Bayesian Prediction Intervals for Assessing \u3cem\u3eP\u3c/em\u3e-Value Variability in Prospective Replication Studies

Increased availability of data and accessibility of computational tools in recent years have created an unprecedented upsurge of scientific studies driven by statistical analysis. Limitations inherent to statistics impose constraints on the reliability of conclusions drawn from data, so misuse of statistical methods is a growing concern. Hypothesis and significance testing, and the accompanying P-values are being scrutinized as representing the most widely applied and abused practices. One line of critique is that P-values are inherently unfit to fulfill their ostensible role as measures of credibility for scientific hypotheses. It has also been suggested that while P-values may have their role as summary measures of effect, researchers underappreciate the degree of randomness in the P-value. High variability of P-values would suggest that having obtained a small P-value in one study, one is, nevertheless, still likely to obtain a much larger P-value in a similarly powered replication study. Thus, “replicability of P-value” is in itself questionable. To characterize P-value variability, one can use prediction intervals whose endpoints reflect the likely spread of P-values that could have been obtained by a replication study. Unfortunately, the intervals currently in use, the frequentist P-intervals, are based on unrealistic implicit assumptions. Namely, P-intervals are constructed with the assumptions that imply substantial chances of encountering large values of effect size in an observational study, which leads to bias. The long-run frequentist probability provided by P-intervals is similar in interpretation to that of the classical confidence intervals, but the endpoints of any particular interval lack interpretation as probabilistic bounds for the possible spread of future P-values that may have been obtained in replication studies. Along with classical frequentist intervals, there exists a Bayesian viewpoint toward interval construction in which the endpoints of an interval have a meaningful probabilistic interpretation. We propose Bayesian intervals for prediction of P-value variability in prospective replication studies. Contingent upon approximate prior knowledge of the effect size distribution, our proposed Bayesian intervals have endpoints that are directly interpretable as probabilistic bounds for replication P-values, and they are resistant to selection bias. We showcase our approach by its application to P-values reported for five psychiatric disorders by the Psychiatric Genomics Consortium group

Interval estimation of genetic susceptibility for retrospective case-control studies

BACKGROUND: This article describes classical and Bayesian interval estimation of genetic susceptibility based on random samples with pre-specified numbers of unrelated cases and controls. RESULTS: Frequencies of genotypes in cases and controls can be estimated directly from retrospective case-control data. On the other hand, genetic susceptibility defined as the expected proportion of cases among individuals with a particular genotype depends on the population proportion of cases (prevalence). Given this design, prevalence is an external parameter and hence the susceptibility cannot be estimated based on only the observed data. Interval estimation of susceptibility that can incorporate uncertainty in prevalence values is explored from both classical and Bayesian perspective. Similarity between classical and Bayesian interval estimates in terms of frequentist coverage probabilities for this problem allows an appealing interpretation of classical intervals as bounds for genetic susceptibility. In addition, it is observed that both the asymptotic classical and Bayesian interval estimates have comparable average length. These interval estimates serve as a very good approximation to the "exact" (finite sample) Bayesian interval estimates. Extension from genotypic to allelic susceptibility intervals shows dependency on phenotype-induced deviations from Hardy-Weinberg equilibrium. CONCLUSIONS: The suggested classical and Bayesian interval estimates appear to perform reasonably well. Generally, the use of exact Bayesian interval estimation method is recommended for genetic susceptibility, however the asymptotic classical and approximate Bayesian methods are adequate for sample sizes of at least 50 cases and controls

Action following the discovery of a global association between the whole genome and adverse event risk in a clinical drug-development programme

Observation of adverse drug reactions during drug development can cause closure of the whole programme. However, if association between the genotype and the risk of an adverse event is discovered, then it might suffice to exclude patients of certain genotypes from future recruitment. Various sequential and non-sequential procedures are available to identify an association between the whole genome, or at least a portion of it, and the incidence of adverse events. In this paper we start with a suspected association between the genotype and the risk of an adverse event and suppose that the genetic subgroups with elevated risk can be identified. Our focus is determination of whether the patients identified as being at risk should be excluded from further studies of the drug. We propose using a utility function to determine the appropriate action, taking into account the relative costs of suffering an adverse reaction and of failing to alleviate the patient's disease. Two illustrative examples are presented, one comparing patients who suffer from an adverse event with contemporary patients who do not, and the other making use of a reference control group. We also illustrate two classification methods, LASSO and CART, for identifying patients at risk, but we stress that any appropriate classification method could be used in conjunction with the proposed utility function. Our emphasis is on determining the action to take rather than on providing definitive evidence of an association

