Biostatistics - recent issues

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

Reproducible research and Biostatistics

Peng, R. D. — Tue, 16 Jun 2009 21:52:36 PDT

Air pollution and health in Scotland: a multicity study

Lee, D., Ferguson, C., Mitchell, R. — Tue, 16 Jun 2009 21:52:36 PDT

This paper presents an epidemiological study investigating the effects of long-term air pollution exposure on public health in Scotland, focusing on the 4 major urban areas, Aberdeen, Dundee, Edinburgh, and Glasgow. In particular, the associations between respiratory hospital admissions in 2005 and exposure to both PM₁₀ and NO₂ between 2002 and 2004 are estimated using a small-area ecological design. The implementation of such studies requires careful consideration of a number of statistical issues, including how to model spatial correlation, identifiability of the model parameters, and the possible effects of ecological bias. The results show that long-term exposures (over 3 years) to PM₁₀ and NO₂ are significantly associated with respiratory hospital admissions in Edinburgh and Glasgow, whereas the risks for Aberdeen and Dundee are generally positive but nonsignificant.

A simulation-approximation approach to sample size planning for high-dimensional classification studies

de Valpine, P., Bitter, H.-M., Brown, M. P. S., Heller, J. — Tue, 16 Jun 2009 21:52:36 PDT

Classification studies with high-dimensional measurements and relatively small sample sizes are increasingly common. Prospective analysis of the role of sample sizes in the performance of such studies is important for study design and interpretation of results, but the complexity of typical pattern discovery methods makes this problem challenging. The approach developed here combines Monte Carlo methods and new approximations for linear discriminant analysis, assuming multivariate normal distributions. Monte Carlo methods are used to sample the distribution of which features are selected for a classifier and the mean and variance of features given that they are selected. Given selected features, the linear discriminant problem involves different distributions of training data and generalization data, for which 2 approximations are compared: one based on Taylor series approximation of the generalization error and the other on approximating the discriminant scores as normally distributed. Combining the Monte Carlo and approximation approaches to different aspects of the problem allows efficient estimation of expected generalization error without full simulations of the entire sampling and analysis process. To evaluate the method and investigate realistic study design questions, full simulations are used to ask how validation error rate depends on the strength and number of informative features, the number of noninformative features, the sample size, and the number of features allowed into the pattern. Both approximation methods perform well for most cases but only the normal discriminant score approximation performs well for cases of very many weakly informative or uninformative dimensions. The simulated cases show that many realistic study designs will typically estimate substantially suboptimal patterns and may have low probability of statistically significant validation results.

Efficient parameter estimation in longitudinal data analysis using a hybrid GEE method

Leung, D. H. Y., Wang, Y.-G., Zhu, M. — Tue, 16 Jun 2009 21:52:36 PDT

The method of generalized estimating equations (GEEs) provides consistent estimates of the regression parameters in a marginal regression model for longitudinal data, even when the working correlation model is misspecified (Liang and Zeger, 1986). However, the efficiency of a GEE estimate can be seriously affected by the choice of the working correlation model. This study addresses this problem by proposing a hybrid method that combines multiple GEEs based on different working correlation models, using the empirical likelihood method (Qin and Lawless, 1994). Analyses show that this hybrid method is more efficient than a GEE using a misspecified working correlation model. Furthermore, if one of the working correlation structures correctly models the within-subject correlations, then this hybrid method provides the most efficient parameter estimates. In simulations, the hybrid method's finite-sample performance is superior to a GEE under any of the commonly used working correlation models and is almost fully efficient in all scenarios studied. The hybrid method is illustrated using data from a longitudinal study of the respiratory infection rates in 275 Indonesian children.

