S. Stanley Young

Testing association of statistically inferred haplotypes with discrete and continuous traits in samples of unrelated individuals.

There have been increasing efforts to relate drug efficacy and disease predisposition with genetic polymorphisms. We present statistical tests for association of haplotype frequencies with discrete and continuous traits in samples of unrelated individuals. Haplotype frequencies are estimated through the expectation-maximization algorithm, and each individual in the sample is expanded into all possible haplotype configurations with corresponding probabilities, conditional on their genotype. A regression-based approach is then used to relate inferred haplotype probabilities to the response. The relationship of this technique to commonly used approaches developed for case-control data is discussed. We confirm the proper size of the test under H₀ and find an increase in power under the alternative by comparing test results using inferred haplotypes with single-marker tests using simulated data. More importantly, analysis of real data comprised of a dense map of single nucleotide polymorphisms spaced along a 12-cM chromosomal region allows us to confirm the utility of the haplotype approach as well as the validity and usefulness of the proposed statistical technique. The method appears to be successful in relating data from multiple, correlated markers to response.

p Value Adjustments for Multiple Tests in Multivariate Binomial Models

Abstract Data from rodent carcinogenicity (preclinical) and clinical studies involving new drugs may be modeled as having come from multivariate binomial distributions. In two-year rodent carcinogenicity studies, there are typically 20–50 tissues examined for occurrence of any of several possible lesions. For a particular treatment group, the number of occurrences of a particular lesion at a particular tissue may be modeled as binomial, and the vector of such frequencies may be considered multivariate binomial with unspecified dependence structure. The same model may also apply to clinical side-effects data; in this case the marginal frequencies may represent occurrences of events ranging from headaches to ingrown toenails. Frequently, the goal of such studies is to isolate site-specific significant differences between treatment and control groups. For example, in rodent carcinogenicity analyses it is generally not sufficient to claim that a new compound causes an increase in tumors at some unspecified si...

Multiple tests for genetic effects in association studies.

1. Introduction Many common human diseases have a genetic component as measured by familial studies. Metabolic disorders such as diabetes, cardiovascular diseases such as high blood pressure, psychiatric disorders such as schizophrenia, and neurodegenerative diseases such as Alzheimers disease all are thought to have a hereditary component. In some diseases the genetic control is through a single gene, while in others, multiple genes interact in complex ways with environmental factors to produce the disease (1 – 5). Data are and will become increasingly available to attempt to link genes to disease phenotype(s). Linkage studies, although powerful for screening relatively large chromosomal regions, lack needed precision because of the constraints imposed by the number of recombination events during generations contained in the pedigree (6). Recently, researchers have attempted to develop techniques that exploit possibilities of fine mapping due to linkage disequilibrium between genetic markers and disease genes. Typing single nucleotide polymorphism markers (SNPs) inside of candidate regions provides a potential means for such analysis (7); however, the problem remains in that the complex diseases are very likely to have multiple etiologies. Consider control of essential hypertension. It has a measured heritability of 3 45%, yet the identification of specific genes remains unclear. Many candidate genes for essential hypertension have been identified and, in a particular individual, a combination of some few of these genes might lead to disease. There is a need for a statistical strategy to analyze these complex experiments, given the multiple testing implied by multiple candidate genes and the risk of false associations. In this chapter we discuss primarily methods for controlling

Using prior information to allocate significance levels for multiple endpoints

We maximize power in a replicated clinical trial involving multiple endpoints by adjusting the individual significance levels for each hypothesis, using preliminary data to obtain the optimal adjustments. The levels are constrained to control the familywise error rate. Power is defined as the expected number of significances, where expectations are taken with respect to the posterior distributions of the non-centrality parameters under non-informative priors. Sample size requirements for the replicate study are given. Intuitive principles such as downweighting insignificant variables from a preliminary study and giving primary endpoints more emphasis are justifiable within the conceptual framework.

