Biostatistics - current issue

Estimation and inference for case-control studies with multiple non-gold standard exposure assessments: with an occupational health application

Chu, H., Cole, S. R., Wei, Y., Ibrahim, J. G. — Fri, 11 Sep 2009 10:58:58 PDT

In occupational case–control studies, work-related exposure assessments are often fallible measures of the true underlying exposure. In lieu of a gold standard, often more than 2 imperfect measurements (e.g. triads) are used to assess exposure. While methods exist to assess the diagnostic accuracy in the absence of a gold standard, these methods are infrequently used to correct for measurement error in exposure–disease associations in occupational case–control studies. Here, we present a likelihood-based approach that (a) provides evidence regarding whether the misclassification of tests is differential or nondifferential; (b) provides evidence whether the misclassification of tests is independent or dependent conditional on latent exposure status, and (c) estimates the measurement error–corrected exposure–disease association. These approaches use information from all imperfect assessments simultaneously in a unified manner, which in turn can provide a more accurate estimate of exposure–disease association than that based on individual assessments. The performance of this method is investigated through simulation studies and applied to the National Occupational Hazard Survey, a case–control study assessing the association between asbestos exposure and mesothelioma.

A novel approach to cancer staging: application to esophageal cancer

Ishwaran, H., Blackstone, E. H., Apperson-Hansen, C., Rice, T. W. — Fri, 11 Sep 2009 10:58:58 PDT

A novel 3-step random forests methodology involving survival data (survival forests), ordinal data (multiclass forests), and continuous data (regression forests) is introduced for cancer staging. The methodology is illustrated for esophageal cancer using worldwide esophageal cancer collaboration data involving 4627 patients.

Variable selection and dependency networks for genomewide data

Dobra, A. — Fri, 11 Sep 2009 10:58:58 PDT

We describe a new stochastic search algorithm for linear regression models called the bounded mode stochastic search (BMSS). We make use of BMSS to perform variable selection and classification as well as to construct sparse dependency networks. Furthermore, we show how to determine genetic networks from genomewide data that involve any combination of continuous and discrete variables. We illustrate our methodology with several real-world data sets.

A semiparametric 2-part mixed-effects heteroscedastic transformation model for correlated right-skewed semicontinuous data

Lin, H., Zhou, X.-H. — Fri, 11 Sep 2009 10:58:58 PDT

In longitudinal or hierarchical structure studies, we often encounter a semicontinuous variable that has a certain proportion of a single value and a continuous and skewed distribution among the rest of values. In this paper, we propose a new semiparametric 2-part mixed-effects transformation model to fit correlated skewed semicontinuous data. In our model, we allow the transformation to be nonparametric. Fitting the proposed model faces computational challenges due to intractable numerical integrations. We derive the estimates for the parameter and the transformation function based on an approximate likelihood, which has high-order accuracy but less computational burden. We also propose an estimator for the expected value of the semicontinuous outcome on the original scale. Finally, we apply the proposed methods to a clinical study on effectiveness of a collaborative care treatment on late-life depression on health care costs.

Rank-based estimation in the {ell}1-regularized partly linear model for censored outcomes with application to integrated analyses of clinical predictors and gene expression data

Johnson, B. A. — Fri, 11 Sep 2009 10:58:58 PDT

We consider estimation and variable selection in the partial linear model for censored data. The partial linear model for censored data is a direct extension of the accelerated failure time model, the latter of which is a very important alternative model to the proportional hazards model. We extend rank-based lasso-type estimators to a model that may contain nonlinear effects. Variable selection in such partial linear model has direct application to high-dimensional survival analyses that attempt to adjust for clinical predictors. In the microarray setting, previous methods can adjust for other clinical predictors by assuming that clinical and gene expression data enter the model linearly in the same fashion. Here, we select important variables after adjusting for prognostic clinical variables but the clinical effects are assumed nonlinear. Our estimator is based on stratification and can be extended naturally to account for multiple nonlinear effects. We illustrate the utility of our method through simulation studies and application to the Wisconsin prognostic breast cancer data set.