A note on oligonucleotide expression values not being normally distributed

Hardin, J., Wilson, J. — Tue, 16 Jun 2009 21:52:36 PDT

Novel techniques for analyzing microarray data are constantly being developed. Though many of the methods contribute to biological discoveries, inability to properly evaluate the novel techniques limits their ability to advance science. Because the underlying distribution of microarray data is unknown, novel methods are typically tested against the assumed normal distribution. However, microarray data are not, in fact, normally distributed, and assuming so can have misleading consequences. Using an Affymetrix technical replicate spike-in data set, we show that oligonucleotide expression values are not normally distributed for any of the standard methods for calculating expression values. The resulting data tend to have a large proportion of skew and heavy tailed genes. Additionally, we show that standard methods can give unexpected and misleading results when the data are not well approximated by the normal distribution. Robust methods are therefore recommended when analyzing microarray data. Additionally, new techniques should be evaluated with skewed and/or heavy-tailed data distributions.

Conditional GEE for recurrent event gap times

Clement, D. Y., Strawderman, R. L. — Tue, 16 Jun 2009 21:52:36 PDT

This paper deals with the analysis of recurrent event data subject to censored observation. Using a suitable adaptation of generalized estimating equations for longitudinal data, we propose a straightforward methodology for estimating the parameters indexing the conditional means and variances of the process interevent (i.e. gap) times. The proposed methodology permits the use of both time-fixed and time-varying covariates, as well as transformations of the gap times, creating a flexible and useful class of methods for analyzing gap-time data. Censoring is dealt with by imposing a parametric assumption on the censored gap times, and extensive simulation results demonstrate the relative robustness of parameter estimates even when this parametric assumption is incorrect. A suitable large-sample theory is developed. Finally, we use our methods to analyze data from a randomized trial of asthma prevention in young children.

Estimating equation-based causality analysis with application to microarray time series data

Hu, J., Hu, F. — Tue, 16 Jun 2009 21:52:36 PDT

Microarray time-course data can be used to explore interactions among genes and infer gene network. The crucial step in constructing gene network is to develop an appropriate causality test. In this regard, the expression profile of each gene can be treated as a time series. A typical existing method establishes the Granger causality based on Wald type of test, which relies on the homoscedastic normality assumption of the data distribution. However, this assumption can be seriously violated in real microarray experiments and thus may lead to inconsistent test results and false scientific conclusions. To overcome the drawback, we propose an estimating equation–based method which is robust to both heteroscedasticity and nonnormality of the gene expression data. In fact, it only requires the residuals to be uncorrelated. We will use simulation studies and a real-data example to demonstrate the applicability of the proposed method.

An insight into high-resolution mass-spectrometry data

Eckel-passow, J. E., Oberg, A. L., Therneau, T. M., Bergen, H. R. — Tue, 16 Jun 2009 21:52:36 PDT

Mass spectrometry is a powerful tool with much promise in global proteomic studies. The discipline of statistics offers robust methodologies to extract and interpret high-dimensional mass-spectrometry data and will be a valuable contributor to the field. Here, we describe the process by which data are produced, characteristics of the data, and the analytical preprocessing steps that are taken in order to interpret the data and use it in downstream statistical analyses. Because of the complexity of data acquisition, statistical methods developed for gene expression microarray data are not directly applicable to proteomic data. Areas in need of statistical research for proteomic data include alignment, experimental design, abundance normalization, and statistical analysis.

Frailty modeling of bimodal age-incidence curves of nasopharyngeal carcinoma in low-risk populations

Haugen, M., Bray, F., Grotmol, T., Tretli, S., Aalen, O. O., Moger, T. A. — Tue, 16 Jun 2009 21:52:36 PDT

The incidence of nasopharyngeal carcinoma (NPC) varies widely according to age at diagnosis, geographic location, and ethnic background. On a global scale, NPC incidence is common among specific populations primarily living in southern and eastern Asia and northern Africa, but in most areas, including almost all western countries, it remains a relatively uncommon malignancy. Specific to these low-risk populations is a general observation of possible bimodality in the observed age-incidence curves. We have developed a multiplicative frailty model that allows for the demonstrated points of inflection at ages 15–24 and 65–74. The bimodal frailty model has 2 independent compound Poisson-distributed frailties and gives a significant improvement in fit over a unimodal frailty model. Applying the model to population-based cancer registry data worldwide, 2 biologically relevant estimates are derived, namely the proportion of susceptible individuals and the number of genetic and epigenetic events required for the tumor to develop. The results are critically compared and discussed in the context of existing knowledge of the epidemiology and pathogenesis of NPC.

