Scalable Bayesian Divergence Time Estimation With Ratio Transformations.

Divergence time estimation is crucial to provide temporal signals for dating biologically important events from species divergence to viral transmissions in space and time. With the advent of high-throughput sequencing, recent Bayesian phylogenetic studies have analyzed hundreds to thousands of sequences. Such large-scale analyses challenge divergence time reconstruction by requiring inference on highly correlated internal node heights that often become computationally infeasible. To overcome this limitation, we explore a ratio transformation that maps the original $N-1$ internal node heights into a space of one height parameter and $N-2$ ratio parameters. To make the analyses scalable, we develop a collection of linear-time algorithms to compute the gradient and Jacobian-associated terms of the log-likelihood with respect to these ratios. We then apply Hamiltonian Monte Carlo sampling with the ratio transform in a Bayesian framework to learn the divergence times in 4 pathogenic viruses (West Nile virus, rabies virus, Lassa virus, and Ebola virus) and the coralline red algae. Our method both resolves a mixing issue in the West Nile virus example and improves inference efficiency by at least 5-fold for the Lassa and rabies virus examples as well as for the algae example. Our method now also makes it computationally feasible to incorporate mixed-effects molecular clock models for the Ebola virus example, confirms the findings from the original study, and reveals clearer multimodal distributions of the divergence times of some clades of interest.

Low-coverage whole genome sequencing for highly accurate population assignment: Mapping migratory connectivity in the American Redstart (Setophaga ruticilla).

Understanding the geographic linkages among populations across the annual cycle is an essential component for understanding the ecology and evolution of migratory species and for facilitating their effective conservation. While genetic markers have been widely applied to describe migratory connections, the rapid development of new sequencing methods, such as low-coverage whole genome sequencing (lcWGS), provides new opportunities for improved estimates of migratory connectivity. Here, we use lcWGS to identify fine-scale population structure in a widespread songbird, the American Redstart (Setophaga ruticilla), and accurately assign individuals to genetically distinct breeding populations. Assignment of individuals from the nonbreeding range reveals population-specific patterns of varying migratory connectivity. By combining migratory connectivity results with demographic analysis of population abundance and trends, we consider full annual cycle conservation strategies for preserving numbers of individuals and genetic diversity. Notably, we highlight the importance of the Northern Temperate-Greater Antilles migratory population as containing the largest proportion of individuals in the species. Finally, we highlight valuable considerations for other population assignment studies aimed at using lcWGS. Our results have broad implications for improving our understanding of the ecology and evolution of migratory species through conservation genomics approaches.

On the Q statistic with constant weights in meta-analysis of binary outcomes.

BACKGROUND: Cochran's Q statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value (under an incorrect null distribution) is part of several popular estimators of the between-study variance, [Formula: see text]. Those applications generally do not account for use of the studies' estimated variances in the inverse-variance weights that define Q (more explicitly, [Formula: see text]). Importantly, those weights make approximating the distribution of [Formula: see text] rather complicated. METHODS: As an alternative, we are investigating a Q statistic, [Formula: see text], whose constant weights use only the studies' arm-level sample sizes. For log-odds-ratio (LOR), log-relative-risk (LRR), and risk difference (RD) as the measures of effect, we study, by simulation, approximations to distributions of [Formula: see text] and [Formula: see text], as the basis for tests of heterogeneity. RESULTS: The results show that: for LOR and LRR, a two-moment gamma approximation to the distribution of [Formula: see text] works well for small sample sizes, and an approximation based on an algorithm of Farebrother is recommended for larger sample sizes. For RD, the Farebrother approximation works very well, even for small sample sizes. For [Formula: see text], the standard chi-square approximation provides levels that are much too low for LOR and LRR and too high for RD. The Kulinskaya et al. (Res Synth Methods 2:254-70, 2011) approximation for RD and the Kulinskaya and Dollinger (BMC Med Res Methodol 15:49, 2015) approximation for LOR work well for [Formula: see text] but have some convergence issues for very small sample sizes combined with small probabilities. CONCLUSIONS: The performance of the standard [Formula: see text] approximation is inadequate for all three binary effect measures. Instead, we recommend a test of heterogeneity based on [Formula: see text] and provide practical guidelines for choosing an appropriate test at the .05 level for all three effect measures.

Power and sample size for observational studies of point exposure effects.

