Polyhedral inclusion-exclusion

Motivated by numerical computations to solve probabilistic constrained stochastic programming problems, we derive a new identity claiming that many terms are cancelled out in the inclusion-exclusion formula expressing the complement of a Euclidean polyhedron

Estimation of CpG Coverage in Whole Methylome Next-Generation Sequencing Studies

Background Methylation studies are a promising complement to genetic studies of DNA sequence. However, detailed prior biological knowledge is typically lacking, so methylome-wide association studies (MWAS) will be critical to detect disease relevant sites. A cost-effective approach involves the next-generation sequencing (NGS) of single-end libraries created from samples that are enriched for methylated DNA fragments. A limitation of single-end libraries is that the fragment size distribution is not observed. This hampers several aspects of the data analysis such as the calculation of enrichment measures that are based on the number of fragments covering the CpGs. Results We developed a non-parametric method that uses isolated CpGs to estimate sample-specific fragment size distributions from the empirical sequencing data. Through simulations we show that our method is highly accurate. While the traditional (extended) read count methods resulted in severely biased coverage estimates and introduces artificial inter-individual differences, through the use of the estimated fragment size distributions we could remove these biases almost entirely. Furthermore, we found correlations of 0.999 between coverage estimates obtained using fragment size distributions that were estimated with our method versus those that were “observed” in paired-end sequencing data. Conclusions We propose a non-parametric method for estimating fragment size distributions that is highly precise and can improve the analysis of cost-effective MWAS studies that sequence single-end libraries created from samples that are enriched for methylated DNA fragments

Optimal designs for two-stage genome-wide association studies

Genome-wide association (GWA) studies require genotyping hundreds of thousands of markers on thousands of subjects, and are expensive at current genotyping costs. To conserve resources, many GWA studies are adopting a staged design in which a proportion of the available samples are genotyped on all markers in stage 1, and a proportion of these markers are genotyped on the remaining samples in stage 2. We describe a strategy for designing cost-effective two-stage GWA studies. Our strategy preserves much of the power of the corresponding one-stage design and minimizes the genotyping cost of the study while allowing for differences in per genotyping cost between stages 1 and 2. We show that the ratio of stage 2 to stage 1 per genotype cost can strongly influence both the optimal design and the genotyping cost of the study. Increasing the stage 2 per genotype cost shifts more of the genotyping and study cost to stage 1, and increases the cost of the study. This higher cost can be partially mitigated by adopting a design with reduced power while preserving the false positive rate or by increasing the false positive rate while preserving power. For example, reducing the power preserved in the two-stage design from 99 to 95% that of the one-stage design decreases the two-stage study cost by ∼15%. Alternatively, the same cost savings can be had by relaxing the false positive rate by 2.5-fold, for example from 1/300,000 to 2.5/300,000, while retaining the same power. Genet. Epidemiol . 2007. © 2007 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57367/1/20240_ftp.pd

Towards Accurate Estimation of the Proportion of True Null Hypotheses in Multiple Testing

BACKGROUND: Biomedical researchers are now often faced with situations where it is necessary to test a large number of hypotheses simultaneously, eg, in comparative gene expression studies using high-throughput microarray technology. To properly control false positive errors the FDR (false discovery rate) approach has become widely used in multiple testing. The accurate estimation of FDR requires the proportion of true null hypotheses being accurately estimated. To date many methods for estimating this quantity have been proposed. Typically when a new method is introduced, some simulations are carried out to show the improved accuracy of the new method. However, the simulations are often very limited to covering only a few points in the parameter space. RESULTS: Here I have carried out extensive in silico experiments to compare some commonly used methods for estimating the proportion of true null hypotheses. The coverage of these simulations is unprecedented thorough over the parameter space compared to typical simulation studies in the literature. Thus this work enables us to draw conclusions globally as to the performance of these different methods. It was found that a very simple method gives the most accurate estimation in a dominantly large area of the parameter space. Given its simplicity and its overall superior accuracy I recommend its use as the first choice for estimating the proportion of true null hypotheses in multiple testing

Strategic management and the perception of order.

Retrospective sense-making produces a perception of a world more orderly than it is. In retrospect we recall the actual outcome of a situation as more predictable than it really seemed in prospect. Thus, we see outcomes as unsurprising, as relatively predictable before hand. A key question, and the one which is the central focus of this paper, is, what effect does this inflated perception of order have on strategic management? Three studies presented here suggest that: (1) Knowing eventual outcomes often distorts later reevaluations of initial decisions. Advanced strategy students analyzing a complex business case were unable to ignore information concerning the outcome of decisions made in the case and systematically distorted their evaluations of initial decisions and projections for the future. (2) Access to environmental history and comparative feedback may impede performance by leading decision makers to expect the future to be more predictable than it is. These factors led to persistent poor performance in a dynamic resource allocation task. (3) Remedial efforts aimed at correcting the bias should focus on cognitive factors to a greater degree than motivational factors. Large and equal hindsight shifts were produced in two groups of students by presenting outcomes as either "real" or as the result of a coin flip, which appears to weaken a self-flattery explanation of hindsight shift and give support to a cognitive account. Research and practical implications are suggested

Agency, Strategic Entrepreneurship and the Performance of Private Equity-Backed Buyouts.

Closed accessAgency theory has focused on buyouts as a governance and control device to increase profitability, organizational efficiency, and limited attention to growth. A strategic entrepreneurship view of buyouts incorporates upside incentives for value creation associated with growth as well as efficiency gains. In this paper, we develop the complementarity between agency theory and strategic entrepreneurship perspectives to examine the performance implications for different types of buyouts. Further, we study how the involvement of private equity (PE) firms is related to the performance of the post-buyout firm. These issues are examined for a sample of 238 PE-backed buyouts in the UK between 1993 and 2003. Implications for theory and practice are suggested