A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis

Witten, D. M., Tibshirani, R., Hastie, T. — Tue, 16 Jun 2009 21:52:36 PDT

We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as , where d_k, u_k, and v_k minimize the squared Frobenius norm of X , subject to penalties on u_k and v_k. This results in a regularized version of the singular value decomposition. Of particular interest is the use of L₁-penalties on u_k and v_k, which yields a decomposition of X using sparse vectors. We show that when the PMD is applied using an L₁-penalty on v_k but not on u_k, a method for sparse principal components results. In fact, this yields an efficient algorithm for the "SCoTLASS" proposal (Jolliffe and others 2003) for obtaining sparse principal components. This method is demonstrated on a publicly available gene expression data set. We also establish connections between the SCoTLASS method for sparse principal component analysis and the method of Zou and others (2006). In addition, we show that when the PMD is applied to a cross-products matrix, it results in a method for penalized canonical correlation analysis (CCA). We apply this penalized CCA method to simulated data and to a genomic data set consisting of gene expression and DNA copy number measurements on the same set of samples.

Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: a joint modeling approach

Proust-Lima, C., Taylor, J. M. G. — Tue, 16 Jun 2009 21:52:36 PDT

Prostate-specific antigen (PSA) is a biomarker routinely and repeatedly measured on prostate cancer patients treated by radiation therapy (RT). It was shown recently that its whole pattern over time rather than just its current level was strongly associated with prostate cancer recurrence. To more accurately guide clinical decision making, monitoring of PSA after RT would be aided by dynamic powerful prognostic tools that incorporate the complete posttreatment PSA evolution. In this work, we propose a dynamic prognostic tool derived from a joint latent class model and provide a measure of variability obtained from the parameters asymptotic distribution. To validate this prognostic tool, we consider predictive accuracy measures and provide an empirical estimate of their variability. We also show how to use them in the longitudinal context to compare the dynamic prognostic tool we developed with a proportional hazard model including either baseline covariates or baseline covariates and the expected level of PSA at the time of prediction in a landmark model. Using data from 3 large cohorts of patients treated after the diagnosis of prostate cancer, we show that the dynamic prognostic tool based on the joint model reduces the error of prediction and offers a powerful tool for individual prediction.

Testing the prediction error difference between 2 predictors

van de Wiel, M. A., Berkhof, J., van Wieringen, W. N. — Tue, 16 Jun 2009 21:52:36 PDT

We develop an inference framework for the difference in errors between 2 prediction procedures. The 2 procedures may differ in any aspect and possibly utilize different sets of covariates. We apply training and testing on the same data set, which is accommodated by sample splitting. For each split, both procedures predict the response of the same samples, which results in paired residuals to which a signed-rank test is applied. Multiple splits result in multiple p-values. The median p-value and the mean inverse normal transformed p-value are proposed as summary (test) statistics, for which bounds on the overall type I error rate under a variety of assumptions are proven. A simulation study is performed to check type I error control of the least conservative bound. Moreover, it confirms superior power of our method with respect to a one-split approach. Our inference framework is applied to genomic survival data sets to study 2 issues: compare lasso and ridge regression and decide upon use of both methylation and gene expression markers or the latter only. The framework easily accommodates any prediction paradigm and allows comparing any 2, possibly nonmodel-based, prediction procedures.

Optimal designs for 2-color microarray experiments

Sanchez, P. S., Glonek, G. F. V. — Tue, 16 Jun 2009 21:52:36 PDT

Statisticians can play a crucial role in the design of gene expression studies to ensure the most effective allocation of available resources. This paper considers Pareto optimal designs for gene expression studies involving 2-color microarrays. Pareto optimality enables the recommendation of designs that are particularly efficient for the effects of most interest to biologists. This is relevant in the microarray context where analysis is typically carried out separately for those effects. Our approach will allow for effects of interest that correspond to contrasts rather than solely considering parameters of the linear model. We further develop the approach to cater for additional experimental considerations such as contrasts that are of equal scientific interest. This amounts to partitioning all relevant contrasts into subsets of effects that are of equal importance. Based on the partitions, a penalty is employed in order to recommend designs for complex and varied microarray experiments. Finally, we address the issue of gene-specific dye bias. We illustrate using studies of leukemia and breast cancer.