Inverse probability of treatment weights (IPTWs) are commonly used to control for confounding when estimating causal effects of point exposures from observational data. When planning a study that will be analyzed with IPTWs, determining the required sample size for a given level of statistical power is challenging because of the effect of weighting on the variance of the estimated causal means. This paper considers the utility of the design effect to quantify the effect of weighting on the precision of causal estimates. The design effect is defined as the ratio of the variance of the causal mean estimator divided by the variance of a naïve estimator if, counter to fact, no confounding had been present and weights were not needed. A simple, closed-form approximation of the design effect is derived that is outcome invariant and can be estimated during the study design phase. Once the design effect is approximated for each treatment group, sample size calculations are conducted as for a randomized trial, but with variances inflated by the design effects to account for weighting. Simulations demonstrate the accuracy of the design effect approximation, and practical considerations are discussed.

Propensity-score-based meta-analytic predictive prior for incorporating real-world and historical data.

As the availability of real-world data sources (eg, EHRs, claims data, registries) and historical data has rapidly surged in recent years, there is an increasing interest and need from investigators and health authorities to leverage all available information to reduce patient burden and accelerate both drug development and regulatory decision making. Bayesian meta-analytic approaches are a popular historical borrowing method that has been developed to leverage such data using robust hierarchical models. The model structure accounts for various degrees of between-trial heterogeneity, resulting in adaptively discounting the external information in the case of data conflict. In this article, we propose to integrate the propensity score method and Bayesian meta-analytic-predictive (MAP) prior to leverage external real-world and historical data. The propensity score methodology is applied to select a subset of patients from external data that are similar to those in the current study with regards to key baseline covariates and to stratify the selected patients together with those in the current study into more homogeneous strata. The MAP prior approach is used to obtain stratum-specific MAP prior and derive the overall propensity score integrated meta-analytic predictive (PS-MAP) prior. Additionally, we allow for tuning the prior effective sample size for the proposed PS-MAP prior, which quantifies the amount of information borrowed from external data. We evaluate the performance of the proposed PS-MAP prior by comparing it to the existing propensity score-integrated power prior approach in a simulation study and illustrate its implementation with an example of a single-arm phase II trial.

Quantification of prior impact in terms of effective current sample size.

Bayesian methods allow borrowing of historical information through prior distributions. The concept of prior effective sample size (prior ESS) facilitates quantification and communication of such prior information by equating it to a sample size. Prior information can arise from historical observations; thus, the traditional approach identifies the ESS with such a historical sample size. However, this measure is independent of newly observed data, and thus would not capture an actual "loss of information" induced by the prior in case of prior-data conflict. We build on a recent work to relate prior impact to the number of (virtual) samples from the current data model and introduce the effective current sample size (ECSS) of a prior, tailored to the application in Bayesian clinical trial designs. Special emphasis is put on robust mixture, power, and commensurate priors. We apply the approach to an adaptive design in which the number of recruited patients is adjusted depending on the effective sample size at an interim analysis. We argue that the ECSS is the appropriate measure in this case, as the aim is to save current (as opposed to historical) patients from recruitment. Furthermore, the ECSS can help overcome lack of consensus in the ESS assessment of mixture priors and can, more broadly, provide further insights into the impact of priors. An R package accompanies the paper.

kg_nchs: A command for Korn-Graubard confidence intervals and National Center for Health Statistics' Data Presentation Standards for Proportions.

In August 2017 the National Center for Health Statistics (NCHS), part of the U.S. Federal Statistical System, published new standards for determining the reliability of proportions estimated using their data. These standards require an individual to take the Korn-Graubard confidence interval (CI), along with CI widths, sample size, and degrees of freedom, to assess reliability of a proportion and determine if it can be presented. The assessment itself involves determining if several conditions are met. This manuscript presents kg_nchs, a postestimation command that is used following svy: proportion. It allows Stata users to (a) calculate the Korn-Graubard CI and associated statistics used in applying the NCHS presentation standards for proportions, and (b) display a series of three dichotomous flags that show if the standards are met. The empirical examples provided show how kg_nchs can be used to easily apply the standards and prevent Stata users from needing to perform manual calculations. While developed for NCHS survey data, this command can also be used with data that stems from any survey with a complex sample design.

Quantifying and presenting overall evidence in network meta-analysis.

