Biostatistics - Advance Access

The use of baseline covariates in crossover studies

Kenward, M. G., Roger, J. H. — Fri, 13 Nov 2009 12:13:15 PST

It is our experience that in many settings, crossover trials that have within-period baseline measurements are analyzed wrongly. A "conventional" analysis of covariance in this setting uses each baseline as a covariate for the following outcome variable in the same period but not for any other outcome. If used with random subject effects such an analysis leads to biased treatment comparisons; this is an example of cross-level bias. Using a postulated covariance structure that reflects the symmetry of the crossover setting, we quantify such bias and, at the same time, investigate potential gains and losses in efficiency through the use of the baselines. We then describe alternative methods of analysis that avoid the cross-level bias. The development is illustrated throughout with 2 example trials, one balanced and orthogonal and one highly unbalanced and nonorthogonal.

PICNIC: an algorithm to predict absolute allelic copy number variation with microarray cancer data

Thu, 15 Oct 2009 18:49:20 PDT

High-throughput oligonucleotide microarrays are commonly employed to investigate genetic disease, including cancer. The algorithms employed to extract genotypes and copy number variation function optimally for diploid genomes usually associated with inherited disease. However, cancer genomes are aneuploid in nature leading to systematic errors when using these techniques. We introduce a preprocessing transformation and hidden Markov model algorithm bespoke to cancer. This produces genotype classification, specification of regions of loss of heterozygosity, and absolute allelic copy number segmentation. Accurate prediction is demonstrated with a combination of independent experimental techniques. These methods are exemplified with affymetrix genome-wide SNP6.0 data from 755 cancer cell lines, enabling inference upon a number of features of biological interest. These data and the coded algorithm are freely available for download.

Varying-coefficient models for longitudinal processes with continuous-time informative dropout

Su, L., Hogan, J. W. — Thu, 15 Oct 2009 18:49:19 PDT

Dropout is a common occurrence in longitudinal studies. Building upon the pattern-mixture modeling approach within the Bayesian paradigm, we propose a general framework of varying-coefficient models for longitudinal data with informative dropout, where measurement times can be irregular and dropout can occur at any point in continuous time (not just at observation times) together with administrative censoring. Specifically, we assume that the longitudinal outcome process depends on the dropout process through its model parameters. The unconditional distribution of the repeated measures is a mixture over the dropout (administrative censoring) time distribution, and the continuous dropout time distribution with administrative censoring is left completely unspecified. We use Markov chain Monte Carlo to sample from the posterior distribution of the repeated measures given the dropout (administrative censoring) times; Bayesian bootstrapping on the observed dropout (administrative censoring) times is carried out to obtain marginal covariate effects. We illustrate the proposed framework using data from a longitudinal study of depression in HIV-infected women; the strategy for sensitivity analysis on unverifiable assumption is also demonstrated.

Bayesian random-effects threshold regression with application to survival data with nonproportional hazards

Pennell, M. L., Whitmore, G. A., Ting Lee, M.-L. — Wed, 14 Oct 2009 01:19:33 PDT

In epidemiological and clinical studies, time-to-event data often violate the assumptions of Cox regression due to the presence of time-dependent covariate effects and unmeasured risk factors. An alternative approach, which does not require proportional hazards, is to use a first hitting time model which treats a subject's health status as a latent stochastic process that fails when it reaches a threshold value. Although more flexible than Cox regression, existing methods do not account for unmeasured covariates in both the initial state and the rate of the process. To address this issue, we propose a Bayesian methodology that models an individual's health status as a Wiener process with subject-specific initial state and drift. Posterior inference proceeds via a Markov chain Monte Carlo methodology with data augmentation steps to sample the final health status of censored observations. We apply our method to data from melanoma patients with nonproportional hazards and find interesting differences from a similar model without random effects. In a simulation study, we show that failure to account for unmeasured covariates can lead to inaccurate estimates of survival probabilities.

Exploratory data analysis in large-scale genetic studies

Teo, Y. Y. — Wed, 14 Oct 2009 01:19:36 PDT

Genome-wide association studies (GWAS) have become the method of choice for investigating the genetic basis of common diseases and complex traits. The immense scale of these experiments is unprecedented, involving thousands of samples and up to a million variables. The careful execution of exploratory data analysis (EDA) prior to the actual genotype–phenotype association analysis is crucial as this identifies problematic samples and poorly assayed genetic polymorphisms that, if undetected, can compromise the outcome of the experiment. EDA of such large-scale genetic data sets thus requires specialized numerical and graphical strategies, and this article provides a review of the current exploratory tools commonly used in GWAS.