Joint analysis of prevalence and incidence data using conditional likelihood

Saarela, O., Kulathinal, S., Karvanen, J. — Tue, 16 Jun 2009 21:52:36 PDT

Disease prevalence is the combined result of duration, disease incidence, case fatality, and other mortality. If information is available on all these factors, and on fixed covariates such as genotypes, prevalence information can be utilized in the estimation of the effects of the covariates on disease incidence. Study cohorts that are recruited as cross-sectional samples and subsequently followed up for disease events of interest produce both prevalence and incidence information. In this paper, we make use of both types of information using a likelihood, which is conditioned on survival until the cross section. In a simulation study making use of real cohort data, we compare the proposed conditional likelihood method to a standard analysis where prevalent cases are omitted and the likelihood expression is conditioned on healthy status at the cross section.

Biostatistics - Referees of Manuscripts Submitted Mid-2007 to Mid-2008

Tue, 16 Jun 2009 21:52:36 PDT

Generalized linear models with unspecified reference distribution

Rathouz, P. J., Gao, L. — Fri, 27 Feb 2009 00:43:53 PST

We propose a new class of semiparametric generalized linear models. As with existing models, these models are specified via a linear predictor and a link function for the mean of response Y as a function of predictors X. Here, however, the "baseline" distribution of Y at a given reference mean µ₀ is left unspecified and is estimated from the data. The response distribution when the mean differs from µ₀ is then generated via exponential tilting of the baseline distribution, yielding a response model that is a natural exponential family, with corresponding canonical link and variance functions. The resulting model has a level of flexibility similar to the popular proportional odds model. Maximum likelihood estimation is developed for response distributions with finite support, and the new model is studied and illustrated through simulations and example analyses from aging research.

Modified test statistics by inter-voxel variance shrinkage with an application to f MRI

Su, S.-C., Caffo, B., Garrett-Mayer, E., Bassett, S. S. — Fri, 27 Feb 2009 00:43:53 PST

Functional magnetic resonance imaging (f MRI) is a noninvasive technique which is commonly used to quantify changes in blood oxygenation and flow coupled to neuronal activation. One of the primary goals of f MRI studies is to identify localized brain regions where neuronal activation levels vary between groups. Single voxel t-tests have been commonly used to determine whether activation related to the protocol differs across groups. Due to the generally limited number of subjects within each study, accurate estimation of variance at each voxel is difficult. Thus, combining information across voxels is desirable in order to improve efficiency. Here, we construct a hierarchical model and apply an empirical Bayesian framework for the analysis of group f MRI data, employing techniques used in high-throughput genomic studies. The key idea is to shrink residual variances by combining information across voxels and subsequently to construct an improved test statistic. This hierarchical model results in a shrinkage of voxel-wise residual sample variances toward a common value. The shrunken estimator for voxel-specific variance components on the group analyses outperforms the classical residual error estimator in terms of mean-squared error. Moreover, the shrunken test statistic decreases false-positive rates when testing differences in brain contrast maps across a wide range of simulation studies. This methodology was also applied to experimental data regarding a cognitive activation task.

Biomarker evaluation and comparison using the controls as a reference population

Huang, Y., Pepe, M. S. — Fri, 27 Feb 2009 00:43:53 PST

The classification accuracy of a continuous marker is typically evaluated with the receiver operating characteristic (ROC) curve. In this paper, we study an alternative conceptual framework, the "percentile value." In this framework, the controls only provide a reference distribution to standardize the marker. The analysis proceeds by analyzing the standardized marker in cases. The approach is shown to be equivalent to ROC analysis. Advantages are that it provides a framework familiar to a broad spectrum of biostatisticians and it opens up avenues for new statistical techniques in biomarker evaluation. We develop several new procedures based on this framework for comparing biomarkers and biomarker performance in different populations. We develop methods that adjust such comparisons for covariates. The methods are illustrated on data from 2 cancer biomarker studies.