Network meta-analysis (NMA) has become an increasingly used tool to compare multiple treatments simultaneously by synthesizing direct and indirect evidence in clinical research. However, many existing studies did not properly report the evidence of treatment comparisons and show the comparison structure to audience. In addition, nearly all treatment networks presented only direct evidence, not overall evidence that can reflect the benefit of performing NMAs. This article classifies treatment networks into three types under different assumptions; they include networks with each treatment comparison's edge width proportional to the corresponding number of studies, sample size, and precision. In addition, three new measures (ie, the effective number of studies, the effective sample size, and the effective precision) are proposed to preliminarily quantify overall evidence gained in NMAs. They permit audience to intuitively evaluate the benefit of performing NMAs, compared with pairwise meta-analyses based on only direct evidence. We use four case studies, including one illustrative example, to demonstrate their derivations and interpretations. Treatment networks may look fairly differently when different measures are used to present the evidence. The proposed measures provide clear information about overall evidence of all treatment comparisons, and they also imply the additional number of studies, sample size, and precision obtained from indirect evidence. Some comparisons may benefit little from NMAs. Researchers are encouraged to present overall evidence of all treatment comparisons, so that audience can preliminarily evaluate the quality of NMAs.

Statistical modeling for Bayesian extrapolation of adult clinical trial information in pediatric drug evaluation.

Children represent a large underserved population of "therapeutic orphans," as an estimated 80% of children are treated off-label. However, pediatric drug development often faces substantial challenges, including economic, logistical, technical, and ethical barriers, among others. Among many efforts trying to remove these barriers, increased recent attention has been paid to extrapolation; that is, the leveraging of available data from adults or older age groups to draw conclusions for the pediatric population. The Bayesian statistical paradigm is natural in this setting, as it permits the combining (or "borrowing") of information across disparate sources, such as the adult and pediatric data. In this paper, authored by the pediatric subteam of the Drug Information Association Bayesian Scientific Working Group and Adaptive Design Working Group, we develop, illustrate, and provide suggestions on Bayesian statistical methods that could be used to design improved pediatric development programs that use all available information in the most efficient manner. A variety of relevant Bayesian approaches are described, several of which are illustrated through 2 case studies: extrapolating adult efficacy data to expand the labeling for Remicade to include pediatric ulcerative colitis and extrapolating adult exposure-response information for antiepileptic drugs to pediatrics.

Phylogenetic effective sample size.

In this paper I address the question-how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes-the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.

Exploring effective sampling design for monitoring soil organic carbon in degraded Tibetan grasslands.

The effects of climate change and human activities on grassland degradation and soil carbon stocks have become a focus of both research and policy. However, lack of research on appropriate sampling design prevents accurate assessment of soil carbon stocks and stock changes at community and regional scales. Here, we conducted an intensive survey with 1196 sampling sites over an area of 190 km(2) of degraded alpine meadow. Compared to lightly degraded meadow, soil organic carbon (SOC) stocks in moderately, heavily and extremely degraded meadow were reduced by 11.0%, 13.5% and 17.9%, respectively. Our field survey sampling design was overly intensive to estimate SOC status with a tolerable uncertainty of 10%. Power analysis showed that the optimal sampling density to achieve the desired accuracy would be 2, 3, 5 and 7 sites per 10 km(2) for lightly, moderately, heavily and extremely degraded meadows, respectively. If a subsequent paired sampling design with the optimum sample size were performed, assuming stock change rates predicted by experimental and modeling results, we estimate that about 5-10 years would be necessary to detect expected trends in SOC in the top 20 cm soil layer. Our results highlight the utility of conducting preliminary surveys to estimate the appropriate sampling density and avoid wasting resources due to over-sampling, and to estimate the sampling interval required to detect an expected sequestration rate. Future studies will be needed to evaluate spatial and temporal patterns of SOC variability.

Risk management for moisture related effects in dry manufacturing processes: a statistical approach.

A risk- and science-based approach to control the quality in pharmaceutical manufacturing includes a full understanding of how product attributes and process parameters relate to product performance through a proactive approach in formulation and process development. For dry manufacturing, where moisture content is not directly manipulated within the process, the variability in moisture of the incoming raw materials can impact both the processability and drug product quality attributes. A statistical approach is developed using individual raw material historical lots as a basis for the calculation of tolerance intervals for drug product moisture content so that risks associated with excursions in moisture content can be mitigated. The proposed method is based on a model-independent approach that uses available data to estimate parameters of interest that describe the population of blend moisture content values and which do not require knowledge of the individual blend moisture content values. Another advantage of the proposed tolerance intervals is that, it does not require the use of tabulated values for tolerance factors. This facilitates the implementation on any spreadsheet program like Microsoft Excel. A computational example is used to demonstrate the proposed method.

How Trustworthy Is Your Tree? Bayesian Phylogenetic Effective Sample Size Through the Lens of Monte Carlo Error.

Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC) run explores the space of phylogenetic trees. In this paper, we investigate the Monte Carlo error of phylogenies, focusing on high-dimensional summaries of the posterior distribution, including variability in estimated edge/branch (known in phylogenetics as "split") probabilities and tree probabilities, and variability in the estimated summary tree. Specifically, we ask if there is any measure of effective sample size (ESS) applicable to phylogenetic trees which is capable of capturing the Monte Carlo error of these three summary measures. We find that there are some ESS measures capable of capturing the error inherent in using MCMC samples to approximate the posterior distributions on phylogenies. We term these tree ESS measures, and identify a set of three which are useful in practice for assessing the Monte Carlo error. Lastly, we present visualization tools that can improve comparisons between multiple independent MCMC runs by accounting for the Monte Carlo error present in each chain. Our results indicate that common post-MCMC workflows are insufficient to capture the inherent Monte Carlo error of the tree, and highlight the need for both within-chain mixing and between-chain convergence assessments.

BayesESS: A tool for quantifying the impact of parametric priors in Bayesian analysis.

Bayesian inference has become an attractive choice for scientists seeking to incorporate prior knowledge into their modeling framework. While the R community has been an important contributor in facilitating Bayesian statistical analyses, software to evaluate the impact of prior knowledge to such modeling framework has been lacking. In this article, we present BayesESS, a comprehensive, free, and open source R package for quantifying the impact of parametric priors in Bayesian analysis. We also introduce an accompanying web-based application for estimating and visualizing Bayesian effective sample size for purposes of conducting or planning Bayesian analyses.

Estimation of heterogeneity variance based on a generalized Q statistic in meta-analysis of log-odds-ratio.

For estimation of heterogeneity variance τ 2 in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized Q statistic, Q F , in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators based on the inverse-variance-weights version of Q , Q IV . In an extensive simulation, we studied the bias (including median bias) of the point estimators and the coverage (including left and right coverage error) of the confidence intervals. Most estimators add 0.5 to each cell of the 2 × 2 table when one cell contains a zero count; we include a version that always adds 0.5 . The results show that: two of the new point estimators and two of the familiar point estimators are almost unbiased when the total sample size n ≥ 250 and the probability in the Control arm ( p iC ) is 0.1, and when n ≥ 100 and p iC is 0.2 or 0.5; for 0.1 ≤ τ 2 ≤ 1 , all estimators have negative bias for small to medium sample sizes, but for larger sample sizes some of the new median-unbiased estimators are almost median-unbiased; choices of interval estimators depend on values of parameters, but one of the new estimators is reasonable when p iC = 0.1 and another, when p iC = 0.2 or p iC = 0.5 ; and lack of balance between left and right coverage errors for small n and/or p iC implies that the available approximations for the distributions of Q IV and Q F are accurate only for larger sample sizes.

Pervasive Downward Bias in Estimates of Liability-Scale Heritability in Genome-wide Association Study Meta-analysis: A Simple Solution.

BACKGROUND: Single nucleotide polymorphism-based heritability is a fundamental quantity in the genetic analysis of complex traits. For case-control phenotypes, for which the continuous distribution of risk in the population is unobserved, observed-scale heritability estimates must be transformed to the more interpretable liability scale. This article describes how the field standard approach incorrectly performs the liability correction in that it does not appropriately account for variation in the proportion of cases across the cohorts comprising the meta-analysis. We propose a simple solution that incorporates cohort-specific ascertainment using the summation of effective sample sizes across cohorts. This solution is applied at the stage of single nucleotide polymorphism-based heritability estimation and does not require generating updated meta-analytic genome-wide association study summary statistics. METHODS: We began by performing a series of simulations to examine the ability of the standard approach and our proposed approach to recapture liability-scale heritability in the population. We went on to examine the differences in estimates obtained from these 2 approaches for real data for 12 major case-control genome-wide association studies of psychiatric and neurologic traits. RESULTS: We found that the field standard approach for performing the liability conversion can downwardly bias estimates by as much as approximately 50% in simulation and approximately 30% in real data. CONCLUSIONS: Prior estimates of liability-scale heritability for genome-wide association study meta-analysis may be drastically underestimated. To this end, we strongly recommend using our proposed approach of using the sum of effective sample sizes across contributing cohorts to obtain unbiased estimates.

Intra-cluster correlations in socio-demographic variables and their implications: An analysis based on large-scale surveys in India.

