Prediction of Empirical p Values from Asymptotic p Values for Conditional Logistic Affected Relative Pair Linkage Analysis

Abstract

Objective: p Values are inaccurate for model-free linkage analysis using the conditional logistic model if we assume that the LOD score is asymptotically distributed as a simple mixture of chi-square distributions. When analyzing affected relative pairs alone, permuting the allele sharing of relative pairs does not lead to a useful permutation distribution. As an alternative, we have developed regression prediction models that provide more accurate p values. Methods: Let E_α be the empirical p value, which is the proportion of statistical tests whose LOD score under the null hypothesis exceeds a threshold determined by α, the nominal single test significance value. We used simulated data to obtain values of E_α and compared them with α. We also developed a regression model, based on sample size, number of covariates in the model, α and marker density, to derive predicted p values for both single-point and multipoint analyses. To evaluate our predictions we used another set of simulated data, comparing the Eα for these data with those obtained by using the prediction model, referred to as predicted p values (P_α). Results: Under almost all circumstances the values of P_α were closer to the E_α than were the values of α. Conclusion: The regression models suggested by our analysis provide more accurate alternative p values for model-free linkage analysis when using the conditional logistic model.

Genetic linkage of region containing the CREB1 gene to depressive disorders in families with recurrent, early‐onset, major depression: A re‐analysis and confirmation of sex‐specific effect

“…To establish stable estimates of empirical significance, we generated 10,000 simulated replicates for the sex-dependent models that employed the complete dataset and 50,000 replicates for our most significant findings in the Female-Female ARP subset. Sinha and colleagues (2006) reported that permutation of IBD status between affected relative pairs did not provide the variation needed to adequately construct a proper null distribution. Instead, we used an approach that relies on gene-dropping simulation and re-estimation of simulated null IBD sharing at each iteration (MacCluer et al, 1986; Jung et al, 2006).…”

“…A proposed remedy for this shortcoming has been published and implemented in the LODPAL program of S.A.G.E. version 5.4.1 for datasets containing from 20 to 320 affected relative pairs (ARPs)(Sinha et al, 2006). Using their model, Sinha and coworkers (2006) reported a corrected p value for the peak LOD score observed for one of the models in our published linkage analysis of the CREB1 region, which remained highly significant.…”

“…version 5.4.1 for datasets containing from 20 to 320 affected relative pairs (ARPs)(Sinha et al, 2006). Using their model, Sinha and coworkers (2006) reported a corrected p value for the peak LOD score observed for one of the models in our published linkage analysis of the CREB1 region, which remained highly significant. In this report, we describe a re-analysis of our published evidence of sex-specific linkage of unipolar Mood Disorders to the CREB1 region of chromosome 2q in our sample of 81 RE-MDD families (Zubenko et al, 2002a) using a simulation approach similar to that used by Sinha and colleagues (2006) to directly calculate empirical p values corresponding to our LODPAL LOD scores.…”

Bootstrap Bayesian analysis with applications to gene-environment interaction

“…While much of the recent genetic literature has been dedicated to genomewide association (GWA) designs, many ongoing studies are employing designs such as affected sib-pairs (ASPs) as part of the gene discovery process. In particular, linkage scans are used to identify regions of interest for additional studies, and methods to incorporate covariates and GxE interactions have improved these searches (e.g., [8], [11], [21], [22], [26]). …”

The null distribution of likelihood-ratio statistics in the conditional-logistic linkage model

“…When analyzing affected pairs alone, however, permuting the allele sharing of relative pairs does not lead to a useful permutation distribution. As an alternative, Sinha et al ( 2006 ) developed regression prediction models that provide more accurate p -values under the CL model framework. However, their results are limited to the cases they evaluated, so it is not a general solution for the unknown distribution of the CL-LR statistic.…”