo or standard of care. With a standard parametric random effects modeling approach, the study concluded that ESA administration was significantly associated with increased average mortality risk. In this article we present a simple nonparametric inference procedure for the distribution of the random effects. We re-analyzed the ESA mortality data with the new method. Our results about the center of the random effects distribution were markedly different from those reported by Bennett et al. Moreover, our procedure, which estimates the distribution of the random effects, as opposed to just a simple population average, suggests that the ESA may be beneficial to mortality for approximately a quarter of the study populations. This new meta-analysis technique can be implemented with study-level summary statistics. In contrast to existing methods for parametric random effects models, the validity of our proposal does not require the number of studies involved to be large. From the results of an extensive numerical study, we find that the new procedure performs well even with moderate individual study sample sizes.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS280 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org