Association analyses of clustered competing risks data via cross hazard ratio

Cheng, Y., Fine, J. p., Bandeen-Roche, K. — Tue, 13 Oct 2009 13:14:25 PDT

Bandeen-Roche and Liang (2002, Modelling multivariate failure time associations in the presence of a competing risk. Biometrika 89, 299–314.) tailored Oakes (1989, Bivariate survival models induced by frailties. Journal of the American Statistical Association 84, 487–493.)'s conditional hazard ratio to evaluate cause-specific associations in bivariate competing risks data. In many population-based family studies, one observes complex multivariate competing risks data, where the family sizes may be > 2, certain marginals may be exchangeable, and there may be multiple correlated relative pairs having a given pairwise association. Methods for bivariate competing risks data are inadequate in these settings. We show that the rank correlation estimator of Bandeen-Roche and Liang (2002) extends naturally to general clustered family structures. Consistency, asymptotic normality, and variance estimation are easily obtained with U-statistic theories. A natural by-product is an easily implemented test for constancy of the association over different time regions. In the Cache County Study on Memory in Aging, familial associations in dementia onset are of interest, accounting for death prior to dementia. The proposed methods using all available data suggest attenuation in dementia associations at later ages, which had been somewhat obscured in earlier analyses.

The analysis of heterogeneous time trends in multivariate age-period-cohort models

Riebler, A., Held, L. — Tue, 13 Oct 2009 13:14:25 PDT

Age–period–cohort (APC) models are frequently used to analyze mortality or morbidity rates stratified by age group and period. For the case in which rates are given in different strata, multivariate APC models have been considered only recently. Such models share a set of parameters, for example, the age effects, while the other parameters may vary across strata. We show that differences of strata-specific effects are identifiable. We then propose a Bayesian approach based on smoothing priors to estimate multivariate APC models. This provides an alternative to maximum likelihood (ML) estimates of relative risk in the case of equal intervals and gives useful results even in the case of unequal intervals, where ML estimates have severe artifacts. This is illustrated with data on female mortality in Denmark and Norway and data on chronic obstructive pulmonary disease mortality of males in England and Wales, stratified by 3 different areas: Greater London, conurbations excluding Greater London, and nonconurbation areas.

Sample size recalculation in sequential diagnostic trials

Tang, L. L., Liu, A. — Mon, 12 Oct 2009 09:29:38 PDT

Before a comparative diagnostic trial is carried out, maximum sample sizes for the diseased group and the nondiseased group need to be obtained to achieve a nominal power to detect a meaningful difference in diagnostic accuracy. Sample size calculation depends on the variance of the statistic of interest, which is the difference between receiver operating characteristic summary measures of 2 medical diagnostic tests. To obtain an appropriate value for the variance, one often has to assume an arbitrary parametric model and the associated parameter values for the 2 groups of subjects under 2 tests to be compared. It becomes more tedious to do so when the same subject undergoes 2 different tests because the correlation is then involved in modeling the test outcomes. The calculated variance based on incorrectly specified parametric models may be smaller than the true one, which will subsequently result in smaller maximum sample sizes, leaving the study underpowered. In this paper, we develop a nonparametric adaptive method for comparative diagnostic trials to update the sample sizes using interim data, while allowing early stopping during interim analyses. We show that the proposed method maintains the nominal power and type I error rate through theoretical proofs and simulation studies.