A new serially correlated gamma-frailty process for longitudinal count data

Fiocco, M., Putter, H., Van Houwelingen, J.C. — Fri, 27 Feb 2009 00:43:53 PST

We describe a new multivariate gamma distribution and discuss its implication in a Poisson-correlated gamma-frailty model. This model is introduced to account for between-subjects correlation occurring in longitudinal count data. For likelihood-based inference involving distributions in which high-dimensional dependencies are present, it may be useful to approximate likelihoods based on the univariate or bivariate marginal distributions. The merit of composite likelihood is to reduce the computational complexity of the full likelihood. A 2-stage composite-likelihood procedure is developed for estimating the model parameters. The suggested method is applied to a meta-analysis study for survival curves.

Measurement error caused by spatial misalignment in environmental epidemiology

Gryparis, A., Paciorek, C. J., Zeka, A., Schwartz, J., Coull, B. A. — Fri, 27 Feb 2009 00:43:53 PST

In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.

Exact and efficient inference procedure for meta-analysis and its application to the analysis of independent 2 x 2 tables with all available data but without artificial continuity correction

Tian, L., Cai, T., Pfeffer, M. A., Piankov, N., Cremieux, P.-Y., Wei, L. J. — Fri, 27 Feb 2009 00:43:53 PST

Recently, meta-analysis has been widely utilized to combine information across comparative clinical studies for evaluating drug efficacy or safety profile. When dealing with rather rare events, a substantial proportion of studies may not have any events of interest. Conventional methods either exclude such studies or add an arbitrary positive value to each cell of the corresponding 2x2 tables in the analysis. In this article, we present a simple, effective procedure to make valid inferences about the parameter of interest with all available data without artificial continuity corrections. We then use the procedure to analyze the data from 48 comparative trials involving rosiglitazone with respect to its possible cardiovascular toxicity.

A method for constructing a confidence bound for the actual error rate of a prediction rule in high dimensions

Dobbin, K. K. — Fri, 27 Feb 2009 00:43:53 PST

Constructing a confidence interval for the actual, conditional error rate of a prediction rule from multivariate data is problematic because this error rate is not a population parameter in the traditional sense—it is a functional of the training set. When the training set changes, so does this "parameter." A valid method for constructing confidence intervals for the actual error rate had been previously developed by McLachlan. However, McLachlan's method cannot be applied in many cancer research settings because it requires the number of samples to be much larger than the number of dimensions (n >> p), and it assumes that no dimension-reducing feature selection step is performed. Here, an alternative to McLachlan's method is presented that can be applied when p >> n, with an additional adjustment in the presence of feature selection. Coverage probabilities of the new method are shown to be nominal or conservative over a wide range of scenarios. The new method is relatively simple to implement and not computationally burdensome.

Optimal multistage designs--a general framework for efficient genome-wide association studies

Pahl, R., Schafer, H., Muller, H.-H. — Fri, 27 Feb 2009 00:43:53 PST

Genome-wide association studies (GWAS) have become increasingly affordable but they are still costly. Therefore, cost saving 2-stage designs were proposed in the literature. The restriction to 2 stages, however, seems artificial and does not exploit the full potential of the underlying methods. We extend the 2-stage approach to the general framework of any number of stages. Based on the theory of group sequential methods, we derive optimal multistage designs. With current genotyping cost structures, our results suggest that up to 4 stages are sufficient in order to get feasible and efficient designs. Furthermore, we consider the problem of choosing the optimal number of stages depending on the costs of the statistical interim analysis at each stage and provide guidelines for planning the number of stages in practice. In particular, we found that in the majority of cases both 3-stage designs and 4-stage designs are more efficient than 2-stage designs. Although prices for marker panels are showing a continuing downward trend, we still recommend implementing and using optimal multistage designs in practice. In addition to the immediate benefit, it will be necessary to acquire know-how regarding the application of multistage designs in order to be able to adapt the general framework of multistage designs to upcoming technologies in the area of GWAS.