Identifying temporally differentially expressed genes through functional principal components analysis

Liu, X., Yang, M. C. K. — Fri, 11 Sep 2009 10:58:58 PDT

Time course gene microarray is an important tool to identify genes with differential expressions over time. Traditional analysis of variance (ANOVA) type of longitudinal investigation may not be applicable because of irregular time intervals and possible missingness due to contamination in microarray experiments. Functional principal components analysis is proposed to test hypotheses in the change of the mean curves. A permutation test under a mild assumption is used to make the method more robust. The proposed method outperforms the recently developed extraction of differential gene expression and a 2-way mixed effects ANOVA under reasonable gene expression models in simulation. Real data on transcriptional profiles of blood cells microarray from treated and untreated individuals were used to illustrate this method.

SHARE: an adaptive algorithm to select the most informative set of SNPs for candidate genetic association

Dai, J. Y., Leblanc, M., Smith, N. L., Psaty, B., Kooperberg, C. — Fri, 11 Sep 2009 10:58:58 PDT

Association studies have been widely used to identify genetic liability variants for complex diseases. While scanning the chromosomal region 1 single nucleotide polymorphism (SNP) at a time may not fully explore linkage disequilibrium, haplotype analyses tend to require a fairly large number of parameters, thus potentially losing power. Clustering algorithms, such as the cladistic approach, have been proposed to reduce the dimensionality, yet they have important limitations. We propose a SNP-Haplotype Adaptive REgression (SHARE) algorithm that seeks the most informative set of SNPs for genetic association in a targeted candidate region by growing and shrinking haplotypes with 1 more or less SNP in a stepwise fashion, and comparing prediction errors of different models via cross-validation. Depending on the evolutionary history of the disease mutations and the markers, this set may contain a single SNP or several SNPs that lay a foundation for haplotype analyses. Haplotype phase ambiguity is effectively accounted for by treating haplotype reconstruction as a part of the learning procedure. Simulations and a data application show that our method has improved power over existing methodologies and that the results are informative in the search for disease-causal loci.

Sample size calculations for controlling the distribution of false discovery proportion in microarray experiments

Oura, T., Matsui, S., Kawakami, K. — Fri, 11 Sep 2009 10:58:58 PDT

The false discovery proportion (FDP), the proportion of false rejections among all rejections, provides useful criteria for controlling false positives in multiple testing to detect differential genes in microarray experiments. Owing to a substantial variability in FDP for correlated genes, some authors considered controlling actual FDP, instead of its expectation, that is false discovery rate, in multiple testing. However, there has been no attempt to do this in the design of microarray experiments. In this article, we develop a procedure for sample size calculation to control the distributions of FDP and true positives simultaneously under blockwise correlation structures among genes. The sizes of gene blocks, correlation coefficients, and effect sizes within gene blocks can vary across gene blocks. Gene clustering is proposed to identify gene blocks using historical data sets. The adequacy of the procedure is demonstrated using simulated data sets. An application to a clinical study for lymphoma is also provided.

An efficient method for identifying statistical interactors in gene association networks

Andrei, A., Kendziorski, C. — Fri, 11 Sep 2009 10:58:58 PDT

Network reconstruction is a main goal of many biological endeavors. Graphical Gaussian models (GGMs) are often used since the underlying assumptions are well understood, the graph is readily estimated by calculating the partial correlation (paCor) matrix, and its interpretation is straightforward. In spite of these advantages, GGMs are limited in that interactions are not accommodated as the underlying multivariate normality assumption allows for linear dependencies only. As we show, when applied in the presence of interactions, the GGM framework can lead to incorrect inference regarding dependence. Identifying the exact dependence structure in this context is a difficult problem, largely because an analogue of the paCor matrix is not available and dependencies can involve many nodes. We here present a computationally efficient approach to identify bivariate interactions in networks. A key element is recognizing that interactions have a marginal linear effect and as a result information about their presence can be obtained from the paCor matrix. Theoretical derivations for the exact effect are presented and used to motivate the approach; and simulations suggest that the method works well, even in fairly complicated scenarios. Practical advantages are demonstrated in analyses of data from a breast cancer study.

