MULTIPLE DISEASES IN CARRIER PROBABILITY ESTIMATION: ACCOUNTING FOR SURVIVING ALL CANCERS OTHER THAN BREAST AND OVARY IN BRCAPRO

Mendelian models can predict who carries an inherited deleterious mutation of known disease genes based on family history. For example, the BRCAPRO model is commonly used to identify families who carry mutations of BRCA1 and BRCA2, based on familial breast and ovarian cancers. These models incorporate the age of diagnosis of diseases in relatives and current age or age of death. We develop a rigorous foundation for handling multiple diseases with censoring. We prove that any disease unrelated to mutations can be excluded from the model, unless it is sufficiently common and dependent on a mutation-related disease time. Furthermore, if a family member has a disease with higher probability density among mutation carriers, but the model does not account for it, then the carrier probability is deflated. However, even if a family only has diseases the model accounts for, if the model excludes a mutation-related disease, then the carrier probability will be inflated. In light of these results, we extend BRCAPRO to account for surviving all non-breast/ovary cancers as a single outcome. The extension also enables BRCAPRO to extract more useful information from male relatives. Using 1500 familes from the Cancer Genetics Network, accounting for surviving other cancers improves BRCAPRO’s concordance index from 0.758 to 0.762 (p = 0.046), improves its positive predictive value from 35% to 39% (p < 10−6) without impacting its negative predictive value, and improves its overall calibration, although calibration slightly worsens for those with carrier probability < 10%. Copyright c 2000 John Wiley & Sons, Ltd.

THE ROLE OF AN EXPLICIT CAUSAL FRAMEWORK IN AFFECTED SIB PAIR DESIGNS WITH COVARIATES

The affected sib/relative pair (ASP/ARP) design is often used with covariates to find genes that can cause a disease in pathways other than through those covariates. However, such "covariates" can themselves have genetic determinants, and the validity of existing methods has so far only been argued under implicit assumptions. We propose an explicit causal formulation of the problem using potential outcomes and principal stratification. The general role of this formulation is to identify and separate the meaning of the different assumptions that can provide valid causal inference in linkage analysis. This separation helps to (a) develop better methods under explicit assumptions, and (b) show the different ways in which these assumptions can fail, which is necessary for developing further specific designs to test these assumptions and confirm or improve the inference. Using this formulation in the specific problem above, we show that, when the "covariate" (e.g., addiction to smoking) also has genetic determinants, then existing methods, including those previously thought as valid, can declare linkage between the disease and marker loci even when no such linkage exists. We also introduce design strategies to address the problem.

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.

Inequity Measures for Evaluations of Environmental Justice: A Case Study of Close Proximity to Highways in NYC

Assessments of environmental and territorial justice are similar in that both assess whether empirical relations between the spatial arrangement of undesirable hazards (or desirable public goods and services) and socio-demographic groups are consistent with notions of social justice, evaluating the spatial distribution of benefits and burdens (outcome equity) and the process that produces observed differences (process equity. Using proximity to major highways in NYC as a case study, we review methodological issues pertinent to both fields and discuss choice and computation of exposure measures, but focus primarily on measures of inequity. We present inequity measures computed from the empirically estimated joint distribution of exposure and demographics and compare them to traditional measures such as linear regression, logistic regression and Theil’s entropy index. We find that measures computed from the full joint distribution provide more unified, transparent and intuitive operational definitions of inequity and show how the approach can be used to structure siting and decommissioning decisions.

The National Morbidity, Mortality, and Air Pollution Study Database in R

The NMMAPS data package contains daily mortality, air pollution, and weather data originally assembled as part of the National Morbidity,Mortality, and Air Pollution Study (NMMAPS). The data have recently been updated and are available for 108 United States cities for the years 1987--2000. The package provides tools for building versions of the full database in a structured and reproducible manner. These database derivatives may be more suitable for particular analyses. We describe how to use the package to implement a multi-city time series analysis of mortality and PM(10). In addition we demonstrate how to reproduce recent findings based on the NMMAPS data.

Estimating the Number of Essential Genes in a Genome by Random Transposon Mutagenesis

We describe a Bayesian method for estimating the number of essential genes in a genome, on the basis of data on viable mutants for which a single transposon was inserted after a random TA site in a genome,potentially disrupting a gene. The prior distribution for the number of essential genes was taken to be uniform. A Gibbs sampler was used to estimate the posterior distribution. The method is illustrated with simulated data. Further simulations were used to study the performance of the procedure.

TRIO LOGIC REGRESSION - DETECTION OF SNP - SNP INTERACTIONS IN CASE-PARENT TRIOS

Statistical approaches to evaluate higher order SNP-SNP and SNP-environment interactions are critical in genetic association studies, as susceptibility to complex disease is likely to be related to the interaction of multiple SNPs and environmental factors. Logic regression (Kooperberg et al., 2001; Ruczinski et al., 2003) is one such approach, where interactions between SNPs and environmental variables are assessed in a regression framework, and interactions become part of the model search space. In this manuscript we extend the logic regression methodology, originally developed for cohort and case-control studies, for studies of trios with affected probands. Trio logic regression accounts for the linkage disequilibrium (LD) structure in the genotype data, and accommodates missing genotypes via haplotype-based imputation. We also derive an efficient algorithm to simulate case-parent trios where genetic risk is determined via epistatic interactions.

Concordance Probability and Discriminatory Power in Proportional Hazards Regression

The concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models. We derive an analytic expression for the concordance probability in the Cox proportional hazards model. The proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times. For this reason it is asymptotically unbiased, unlike Harrell's c-index based on informative pairs. The asymptotic distribution of the concordance probability estimate is derived using U-statistic theory and the methodology is applied to a predictive model in lung cancer.

