MULTIPLE MODEL EVALUATION ABSENT THE GOLD STANDARD VIA MODEL COMBINATION

We describe a method for evaluating an ensemble of predictive models given a sample of observations comprising the model predictions and the outcome event measured with error. Our formulation allows us to simultaneously estimate measurement error parameters, true outcome — aka the gold standard — and a relative weighting of the predictive scores. We describe conditions necessary to estimate the gold standard and for these estimates to be calibrated and detail how our approach is related to, but distinct from, standard model combination techniques. We apply our approach to data from a study to evaluate a collection of BRCA1/BRCA2 gene mutation prediction scores. In this example, genotype is measured with error by one or more genetic assays. We estimate true genotype for each individual in the dataset, operating characteristics of the commonly used genotyping procedures and a relative weighting of the scores. Finally, we compare the scores against the gold standard genotype and find that Mendelian scores are, on average, the more refined and better calibrated of those considered and that the comparison is sensitive to measurement error in the gold standard.

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.

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.

Estimating Multiple Tumor Transition Rates Based on Data from Survival/Sacrifice Experiments

In this paper, we focus on the model for two types of tumors. Tumor development can be described by four types of death rates and four tumor transition rates. We present a general semi-parametric model to estimate the tumor transition rates based on data from survival/sacrifice experiments. In the model, we make a proportional assumption of tumor transition rates on a common parametric function but no assumption of the death rates from any states. We derived the likelihood function of the data observed in such an experiment, and an EM algorithm that simplified estimating procedures. This article extends work on semi-parametric models for one type of tumor (see Portier and Dinse and Dinse) to two types of tumors.

Multiple Testing With an Empirical Alternative Hypothesis

An optimal multiple testing procedure is identified for linear hypotheses under the general linear model, maximizing the expected number of false null hypotheses rejected at any significance level. The optimal procedure depends on the unknown data-generating distribution, but can be consistently estimated. Drawing information together across many hypotheses, the estimated optimal procedure provides an empirical alternative hypothesis by adapting to underlying patterns of departure from the null. Proposed multiple testing procedures based on the empirical alternative are evaluated through simulations and an application to gene expression microarray data. Compared to a standard multiple testing procedure, it is not unusual for use of an empirical alternative hypothesis to increase by 50% or more the number of true positives identified at a given significance level.

MODELING DIFFERENTIATED TREATMENT EFFECTS FOR MULTIPLE OUTCOMES DATA

Multiple outcomes data are commonly used to characterize treatment effects in medical research, for instance, multiple symptoms to characterize potential remission of a psychiatric disorder. Often either a global, i.e. symptom-invariant, treatment effect is evaluated. Such a treatment effect may over generalize the effect across the outcomes. On the other hand individual treatment effects, varying across all outcomes, are complicated to interpret, and their estimation may lose precision relative to a global summary. An effective compromise to summarize the treatment effect may be through patterns of the treatment effects, i.e. "differentiated effects." In this paper we propose a two-category model to differentiate treatment effects into two groups. A model fitting algorithm and simulation study are presented, and several methods are developed to analyze heterogeneity presenting in the treatment effects. The method is illustrated using an analysis of schizophrenia symptom data.

A MULTILEVEL MODEL TO ADDRESS BATCH EFFECTS IN COPY NUMBER ESTIMATION USING SNP ARRAYS

Submicroscopic changes in chromosomal DNA copy number dosage are common and have been implicated in many heritable diseases and cancers. Recent high-throughput technologies have a resolution that permits the detection of segmental changes in DNA copy number that span thousands of basepairs across the genome. Genome-wide association studies (GWAS) may simultaneously screen for copy number-phenotype and SNP-phenotype associations as part of the analytic strategy. However, genome-wide array analyses are particularly susceptible to batch effects as the logistics of preparing DNA and processing thousands of arrays often involves multiple laboratories and technicians, or changes over calendar time to the reagents and laboratory equipment. Failure to adjust for batch effects can lead to incorrect inference and requires inefficient post-hoc quality control procedures that exclude regions that are associated with batch. Our work extends previous model-based approaches for copy number estimation by explicitly modeling batch effects and using shrinkage to improve locus-specific estimates of copy number uncertainty. Key features of this approach include the use of diallelic genotype calls from experimental data to estimate batch- and locus-specific parameters of background and signal without the requirement of training data. We illustrate these ideas using a study of bipolar disease and a study of chromosome 21 trisomy. The former has batch effects that dominate much of the observed variation in quantile-normalized intensities, while the latter illustrates the robustness of our approach to datasets where as many as 25% of the samples have altered copy number. Locus-specific estimates of copy number can be plotted on the copy-number scale to investigate mosaicism and guide the choice of appropriate downstream approaches for smoothing the copy number as a function of physical position. The software is open source and implemented in the R package CRLMM available at Bioconductor (http:www.bioconductor.org).

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.