Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions

It is of interest in some applications to determine whether there is a relationship between a hazard rate function (or a cumulative incidence function) and a mark variable which is only observed at uncensored failure times. We develop nonparametric tests for this problem when the mark variable is continuous. Tests are developed for the null hypothesis that the mark-specific hazard rate is independent of the mark versus ordered and two-sided alternatives expressed in terms of mark-specific hazard functions and mark-specific cumulative incidence functions. The test statistics are based on functionals of a bivariate test process equal to a weighted average of differences between a Nelson--Aalen-type estimator of the mark-specific cumulative hazard function and a nonparametric estimator of this function under the null hypothesis. The weight function in the test process can be chosen so that the test statistics are asymptotically distribution-free.Asymptotically correct critical values are obtained through a simple simulation procedure. The testing procedures are shown to perform well in numerical studies, and are illustrated with an AIDS clinical trial example. Specifically, the tests are used to assess if the instantaneous or absolute risk of treatment failure depends on the amount of accumulation of drug resistance mutations in a subject's HIV virus. This assessment helps guide development of anti-HIV therapies that surmount the problem of drug resistance.

TRENDS IN PARTICULATE MATTER AND MORTALITY: AN APPROACH TO THE ASSESSMENT OF UNMEASURED CONFOUNDING

We propose a method for diagnosing confounding bias under a model which links a spatially and temporally varying exposure and health outcome. We decompose the association into orthogonal components, corresponding to distinct spatial and temporal scales of variation. If the model fully controls for confounding, the exposure effect estimates should be equal at the different temporal and spatial scales. We show that the overall exposure effect estimate is a weighted average of the scale-specific exposure effect estimates. We use this approach to estimate the association between monthly averages of fine particles (PM2.5) over the preceding 12 months and monthly mortality rates in 113 U.S. counties from 2000-2002. We decompose the association between PM2.5 and mortality into two components: 1) the association between “national trends” in PM2.5 and mortality; and 2) the association between “local trends,” defined as county-specificdeviations from national trends. This second component provides evidence as to whether counties having steeper declines in PM2.5 also have steeper declines in mortality relative to their national trends. We find that the exposure effect estimates are different at these two spatio-temporalscales, which raises concerns about confounding bias. We believe that the association between trends in PM2.5 and mortality at the national scale is more likely to be confounded than is the association between trends in PM2.5 and mortality at the local scale. If the association at the national scale is set aside, there is little evidence of an association between 12-month exposure to PM2.5 and mortality.

Power and Robustness of Linkage Tests for Quantitative Traits in General Pedigrees

There are numerous statistical methods for quantitative trait linkage analysis in human studies. An ideal such method would have high power to detect genetic loci contributing to the trait, would be robust to non-normality in the phenotype distribution, would be appropriate for general pedigrees, would allow the incorporation of environmental covariates, and would be appropriate in the presence of selective sampling. We recently described a general framework for quantitative trait linkage analysis, based on generalized estimating equations, for which many current methods are special cases. This procedure is appropriate for general pedigrees and easily accommodates environmental covariates. In this paper, we use computer simulations to investigate the power robustness of a variety of linkage test statistics built upon our general framework. We also propose two novel test statistics that take account of higher moments of the phenotype distribution, in order to accommodate non-normality. These new linkage tests are shown to have high power and to be robust to non-normality. While we have not yet examined the performance of our procedures in the context of selective sampling via computer simulations, the proposed tests satisfy all of the other qualities of an ideal quantitative trait linkage analysis method.

ASSOCIATON TESTS THAT ACCOMMODATE GENOTYPING ERRORS

High-throughput SNP arrays provide estimates of genotypes for up to one million loci, often used in genome-wide association studies. While these estimates are typically very accurate, genotyping errors do occur, which can influence in particular the most extreme test statistics and p-values. Estimates for the genotype uncertainties are also available, although typically ignored. In this manuscript, we develop a framework to incorporate these genotype uncertainties in case-control studies for any genetic model. We verify that using the assumption of a “local alternative” in the score test is very reasonable for effect sizes typically seen in SNP association studies, and show that the power of the score test is simply a function of the correlation of the genotype probabilities with the true genotypes. We demonstrate that the power to detect a true association can be substantially increased for difficult to call genotypes, resulting in improved inference in association studies.