A hidden Markov random field model for genome-wide association studies

Li, H., Wei, Z., Maris, J. — Mon, 12 Oct 2009 09:29:37 PDT

Genome-wide association studies (GWAS) are increasingly utilized for identifying novel susceptible genetic variants for complex traits, but there is little consensus on analysis methods for such data. Most commonly used methods include single single nucleotide polymorphism (SNP) analysis or haplotype analysis with Bonferroni correction for multiple comparisons. Since the SNPs in typical GWAS are often in linkage disequilibrium (LD), at least locally, Bonferroni correction of multiple comparisons often leads to conservative error control and therefore lower statistical power. In this paper, we propose a hidden Markov random field model (HMRF) for GWAS analysis based on a weighted LD graph built from the prior LD information among the SNPs and an efficient iterative conditional mode algorithm for estimating the model parameters. This model effectively utilizes the LD information in calculating the posterior probability that an SNP is associated with the disease. These posterior probabilities can then be used to define a false discovery controlling procedure in order to select the disease-associated SNPs. Simulation studies demonstrated the potential gain in power over single SNP analysis. The proposed method is especially effective in identifying SNPs with borderline significance at the single-marker level that nonetheless are in high LD with significant SNPs. In addition, by simultaneously considering the SNPs in LD, the proposed method can also help to reduce the number of false identifications of disease-associated SNPs. We demonstrate the application of the proposed HMRF model using data from a case–control GWAS of neuroblastoma and identify 1 new SNP that is potentially associated with neuroblastoma.

Semiparametric estimation of the average causal effect of treatment on an outcome measured after a postrandomization event, with missing outcome data

Gilbert, P. B., Jin, Y. — Thu, 08 Oct 2009 11:07:25 PDT

In the past decade, several principal stratification–based statistical methods have been developed for testing and estimation of a treatment effect on an outcome measured after a postrandomization event. Two examples are the evaluation of the effect of a cancer treatment on quality of life in subjects who remain alive and the evaluation of the effect of an HIV vaccine on viral load in subjects who acquire HIV infection. However, in general the developed methods have not addressed the issue of missing outcome data, and hence their validity relies on a missing completely at random (MCAR) assumption. Because in many applications the MCAR assumption is untenable, while a missing at random (MAR) assumption is defensible, we extend the semiparametric likelihood sensitivity analysis approach of Gilbert and others (2003) and Jemiai and Rotnitzky (2005) to allow the outcome to be MAR. We combine these methods with the robust likelihood–based method of Little and An (2004) for handling MAR data to provide semiparametric estimation of the average causal effect of treatment on the outcome. The new method, which does not require a monotonicity assumption, is evaluated in a simulation study and is applied to data from the first HIV vaccine efficacy trial.

Trend tests for genetic association using population-based cross-sectional complex survey data

She, D., Li, Y., Zhang, H., Graubard, B. I., Li, Z. — Thu, 10 Sep 2009 11:58:08 PDT

Genetic data collected from surveys such as the Third National Health and Nutrition Examination Survey (NHANES III) enable researchers to investigate the association between wide varieties of health factors and genetic variation for the US population. Tests for trend in disease with increasing number of alleles have been developed for simple random samples. However, surveys such as the NHANES III have complex sample designs involving multistage cluster sampling and sample weighting. These types of sample designs can affect Type I error and power properties of statistical tests based on simple random samples. In order to address these issues, we have derived tests of trend based on Wald and quasi-score statistics, with and without assuming a genetic model, that account for the complex sampling design. The finite-sample properties of the proposed test procedures are evaluated via Monte Carlo simulation studies. We make recommendations about the choice of the test statistic depending on whether or not the underlying genetic model is known. Proposed test statistics are applied to NHANES III data to test for associations between the locus ADRB2 (rs1042713) and obesity, between VDR (rs2239185) and high blood lead level, and between TGFB1 (rs1982073) and asthma.

Bayesian mixture modeling using a hybrid sampler with application to protein subfamily identification

Fong, Y., Wakefield, J., Rice, K. — Thu, 20 Aug 2009 08:40:55 PDT

Predicting protein function is essential to advancing our knowledge of biological processes. This article is focused on discovering the functional diversification within a protein family. A Bayesian mixture approach is proposed to model a protein family as a mixture of profile hidden Markov models. For a given mixture size, a hybrid Markov chain Monte Carlo sampler comprising both Gibbs sampling steps and hierarchical clustering–based split/merge proposals is used to obtain posterior inference. Inference for mixture size concentrates on comparing the integrated likelihoods. The choice of priors is critical with respect to the performance of the procedure. Through simulation studies, we show that 2 priors that are based on independent data sets allow correct identification of the mixture size, both when the data are homogeneous and when the data are generated from a mixture. We illustrate our method using 2 sets of real protein sequences.