Large recursive partitioning analysis of complex disease pharmacogenetic studies. II. Statistical considerations

Identifying genetic variations predictive of important phenotypes, such as disease susceptibility, drug efficacy, and adverse events, remains a challenging task. There are individual polymorphisms that can be tested one at a time, but there is the more difficult problem of the identification of combinations of polymorphisms or even more complex interactions of genes with environmental factors. Diseases, drug responses or side effects can result from different mechanisms. Identification of subgroups of people where there is a common mechanism is a problem for diagnosis and prescribing of treatment. Recursive partitioning (RP) is a simple statistical tool for segmenting a population into non-overlapping groups where the response of interest, disease susceptibility, drug efficacy and adverse events are more homogeneous within the segments. We suggest that the use of RP is not only more technically feasible than other search methods but it is less susceptible to multiple-testing problems. The numbers of combinations of gene-gene and gene-environment interactions is potentially astronomical and RP greatly reduces the effective search and inference space. Moreover, the certain reliance of RP on the presence of marginal effects is justifiable as was found by using analytical and numerical arguments. In the context of haplotype analysis, results suggest that the analysis of individual SNPs is likely to be successful even when susceptibilities are determined by haplotypes. Retrospective clinical studies where cases and controls are collected will be a common design. This report provides methods that can be used to adjust the RP analysis to reflect the population incidence of the response of interest. Confidence limits on the incidence of the response in the segmented subgroups are also discussed. RP is a straightforward way to create realistic subgroups, and prediction intervals for the within-subgroup disease incidence are easily obtained.

PM 2.5 and ozone, indicators of air quality, and acute deaths in California, 2004–2007

ABSTRACT Since the London Great Smog of 1952 was estimated to have killed over 4000 people, scientists have studied the relationship between air quality and acute mortality. Currently, the association between air quality and acute deaths is usually taken as evidence for causality. As air quality has markedly improved since 1952, do contemporary datasets support this view? We use a large dataset, eight air basins in California for the years 2004–2007, to examine the possible association of ozone and PM2.5 with acute deaths after statistically removing seasonal and weather effects. Our analysis dataset is available on request. We conducted a regression‐corrected, case‐crossover analysis for all non‐accidental deaths age 75 and older. We used stepwise regression to examine three causes of death. After seasonal and weather adjustments, there was essentially no predictive power of ozone or PM2.5 for acute deaths. The case‐crossover analysis produced odds ratio very close to 1.000 (no effect). The very narrow confidence limits indicated good statistical power. We study recent air quality in both time‐stratified, symmetric, bidirectional case‐crossover and time series regression and both give consistent results. There is no statistically significant association between either ozone or PM2.5 and acute human mortality. In the absence of an association, causality is in question. HIGHLIGHTSCalifornia air quality and daily deaths are analyzed, 2004–2007.Two methods of analysis are used: Time series regression and Case‐crossover.No association of acute deaths with levels of PM2.5 or ozone is found.The data set and analysis code is available.With no association, causation is called into question for California.

Time series smoother for effect detection

In environmental epidemiology, it is often encountered that multiple time series data with a long-term trend, including seasonality, cannot be fully adjusted by the observed covariates. The long-term trend is difficult to separate from abnormal short-term signals of interest. This paper addresses how to estimate the long-term trend in order to recover short-term signals. Our case study demonstrates that the current spline smoothing methods can result in significant positive and negative cross-correlations from the same dataset, depending on how the smoothing parameters are chosen. To circumvent this dilemma, three classes of time series smoothers are proposed to detrend time series data. These smoothers do not require fine tuning of parameters and can be applied to recover short-term signals. The properties of these smoothers are shown with both a case study using a factorial design and a simulation study using datasets generated from the original dataset. General guidelines are provided on how to discover short-term signals from time series with a long-term trend. The benefit of this research is that a problem is identified and characteristics of possible solutions are determined.

Resampling-Based Multiple Testing: Examples and Methods for p-Value Adjustment.

Resampling-Based Adjustments: Basic Concepts. Continuous Data Applications: Univariate Analysis. Continuous Data Applications: Multivariate Analysis. Binary Data Applications. Further Topics. Practical Applications. Appendices. References. List of Algorithms. List of Examples. Indexes.