Bayesian inference for within-herd prevalence of Leptospira interrogans serovar Hardjo using bulk milk antibody testing

Lewis, F. I., Gunn, G. J., Mckendrick, I. J., Murray, F. M. — Fri, 11 Sep 2009 10:58:58 PDT

Leptospirosis is the most widespread zoonosis throughout the world and human mortality from severe disease forms is high even when optimal treatment is provided. Leptospirosis is also one of the most common causes of reproductive losses in cattle worldwide and is associated with significant economic costs to the dairy farming industry. Herds are tested for exposure to the causal organism either through serum testing of individual animals or through testing bulk milk samples. Using serum results from a commonly used enzyme-linked immunosorbent assay (ELISA) test for Leptospira interrogans serovar Hardjo (L. hardjo) on samples from 979 animals across 12 Scottish dairy herds and the corresponding bulk milk results, we develop a model that predicts the mean proportion of exposed animals in a herd conditional on the bulk milk test result. The data are analyzed through use of a Bayesian latent variable generalized linear mixed model to provide estimates of the true (but unobserved) level of exposure to the causal organism in each herd in addition to estimates of the accuracy of the serum ELISA. We estimate 95% confidence intervals for the accuracy of the serum ELISA of (0.688, 0.987) and (0.975, 0.998) for test sensitivity and specificity, respectively. Using a percentage positivity cutoff in bulk milk of at most 41% ensures that there is at least a 97.5% probability of less than 5% of the herd being exposed to L. hardjo. Our analyses provide strong statistical evidence in support of the validity of interpreting bulk milk samples as a proxy for individual animal serum testing. The combination of validity and cost-effectiveness of bulk milk testing has the potential to reduce the risk of human exposure to leptospirosis in addition to offering significant economic benefits to the dairy industry.

Estimating dementia-free life expectancy for Parkinson's patients using Bayesian inference and microsimulation

van den Hout, A., Matthews, F. E. — Fri, 11 Sep 2009 10:58:58 PDT

Interval-censored longitudinal data taken from a Norwegian study of individuals with Parkinson's disease are investigated with respect to the onset of dementia. Of interest are risk factors for dementia and the subdivision of total life expectancy (LE) into LE with and without dementia. To estimate LEs using extrapolation, a parametric continuous-time 3-state illness–death Markov model is presented in a Bayesian framework. The framework is well suited to allow for heterogeneity via random effects and to investigate additional computation using model parameters. In the estimation of LEs, microsimulation is used to take into account random effects. Intensities of moving between the states are allowed to change in a piecewise-constant fashion by linking them to age as a time-dependent covariate. Possible right censoring at the end of the follow-up can be incorporated. The model is applicable in many situations where individuals are followed over a long time period. In describing how a disease develops over time, the model can help to predict future need for health care.

A mixed model framework for teratology studies

Braeken, J., Tuerlinckx, F. — Fri, 11 Sep 2009 10:58:58 PDT

A mixed model framework is presented to model the characteristic multivariate binary anomaly data as provided in some teratology studies. The key features of the model are the incorporation of covariate effects, a flexible random effects distribution by means of a finite mixture, and the application of copula functions to better account for the relation structure of the anomalies. The framework is motivated by data of the Boston Anticonvulsant Teratogenesis study and offers an integrated approach to investigate substantive questions, concerning general and anomaly-specific exposure effects of covariates, interrelations between anomalies, and objective diagnostic measurement.