Statistical monitoring of clinical trials with multivariate response and/or multiple arms: a flexible approach

Zhao, L., Hu, X. J., Lagakos, S. W. — Fri, 27 Feb 2009 00:43:54 PST

Randomized clinical trials with a multivariate response and/or multiple treatment arms are increasingly common, in part because of their efficiency and a greater concern about balancing risks with benefits. In some trials, the specific types and magnitudes of treatment group differences that would warrant early termination cannot easily be specified prior to the onset of the trial and/or could change as the trial progresses. This underscores the need for more flexible monitoring methods than traditional approaches. This paper extends the repeated confidence bands approach for interim monitoring to more general settings where there can be a multivariate response and/or multiple treatment arms and where the metrics for comparing treatment groups can change during the conduct of the trial. We illustrate the approach using the results of a recent AIDS clinical trial and examine its efficiency and robustness via simulation.

Optimal 2-stage design with given power in association studies

Wang, J., Liang, H., Zou, G. — Fri, 27 Feb 2009 00:43:54 PST

Statistical independence of the colocalized association signals for type 1 diabetes and RPS26 gene expression on chromosome 12q13

Plagnol, V., Smyth, D. J., Todd, J. A., Clayton, D. G. — Fri, 27 Feb 2009 00:43:54 PST

Following the recent success of genome-wide association studies in uncovering disease-associated genetic variants, the next challenge is to understand how these variants affect downstream pathways. The most proximal trait to a disease-associated variant, most commonly a single nucleotide polymorphism (SNP), is differential gene expression due to the cis effect of SNP alleles on transcription, translation, and/or splicing gene expression quantitative trait loci (eQTL). Several genome-wide SNP–gene expression association studies have already provided convincing evidence of widespread association of eQTLs. As a consequence, some eQTL associations are found in the same genomic region as a disease variant, either as a coincidence or a causal relationship. Cis-regulation of RPS26 gene expression and a type 1 diabetes (T1D) susceptibility locus have been colocalized to the 12q13 genomic region. A recent study has also suggested RPS26 as the most likely susceptibility gene for T1D in this genomic region. However, it is still not clear whether this colocalization is the result of chance alone or if RPS26 expression is directly correlated with T1D susceptibility, and therefore, potentially causal. Here, we derive and apply a statistical test of this hypothesis. We conclude that RPS26 expression is unlikely to be the molecular trait responsible for T1D susceptibility at this locus, at least not in a direct, linear connection.

Bayesian graphical models for regression on multiple data sets with different variables

Jackson, C. H., Best, N. G., Richardson, S. — Fri, 27 Feb 2009 00:43:54 PST

Routinely collected administrative data sets, such as national registers, aim to collect information on a limited number of variables for the whole population. In contrast, survey and cohort studies contain more detailed data from a sample of the population. This paper describes Bayesian graphical models for fitting a common regression model to a combination of data sets with different sets of covariates. The methods are applied to a study of low birth weight and air pollution in England and Wales using a combination of register, survey, and small-area aggregate data. We discuss issues such as multiple imputation of confounding variables missing in one data set, survey selection bias, and appropriate propagation of information between model components. From the register data, there appears to be an association between low birth weight and environmental exposure to NO₂, but after adjusting for confounding by ethnicity and maternal smoking by combining the register and survey data under our models, we find there is no significant association. However, NO₂ was associated with a small but significant reduction in birth weight, modeled as a continuous variable.