Sequential Quantitative Trait Locus Mapping in Experimental Crosses

The etiology of complex diseases is heterogeneous. The presence of risk alleles in one or more genetic loci affects the function of a variety of intermediate biological pathways, resulting in the overt expression of disease. Hence, there is an increasing focus on identifying the genetic basis of disease by sytematically studying phenotypic traits pertaining to the underlying biological functions. In this paper we focus on identifying genetic loci linked to quantitative phenotypic traits in experimental crosses. Such genetic mapping methods often use a one stage design by genotyping all the markers of interest on the available subjects. A genome scan based on single locus or multi-locus models is used to identify the putative loci. Since the number of quantitative trait loci (QTLs) is very likely to be small relative to the number of markers genotyped, a one-stage selective genotyping approach is commonly used to reduce the genotyping burden, whereby markers are genotyped solely on individuals with extreme trait values. This approach is powerful in the presence of a single quantitative trait locus (QTL) but may result in substantial loss of information in the presence of multiple QTLs. Here we investigate the efficiency of sequential two stage designs to identify QTLs in experimental populations. Our investigations for backcross and F2 crosses suggest that genotyping all the markers on 60% of the subjects in Stage 1 and genotyping the chromosomes significant at 20% level using additional subjects in Stage 2 and testing using all the subjects provides an efficient approach to identify the QTLs and utilizes only 70% of the genotyping burden relative to a one stage design, regardless of the heritability and genotyping density. Complex traits are a consequence of multiple QTLs conferring main effects as well as epistatic interactions. We propose a two-stage analytic approach where a single-locus genome scan is conducted in Stage 1 to identify promising chromosomes, and interactions are examined using the loci on these chromosomes in Stage 2. We examine settings under which the two-stage analytic approach provides sufficient power to detect the putative QTLs.

A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

This paper presents a fully Bayesian approach that simultaneously combines basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, sub-system or system failure events. The full Bayesian approach also allows the highest-level data that are usually available for existing facilities to be automatically propagated to lower levels. A simple example illustrates the proposed approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.

Classification and selection of biomarkers in genomic data using LASSO

High-throughput gene expression technologies such as microarrays have been utilized in a variety of scientific applications. Most of the work has been on assessing univariate associations between gene expression with clinical outcome (variable selection) or on developing classification procedures with gene expression data (supervised learning). We consider a hybrid variable selection/classification approach that is based on linear combinations of the gene expression profiles that maximize an accuracy measure summarized using the receiver operating characteristic curve. Under a specific probability model, this leads to consideration of linear discriminant functions. We incorporate an automated variable selection approach using LASSO. An equivalence between LASSO estimation with support vector machines allows for model fitting using standard software. We apply the proposed method to simulated data as well as data from a recently published prostate cancer study.

Performance of the Halex in Logitudinal Studies of Older Adults

Goal: The Halex is an indicator of health status that combines self-rated health and activity limitations, which has been used by NCHS to predict future years of healthy life. The scores for each health state were developed based on strong assumptions, notably that a person in excellent health with ADL disabilities is as healthy as a person in poor health with no disabilities. Our goal was to examine the performance of the Halex as a longitudinal measure of health for older adults, and to improve the scoring if necessary. Methods: We used data from the Cardiovascular Health Study (CHS) to compare the relationship of baseline health to health 2 years later. Subject ages ranged from 65 to 103 (mean age 75). A total of 40,827 transitions were available for analysis. We examined whether Halex scores at time 0 were related monotonically to scores two years later, and iterated the original scores to improve the fit over time. Findings: The original Halex scores were not consistent over time. Persons in excellent health with ADL limitations were much healthier 2 years later than people in poor health with no limitations, even though they had been assumed to have identical health. People with ADL limitations had higher scores than predicted. The assumptions made in creating the Halex were not upheld in the data. Conclusions: The new iterated scores are specific to older adults, are appropriate for longitudinal data, and are relatively assumption-free. We recommend the use of these new scores for longitudinal studies of older adults that use the Halex health states.

Modeling Breastmilk Infectivity in HIV-1 Infected Mothers

Estimation of breastmilk infectivity in HIV-1 infected mothers is difficult because transmission can occur while the fetus is in-utero, during delivery, or through breastfeeding. Since transmission can only be detected through periodic testing, however, it may be impossible to determine the actual mode of transmission in any individual child. In this paper we develop a model to estimate breastmilk infectivity as well as the probabilities of in-utero and intrapartum transmission. In addition, the model allows separate estimation of early and late breastmilk infectivity and individual variation in maternal infectivity. Methods for hypothesis testing of binary risk factors and a method for assessing goodness of fit are also described. Data from a randomized trial of breastfeeding versus formula feeding among HIV-1 infected mothers in Nairobi, Kenya are used to illustrate the methods.

Selection of Matching Variables in Community Health Intervention Trials

In a matched experimental design, the effectiveness of matching in reducing bias and increasing power depends on the strength of the association between the matching variable and the outcome of interest. In particular, in the design of a community health intervention trial, the effectiveness of a matched design, where communities are matched according to some community characteristic, depends on the strength of the correlation between the matching characteristic and the change in the health behavior being measured. We attempt to estimate the correlation between community characteristics and changes in health behaviors in four datasets from community intervention trials and observational studies. Community characteristics that are highly correlated with changes in health behaviors would potentially be effective matching variables in studies of health intervention programs designed to change those behaviors. Among the community characteristics considered, the urban-rural character of the community was the most highly correlated with changes in health behaviors. The correlations between Per Capita Income, Percent Low Income & Percent aged over 65 and changes in health behaviors were marginally statistically significant (p < 0.08).