Second-order estimating equations for the analysis of clustered current status data

Cook, R. J., Tolusso, D. — Fri, 11 Sep 2009 10:58:58 PDT

With clustered event time data, interest most often lies in marginal features such as quantiles or probabilities from the marginal event time distribution or covariate effects on marginal hazard functions. Copula models offer a convenient framework for modeling. We present methods of estimating the baseline marginal distributions, covariate effects, and association parameters for clustered current status data based on second-order generalized estimating equations. We examine the efficiency gains realized from using second-order estimating equations compared with first-order equations, issues of copula misspecification, and apply the methods to motivating studies including one on the incidence of joint damage in patients with psoriatic arthritis.

A continuous-index hidden Markov jump process for modeling DNA copy number data

Stjernqvist, S., Ryden, T. — Fri, 11 Sep 2009 10:58:58 PDT

The number of copies of DNA in human cells can be measured using array comparative genomic hybridization (aCGH), which provides intensity ratios of sample to reference DNA at genomic locations corresponding to probes on a microarray. In the present paper, we devise a statistical model, based on a latent continuous-index Markov jump process, that is aimed to capture certain features of aCGH data, including probes that are unevenly long, unevenly spaced, and overlapping. The model has a continuous state space, with 1 state representing a normal copy number of 2, and the rest of the states being either amplifications or deletions. We adopt a Bayesian approach and apply Markov chain Monte Carlo (MCMC) methods for estimating the parameters and the Markov process. The model can be applied to data from both tiling bacterial artificial chromosome arrays and oligonucleotide arrays. We also compare a model with normal distributed noise to a model with t-distributed noise, showing that the latter is more robust to outliers.

Bayesian inference for stochastic multitype epidemics in structured populations using sample data

O'Neill, P. D. — Fri, 11 Sep 2009 10:58:58 PDT

This paper is concerned with the development of new methods for Bayesian statistical inference for structured-population stochastic epidemic models, given data in the form of a sample from a population with known structure. Specifically, the data are assumed to consist of final outcome information, so that it is known whether or not each individual in the sample ever became a clinical case during the epidemic outbreak. The objective is to make inference for the infection rate parameters in the underlying model of disease transmission. The principal challenge is that the required likelihood of the data is intractable in all but the simplest cases. Demiris and O'Neill (2005b) used data augmentation methods involving a certain random graph in a Markov chain Monte Carlo setting to address this situation in the special case where the sample is the same as the entire population. Here, we take an approach relying on broadly similar principles, but for which the implementation details are markedly different. Specifically, to cover the general case of sample data, we use an alternative data augmentation scheme and employ noncentering methods. The methods are illustrated using data from an influenza outbreak.

Modeling between-trial variance structure in mixed treatment comparisons

Lu, G., Ades, A. — Fri, 11 Sep 2009 10:58:58 PDT

In mixed treatment comparison (MTC) meta-analysis, modeling the heterogeneity in between-trial variances across studies is a difficult problem because of the constraints on the variances inherited from the MTC structure. Starting from a consistent Bayesian hierarchical model for the mean treatment effects, we represent the variance configuration by a set of triangle inequalities on the standard deviations. We take the separation strategy (Barnard and others, 2000) to specify prior distributions for standard deviations and correlations separately. The covariance matrix of the latent treatment arm effects can be employed as a vehicle to load the triangular constraints, which in addition allows incorporation of prior beliefs about the correlations between treatment effects. The spherical parameterization based on Cholesky decomposition (Pinheiro and Bates, 1996) is used to generate a positive-definite matrix for the prior correlations in Markov chain Monte Carlo (MCMC). Elicited prior information on correlations between treatment arms is introduced in the form of its equivalent data likelihood. The procedure is implemented in a MCMC framework and illustrated with example data sets from medical research practice.

Letter to the editor

Rucker, G., Schumacher, M. — Fri, 11 Sep 2009 10:58:58 PDT

Index

Fri, 11 Sep 2009 10:58:58 PDT