Individuals who share similar socio-economic and cultural characteristics also share similar health outcomes. Consequently, they have a propensity to cluster together, which results in positive intra-class correlation coefficients (ICCs) in their socio-demographic and behavioural characteristics. In this study, using data from four rounds of the National Family Health Survey (NFHS), we estimated the ICC for selected socio-demographic and behavioural characteristics in rural and urban areas of six states namely Assam, Gujarat, Kerala, Punjab, Uttar Pradesh, and West Bengal. The socio-demographic and behavioural characteristics included religion & caste of the household head, use of contraception & prevalence of anaemia among currently married women and coverage of full immunization services among children aged 12-23 months. ICC was computed at the level ofPrimary Sampling Units (PSUs), that is, villages in rural areas and census enumeration blocks in urban areas. Our research highlights high clustering in terms of religion and caste within PSUs in India. In NFHS-4, the ICCs for religion ranged from the lowest of 0.19 in rural areas of Kerala to the highest of 0.67 in urban areas of West Bengal. For the caste of the household head, the ICCs ranged from the lowest of 0.12 in the urban areas of Punjab to the highest of 0.46 in the rural areas of Assam. In most of the states selected for the study, the values of ICC were higher for the use of family planning methods than for full immunization. The value of ICC for use of contraception was highest for rural areas of Assam (0.15) followed by rural areas of Gujarat (0.13). A higher value of ICC has considerable implications for determining an effective sample size for large-scale surveys. Our findings agree with the fact that for a given cluster size, the higher the value of ICC, the higher is the loss in precision of the estimate. Knowing and taking into account ICCs can be extremely helpful in determining an effective sample size when designing a large-scale demographic and health survey to arrive at estimates of parameters with the desired precision.

Challenges, opportunities and recent advances in near infrared spectroscopy applications for monitoring blend uniformity in the continuous manufacturing of solid oral dosage forms.

Near infrared (NIR) spectroscopy has been widely recognized as a powerful PAT tool for monitoring blend uniformity in continuous manufacturing (CM) processes. However, the dynamic nature of the powder stream and the fast rate at which it moves, compared to batch processes, introduces challenges to NIR quantitative methods for monitoring blend uniformity. For instance, defining the effective sample size interrogated by NIR, selecting the best sampling location for blend monitoring, and ensuring NIR model robustness against influential sources of variability are challenges commonly reported for NIR applications in CM. This article reviews the NIR applications for powder blend monitoring in the continuous manufacturing of solid oral dosage forms, with a particular focus on the challenges, opportunities for method optimization and recent advances with respect three main aspects: effective sample size measured by NIR, probe location and method robustness.

Cumulative meta-analysis: What works.

To present time-varying evidence, cumulative meta-analysis (CMA) updates results of previous meta-analyses to incorporate new study results. We investigate the properties of CMA, suggest possible improvements and provide the first in-depth simulation study of the use of CMA and CUSUM methods for detection of temporal trends in random-effects meta-analysis. We use the standardized mean difference (SMD) as an effect measure of interest. For CMA, we compare the standard inverse-variance-weighted estimation of the overall effect using REML-based estimation of between-study variance τ 2 with the sample-size-weighted estimation of the effect accompanied by Kulinskaya-Dollinger-Bjørkestøl (Biometrics. 2011; 67:203-212) (KDB) estimation of τ 2 . For all methods, we consider Type 1 error under no shift and power under a shift in the mean in the random-effects model. To ameliorate the lack of power in CMA, we introduce two-stage CMA, in which τ 2 is estimated at Stage 1 (from the first 5-10 studies), and further CMA monitors a target value of effect, keeping the τ 2 value fixed. We recommend this two-stage CMA combined with cumulative testing for positive shift in τ 2 . In practice, use of CMA requires at least 15-20 studies.

Estimating the effective sample size in association studies of quantitative traits.

The effective sample size (ESS) is a metric used to summarize in a single term the amount of correlation in a sample. It is of particular interest when predicting the statistical power of genome-wide association studies (GWAS) based on linear mixed models. Here, we introduce an analytical form of the ESS for mixed-model GWAS of quantitative traits and relate it to empirical estimators recently proposed. Using our framework, we derived approximations of the ESS for analyses of related and unrelated samples and for both marginal genetic and gene-environment interaction tests. We conducted simulations to validate our approximations and to provide a quantitative perspective on the statistical power of various scenarios, including power loss due to family relatedness and power gains due to conditioning on the polygenic signal. Our analyses also demonstrate that the power of gene-environment interaction GWAS in related individuals strongly depends on the family structure and exposure distribution. Finally, we performed a series of mixed-model GWAS on data from the UK Biobank and confirmed the simulation results. We notably found that the expected power drop due to family relatedness in the UK Biobank is negligible.