The evidential statistical paradigm in genetics

The PPLD has advantages over conventional regression methods in application to moderately sized genome-wide association studies

In earlier work, we have developed and evaluated an alternative approach to the analysis of GWAS data, based on a statistic called the PPLD. More recently, motivated by a GWAS for genetic modifiers of the X-linked Mendelian disorder Duchenne Muscular Dystrophy (DMD), we adapted the PPLD for application to time-to-event (TE) phenotypes. Because DMD itself is relatively rare, this is a setting in which the very large sample sizes generally assembled for GWAS are simply not attainable. For this reason, statistical methods specially adapted for use in small data sets are required. Here we explore the behavior of the TE-PPLD via simulations, comparing the TE-PPLD with Cox Proportional Hazards analysis in the context of small to moderate sample sizes. Our results will help to inform our approach to the DMD study going forward, and they illustrate several respects in which the TE-PPLD, and by extension the original PPLD, offer advantages over regression-based approaches to GWAS in this context.

Complementing the P-value from null-hypothesis significance testing with a Bayes factor from null-hypothesis Bayesian testing

BACKGROUND

Classical frequentist statistics, including null-hypothesis significance testing (NHST), dominates nursing and medical research analysis. However, there is increasing recognition that null-hypothesis Bayesian testing (NHBT) merits inclusion in healthcare research analysis.

AIM

To recommend that researchers complement the P-value from NHST with a Bayes factor from NHBT in their research analysis.

DISCUSSION

Reporting the P-value and a Bayes factor clarifies results that may be difficult to interpret using the P-value alone.

CONCLUSION

NHBT offers statistical and practical advantages that complement NHST.

Presidential address: Six open questions to genetic epidemiologists

Given the rapid pace with which genomics and other ‐omics disciplines are evolving, it is sometimes necessary to shift down a gear to consider more general scientific questions. In this line, in my presidential address I formulate six questions for genetic epidemiologists to ponder on. These cover the areas of reproducibility, statistical significance, chance findings, precision medicine and related fields such as bioinformatics and data science. Possible hints at responses are presented to foster our further discussion of these topics.

The evidential statistical paradigm in genetics

Concerns over reproducibility in research has reinvigorated the discourse on P-values as measures of statistical evidence. In a position statement by the American Statistical Association board of directors, they warn of P-value misuse and refer to the availability of alternatives. Despite the common practice of comparing P-values across different hypothesis tests in genetics, it is well-appreciated that P-values must be interpreted alongside the sample size and experimental design used for their computation. Here, we discuss the evidential statistical paradigm (EP), an alternative to Bayesian and Frequentist paradigms, that has been implemented in human genetics studies. Using applications in Cystic Fibrosis genetic association analyses, and describing recent theoretical developments, we review how to measure statistical evidence using the EP in the presence of covariates, model misspecification, and for composite hypotheses. Novel graphical displays are presented, and software for their computation is highlighted. The implications of multiple hypothesis testing for the EP are delineated in the analyses, demonstrating a view more consistent with scientific reasoning; the EP provides a theoretical justification for replication that is a requirement in genetic association studies. As genetic studies grow in size and complexity, a fresh look at measures of statistical evidence that are sensible amid the analysis of big data are required.

Genetic association analysis with pedigrees: Direct inference using the composite likelihood ratio

The likelihood function represents statistical evidence given data and a model. The evidential paradigm (EP), an alternative to Bayesian and Frequentist paradigms, provides considerable theory demonstrating evidence strength for different parameter values via the ratio of likelihoods at different parameter values; thus, enabling inference directly from the likelihood function. The likelihood function, however, can be difficult to compute; for example, in genetic association studies with a binary outcome in large pedigrees. Composite likelihood (CL) is an alternative when the real likelihood is intractable. We show CLs have the two large sample properties of the EP for reliable evidence interpretation: (1) CL supports the true value over a false value by an arbitrarily large factor; and (2) the probability of favouring a false value over the true value is small and bounded. Using simulation, and in a genetic association analysis of reading disability (RD) in large rolandic epilepsy pedigrees, we show that the CL approach yields valid statistical inference and identifies RD associated variants. When compared to analyses using generalized estimating equations, results show a similar prioritization of SNPs, although the CL approach provides additional complementary information, and more intuitive solutions to the multiple hypothesis testing problem.