QUANTIFYING UNCERTAINTY IN GENOTYPE CALLS

Genome-wide association studies (GWAS) are used to discover genes underlying complex, heritable disorders for which less powerful study designs have failed in the past. The number of GWAS has skyrocketed recently with findings reported in top journals and the mainstream media. Mircorarrays are the genotype calling technology of choice in GWAS as they permit exploration of more than a million single nucleotide polymorphisms (SNPs)simultaneously. The starting point for the statistical analyses used by GWAS, to determine association between loci and disease, are genotype calls (AA, AB, or BB). However, the raw data, microarray probe intensities, are heavily processed before arriving at these calls. Various sophisticated statistical procedures have been proposed for transforming raw data into genotype calls. We find that variability in microarray output quality across different SNPs, different arrays, and different sample batches has substantial inuence on the accuracy of genotype calls made by existing algorithms. Failure to account for these sources of variability, GWAS run the risk of adversely affecting the quality of reported findings. In this paper we present solutions based on a multi-level mixed model. Software implementation of the method described in this paper is available as free and open source code in the crlmm R/BioConductor.

A Cox Model for Biostatistics of the Future

Professor Sir David R. Cox (DRC) is widely acknowledged as among the most important scientists of the second half of the twentieth century. He inherited the mantle of statistical science from Pearson and Fisher, advanced their ideas, and translated statistical theory into practice so as to forever change the application of statistics in many fields, but especially biology and medicine. The logistic and proportional hazards models he substantially developed, are arguably among the most influential biostatistical methods in current practice. This paper looks forward over the period from DRC's 80th to 90th birthdays, to speculate about the future of biostatistics, drawing lessons from DRC's contributions along the way. We consider "Cox's model" of biostatistics, an approach to statistical science that: formulates scientific questions or quantities in terms of parameters gamma in probability models f(y; gamma) that represent in a parsimonious fashion, the underlying scientific mechanisms (Cox, 1997); partition the parameters gamma = theta, eta into a subset of interest theta and other "nuisance parameters" eta necessary to complete the probability distribution (Cox and Hinkley, 1974); develops methods of inference about the scientific quantities that depend as little as possible upon the nuisance parameters (Barndorff-Nielsen and Cox, 1989); and thinks critically about the appropriate conditional distribution on which to base infrences. We briefly review exciting biomedical and public health challenges that are capable of driving statistical developments in the next decade. We discuss the statistical models and model-based inferences central to the CM approach, contrasting them with computationally-intensive strategies for prediction and inference advocated by Breiman and others (e.g. Breiman, 2001) and to more traditional design-based methods of inference (Fisher, 1935). We discuss the hierarchical (multi-level) model as an example of the future challanges and opportunities for model-based inference. We then consider the role of conditional inference, a second key element of the CM. Recent examples from genetics are used to illustrate these ideas. Finally, the paper examines causal inference and statistical computing, two other topics we believe will be central to biostatistics research and practice in the coming decade. Throughout the paper, we attempt to indicate how DRC's work and the "Cox Model" have set a standard of excellence to which all can aspire in the future.

Underestimation of Standard Errors in Multi-Site Time Series Studies

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined. In this paper we investigate the impact of variance underestimation on the pooled relative rate estimate. We focus on two-stage normal-normal hierarchical models and on under- estimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation does not affect the pooled estimate substantially. However, some sensitivity of the pooled estimate to variance underestimation is observed when the number of sites is small and underestimation is severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results, and they can be easily extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity Mortality Air Pollution Study and we found that variance underestimation as much as 40% has little effect on the national average.

Ozone and Mortality: A Meta-Analysis of Time-Series Studies and Comparison to a Multi-City Study (The National Morbidity, Mortality, and Air Pollution Study)

While many time-series studies of ozone and daily mortality identified positive associations,others yielded null or inconclusive results. We performed a meta-analysis of 144 effect estimates from 39 time-series studies, and estimated pooled effects by lags, age groups,cause-specific mortality, and concentration metrics. We compared results to estimates from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS), a time-series study of 95 large U.S. cities from 1987 to 2000. Both meta-analysis and NMMAPS results provided strong evidence of a short-term association between ozone and mortality, with larger effects for cardiovascular and respiratory mortality, the elderly, and current day ozone exposure as compared to other single day lags. In both analyses, results were not sensitive to adjustment for particulate matter and model specifications. In the meta-analysis we found that a 10 ppb increase in daily ozone is associated with a 0.83 (95% confidence interval: 0.53, 1.12%) increase in total mortality, whereas the corresponding NMMAPS estimate is 0.25%(0.12, 0.39%). Meta-analysis results were consistently larger than those from NMMAPS,indicating publication bias. Additional publication bias is evident regarding the choice of lags in time-series studies, and the larger heterogeneity in posterior city-specific estimates in the meta-analysis, as compared with NMAMPS.