Pleiotropic Effects of CSF Levels of Alzheimer’s Disease Proteins

Cerebrospinal fluid (CSF) analytes harbor potential as diagnostic biomarkers for Alzheimer’s Disease (AD). Quantitative measures of CSF proteins comprise a set of often highly correlated endophenotypes that have previously shown promise in genetic analyses (Cruchaga et al., 2013; Kauwe et al., 2014). Pleiotropic impact of genetic variations on this set may provide additional insights into AD pathology at its earliest stages. To determine which specific endophenotypes are pleiotropic, one can employ methods based on the reverse regression of genotype on phenotypes. Recently, we proposed a method based functional linear models (Vsevolozhskaya et al, 2016) that utilizes reverse regression and simultaneously evaluates all variants within a genetic region for an association with multiple correlated phenotypes. Here we apply our novel methodology to explore pleiotropic effects of CSF analtyes using Alzheimer\u27s Disease Neuroimaging Initiative (ADNI) data

Single Channel Analysis of Conductance and Rectification in Cation-selective, Mutant Glycine Receptor Channels

Members of the ligand-gated ion channel superfamily mediate fast synaptic transmission in the nervous system. In this study, we investigate the molecular determinants and mechanisms of ion permeation and ion charge selectivity in this family of channels by characterizing the single channel conductance and rectification of α1 homomeric human glycine receptor channels (GlyRs) containing pore mutations that impart cation selectivity. The A-1'E mutant GlyR and the selectivity double mutant ([SDM], A-1'E, P-2'Δ) GlyR, had mean inward chord conductances (at −60 mV) of 7 pS and mean outward conductances of 11 and 12 pS (60 mV), respectively. This indicates that the mutations have not simply reduced anion permeability, but have replaced the previous anion conductance with a cation one. An additional mutation to neutralize the ring of positive charge at the extracellular mouth of the channel (SDM+R19'A GlyR) made the conductance–voltage relationship linear (14 pS at both 60 and −60 mV). When this external charged ring was made negative (SDM+R19'E GlyR), the inward conductance was further increased (to 22 pS) and now became sensitive to external divalent cations (being 32 pS in their absence). The effects of the mutations to the external ring of charge on conductance and rectification could be fit to a model where only the main external energy barrier height for permeation was changed. Mean outward conductances in the SDM+R19'A and SDM+R19'E GlyRs were increased when internal divalent cations were absent, consistent with the intracellular end of the pore being flanked by fixed negative charges. This supports our hypothesis that the ion charge selectivity mutations have inverted the electrostatic profile of the pore by introducing a negatively charged ring at the putative selectivity filter. These results also further confirm the role of external pore vestibule electrostatics in determining the conductance and rectification properties of the ligand-gated ion channels

Uncovering Local Trends in Genetic Effects of Multiple Phenotypes via Functional Linear Models

Recent technological advances equipped researchers with capabilities that go beyond traditional genotyping of loci known to be polymorphic in a general population. Genetic sequences of study participants can now be assessed directly. This capability removed technology-driven bias toward scoring predominantly common polymorphisms and let researchers reveal a wealth of rare and sample-specific variants. Although the relative contributions of rare and common polymorphisms to trait variation are being debated, researchers are faced with the need for new statistical tools for simultaneous evaluation of all variants within a region. Several research groups demonstrated flexibility and good statistical power of the functional linear model approach. In this work we extend previous developments to allow inclusion of multiple traits and adjustment for additional covariates. Our functional approach is unique in that it provides a nuanced depiction of effects and interactions for the variables in the model by representing them as curves varying over a genetic region. We demonstrate flexibility and competitive power of our approach by contrasting its performance with commonly used statistical tools and illustrate its potential for discovery and characterization of genetic architecture of complex traits using sequencing data from the Dallas Heart Study