R utcor Research R eport

摘要: It has recently become possible to screen hundreds of thousands of genetic markers for their association with diseases. Knowledge of the proportion of markers without effect, p0, and the effect sizes in these massive data sets has an intrinsic value and is required for a wide variety of applications. While numerous algorithms have been developed to estimate p0, hardly any method is available to estimate effect sizes. We propose a maximum likelihood (ML) and a quasi-maximum likelihood (QML) approach for the simultaneous estimation of p0 and the average effect size. The point estimate of any p0 estimator can also be used in a 2-step procedure to estimate the average effect size through these (Q) ML methods. To avoid arbitrary choices of the fine-tuning parameter, needed for some p0 estimators, we also developed a novel p0 estimator where an (optimal) fine-tuning parameter is determined automatically through an iterative procedure. All estimators are illustrated for case-control studies for which we first derive an accurate approximation for the distribution of Pearson’s statistic that depends on a single effect size parameter only. The two-step method appeared more accurate than the simultaneous estimation of both parameters. In this twostep procedure ML outperformed QML. ML combined with the Meinshausen-Rice estimator with fine-tuning parameter α= 0.5 appeared to produce the best results in this genetic application. Our novel estimator was most precise among all studied p0 estimators that did not require the pre-specification of a fine running parameter.Acknowledgements: This work was supported by NIH grant R01 HG004240.