Microarray background correction: maximum likelihood estimation for the normal-exponential convolution

Silver, J. D., Ritchie, M. E., Smyth, G. K. — Fri, 27 Feb 2009 00:43:54 PST

Background correction is an important preprocessing step for microarray data that attempts to adjust the data for the ambient intensity surrounding each feature. The "normexp" method models the observed pixel intensities as the sum of 2 random variables, one normally distributed and the other exponentially distributed, representing background noise and signal, respectively. Using a saddle-point approximation, Ritchie and others (2007) found normexp to be the best background correction method for 2-color microarray data. This article develops the normexp method further by improving the estimation of the parameters. A complete mathematical development is given of the normexp model and the associated saddle-point approximation. Some subtle numerical programming issues are solved which caused the original normexp method to fail occasionally when applied to unusual data sets. A practical and reliable algorithm is developed for exact maximum likelihood estimation (MLE) using high-quality optimization software and using the saddle-point estimates as starting values. "MLE" is shown to outperform heuristic estimators proposed by other authors, both in terms of estimation accuracy and in terms of performance on real data. The saddle-point approximation is an adequate replacement in most practical situations. The performance of normexp for assessing differential expression is improved by adding a small offset to the corrected intensities.

A robust method for finely stratified familial studies with proband-based sampling

Wang, M., Hanfelt, J. J. — Fri, 27 Feb 2009 00:43:54 PST

This paper presents a robust method to conduct inference in finely stratified familial studies under proband-based sampling. We assume that the interest is in both the marginal effects of subject-specific covariates on a binary response and the familial aggregation of the response, as quantified by intrafamilial pairwise odds ratios. We adopt an estimating function for proband-based family studies originally developed by Zhao and others (1998) in the context of an unstratified design and treat the stratification effects as fixed nuisance parameters. Our method requires modeling only the first 2 joint moments of the observations and reduces by 2 orders of magnitude the bias induced by fitting the stratum-specific nuisance parameters. An analytical standard error estimator for the proposed estimator is also provided. The proposed approach is applied to a matched case–control familial study of sleep apnea. A simulation study confirms the usefulness of the approach.

Bias in 2-part mixed models for longitudinal semicontinuous data

Su, L., Tom, B. D. M., Farewell, V. T. — Fri, 27 Feb 2009 00:43:54 PST

Semicontinuous data in the form of a mixture of zeros and continuously distributed positive values frequently arise in biomedical research. Two-part mixed models with correlated random effects are an attractive approach to characterize the complex structure of longitudinal semicontinuous data. In practice, however, an independence assumption about random effects in these models may often be made for convenience and computational feasibility. In this article, we show that bias can be induced for regression coefficients when random effects are truly correlated but misspecified as independent in a 2-part mixed model. Paralleling work on bias under nonignorable missingness within a shared parameter model, we derive and investigate the asymptotic bias in selected settings for misspecified 2-part mixed models. The performance of these models in practice is further evaluated using Monte Carlo simulations. Additionally, the potential bias is investigated when artificial zeros, due to left censoring from some detection or measuring limit, are incorporated. To illustrate, we fit different 2-part mixed models to the data from the University of Toronto Psoriatic Arthritis Clinic, the aim being to examine whether there are differential effects of disease activity and damage on physical functioning as measured by the health assessment questionnaire scores over the course of psoriatic arthritis. Some practical issues on variance component estimation revealed through this data analysis are considered.

A Bayesian model for evaluating influenza antiviral efficacy in household studies with asymptomatic infections

Yang, Y., Halloran, M. E., Longini, I. M. — Fri, 27 Feb 2009 00:43:54 PST

Antiviral agents are an important component in mitigation/containment strategies for pandemic influenza. However, most research for mitigation/containment strategies relies on the antiviral efficacies evaluated from limited data of clinical trials. Which efficacy measures can be reliably estimated from these studies depends on the trial design, the size of the epidemics, and the statistical methods. We propose a Bayesian framework for modeling the influenza transmission dynamics within households. This Bayesian framework takes into account asymptomatic infections and is able to estimate efficacies with respect to protecting against viral infection, infection with clinical disease, and pathogenicity (the probability of disease given infection). We use the method to reanalyze 2 clinical studies of oseltamivir, an influenza antiviral agent, and compare the results with previous analyses. We found significant prophylactic efficacies in reducing the risk of viral infection and infection with disease but no prophylactic efficacy in reducing pathogenicity. We also found significant therapeutic efficacies in reducing pathogenicity and the risk of infection with disease but no therapeutic efficacy in reducing the risk of viral infection in the contacts.