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Analyses of population-based surveys are instrumental to research on prevention and treatment of mental and substance use disorders. Population-based data provides descriptive characteristics of multiple determinants of public health and are typically available to researchers as an annual data release. To provide trends in national estimates or to update the existing ones, a meta-analytical approach to year-by-year data is typically employed with ORs as effect sizes. However, if the estimated ORs exhibit different patterns over time, some normalization of ORs may be warranted. We propose a new normalized measure of effect size and derive an asymptotic distribution for the respective test statistic. The normalization constant is based on the maximum range of the standardized log(OR), for which we establish a connection to the Laplace Limit Constant. Furthermore, we propose to employ standardized log(OR) in a novel way to obtain accurate posterior inference. Through simulation studies, we show that our new statistic is more powerful than the traditional one for testing the hypothesis OR=1. We then applied it to the United States population estimates of co-occurrence of side effect problem-experiences (SEPE) among newly incident cannabis users, based on the the National Survey on Drug Use and Health (NSDUH), 2004-2014., arXiv admin note: substantial text overlap with arXiv:1806.04251

The odds ratio (OR) is a measure of effect size commonly used in observational research. OR reflects statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure to a pollutant. Statistical inference and interval estimation for OR are often performed on the logarithmic scale, due to asymptotic convergence of log(OR) to a normal distribution. Here, we propose a new normalized measure of effect size, $\gamma'$, and derive its asymptotic distribution. We show that the new statistic, based on the $\gamma'$ distribution, is more powerful than the traditional one for testing the hypothesis $H_0$: log(OR)=0. The new normalized effect size is termed `gamma prime' in the spirit of $D'$, a normalized measure of genetic linkage disequilibrium, which ranges from -1 to 1 for a pair of genetic loci. The normalization constant for $\gamma'$ is based on the maximum range of the standardized effect size, for which we establish a peculiar connection to the Laplace Limit Constant. Furthermore, while standardized effects are of little value on their own, we propose a powerful application, in which standardized effects are employed as an intermediate step in an approximate, yet accurate posterior inference for raw effect size measures, such as log(OR) and $\gamma'$.

The odds ratio (OR) is a widely used measure of the effect size in observational research. ORs reflect statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure to a pollutant. Statistical significance and interval estimates are often computed for the logarithm of OR, ln(OR), and depend on the asymptotic standard error of ln(OR). For a sample of size N, the standard error can be written as a ratio of sigma over square root of N, where sigma is the population standard deviation of ln(OR). The ratio of ln(OR) over sigma is a standardized effect size. Unlike correlation, that is another familiar standardized statistic, the standardized ln(OR) cannot reach values of minus one or one. We find that its maximum possible value is given by the Laplace Limit Constant, (LLC=0.6627...), that appears as a condition in solutions to Kepler equation -- one of the central equations in celestial mechanics. The range of the standardized ln(OR) is bounded by minus LLC to LLC, reaching its maximum for ln(OR)~4.7987. This range has implications for analysis of epidemiological associations, affecting the behavior of the reasonable prior distribution for the standardized ln(OR).

Increased availability of data and accessibility of computational tools in recent years have created unprecedented opportunities for scientific research driven by statistical analysis. Inherent limitations of statistics impose constrains on reliability of conclusions drawn from data but misuse of statistical methods is a growing concern. Significance, hypothesis testing and the accompanying P-values are being scrutinized as representing 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 scientific hypothesis's credibility. 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, likely to obtain a much larger P-value in a similarly powered replication study. Thus, "replicability of P-value" is 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 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. As an alternative to P-intervals, we develop a method that gives researchers flexibility by providing them with the means to control these assumptions. Unlike endpoints of P-intervals, endpoints of our intervals are directly interpreted as probabilistic bounds for replication P-values and are resistant to selection bias contingent upon approximate prior knowledge of the effect size distribution., Corrected typos

Increasing accessibility of data to researchers makes it possible to conduct massive amounts of statistical testing. Rather than follow a carefully crafted set of scientific hypotheses with statistical analysis, researchers can now test many possible relations and let P-values or other statistical summaries generate hypotheses for them. Genetic epidemiology field is an illustrative case in this paradigm shift. Driven by technological advances, testing a handful of genetic variants in relation to a health outcome has been abandoned in favor of agnostic screening of the entire genome, followed by selection of top hits, e.g., by selection of genetic variants with the smallest association P-values. At the same time, nearly total lack of replication of claimed associations that has been shaming the field turned to a flow of reports whose findings have been robustly replicating. Researchers may have adopted better statistical practices by learning from past failures, but we suggest that a steep increase in the amount of statistical testing itself is an important factor. Regardless of whether statistical significance has been reached, an increased number of tested hypotheses leads to enrichment of smallest P-values with genuine associations. In this study, we quantify how the expected proportion of genuine signals (EPGS) among top hits changes with an increasing number of tests. When the rate of occurrence of genuine signals does not decrease too sharply to zero as more tests are performed, the smallest P-values are increasingly more likely to represent genuine associations in studies with more tests.

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.

The μ-opioid receptor (OPRM1) is the principal receptor target for both endogenous and exogenous opioid analgesics. There are substantial individual differences in human responses to painful stimuli and to opiate drugs that are attributed to genetic variations in OPRM1. In searching for new functional variants, we employed comparative genome analysis and obtained evidence for the existence of an expanded human OPRM1 gene locus with new promoters, alternative exons and regulatory elements. Examination of polymorphisms within the human OPRM1 gene locus identified strong association between single nucleotide polymorphism (SNP) rs563649 and individual variations in pain perception. SNP rs563649 is located within a structurally conserved internal ribosome entry site (IRES) in the 5′-UTR of a novel exon 13-containing OPRM1 isoforms (MOR-1K) and affects both mRNA levels and translation efficiency of these variants. Furthermore, rs563649 exhibits very strong linkage disequilibrium throughout the entire OPRM1 gene locus and thus affects the functional contribution of the corresponding haplotype that includes other functional OPRM1 SNPs. Our results provide evidence for an essential role for MOR-1K isoforms in nociceptive signaling and suggest that genetic variations in alternative OPRM1 isoforms may contribute to individual differences in opiate responses.

The EGFR belongs to the well-studied ErbB family of receptor tyrosine kinases. EGFR is activated by numerous endogenous ligands that promote cellular growth, proliferation, and tissue regeneration. In the present study, we have demonstrated a role for EGFR and its natural ligand, epiregulin (EREG), in pain processing. We show that inhibition of EGFR with clinically available compounds strongly reduced nocifensive behavior in mouse models of inflammatory and chronic pain. EREG-mediated activation of EGFR enhanced nociception through a mechanism involving the PI3K/AKT/mTOR pathway and matrix metalloproteinase-9. Moreover, EREG application potentiated capsaicin-induced calcium influx in a subset of sensory neurons. Both the EGFR and EREG genes displayed a genetic association with the development of chronic pain in several clinical cohorts of temporomandibular disorder. Thus, EGFR and EREG may be suitable therapeutic targets for persistent pain conditions.