Biostatistics - current issue

Reproducible research and Biostatistics

Peng, R. D. — 2009-06-16

Air pollution and health in Scotland: a multicity study

Lee, D., Ferguson, C., Mitchell, R. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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. — 2009-06-16

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

2009-06-16