Detecting correlation between characters in a comparative analysis with uncertain phylogeny

Abstract.— The importance of accommodating the phylogenetic history of a group when performing a comparative analysis is now widely recognized. The typical approaches either assume the tree is known without error, or they base inferences on a collection of well-supported trees or on a collection of trees generated under a stochastic model of cladogenesis. However, these approaches do not adequately account for the uncertainty of phylogenetic trees in a comparative analysis, especially when data relevant to the phylogeny of a group are available. Here, we develop a method for performing comparative analyses that is based on an extension of Felsenstein's independent contrasts method. Uncertainties in the phylogeny, branch lengths, and other parameters are accommodated by averaging over all possible trees, weighting each by the probability that the tree is correct. We do this in a Bayesian framework and use Markov chain Monte Carlo to perform the high-dimensional summations and integrations required by the analysis. We illustrate the method using comparative characters sampled from Anolis lizards.     

Toward a realistic model of mutations affecting fitness

Analysis of a recent mutation accumulation (MA) experiment has led to the suggestion that as many as one-half of spontaneous mutations in Arabidopsis are advantageous for fitness. We evaluate this in the light of data from other MA experiments, along with molecular evidence, that suggest the vast majority of new mutations are deleterious.     

Testing for genetic evidence of population expansion and contraction: an empirical analysis of microsatellite DNA variation using a hierarchical Bayesian model

The role of past climatic change in shaping the distributions of tropical rain forest vertebrates is central to long-standing hypotheses about the legacy of the Quaternary ice ages. One approach to testing such hypotheses is to use genetic data to infer the demographic history of codistributed species. Population genetic theory that relates the structure of allelic genealogies to historical changes in effective population size can be used to detect a past history of demographic expansion or contraction. The fruit bats Cynopterus sphinx and C. brachyotis (Chiroptera: Pteropodidae) exhibit markedly different distribution patterns across the Indomalayan region and therefore represent an exemplary species pair to use for such tests. The purpose of this study was to test alternative hypotheses about historical patterns of demographic expansion and contraction in C. sphinx and C. brachyotis using a coalescent-based analysis of microsatellite variation. Specifically, we used a hierarchical Bayesian model based on Markov chain Monte Carlo simulations to estimate the posterior distribution of genealogical and demographic parameters. The results revealed strong evidence for population contraction in both species. Evidence for a population contraction in C. brachyotis was expected on the basis of biogeographic considerations. However, similar evidence for population contraction in C. sphinx does not support the hypothesis that this species underwent a pronounced range expansion during the late Quaternary. Genetic evidence for population decline may reflect the consequences of habitat destruction on a more recent time scale.     

Statistical inference for familial disease clusters

In many epidemiologic studies, the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units. The concept of clustering is contrasted with incidence. We assume that all individuals are exchangeable except for their disease status. This assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease, conditional on the number of diseased cases and the distribution of the sizes of the various family units. New parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering. We consider models and an example that takes covariates into account. Ascertainment bias is described and the appropriate sampling distribution is demonstrated. Four numerical examples with real data illustrate these methods.     

The epidemiology and iatrogenic transmission of hepatitis C virus in Egypt: a Bayesian coalescent approach

Hepatitis C virus (HCV) is a leading cause of liver cancer and cirrhosis, and Egypt has possibly the highest HCV prevalence worldwide. In this article we use a newly developed Bayesian inference framework to estimate the transmission dynamics of HCV in Egypt from sampled viral gene sequences, and to predict the public health impact of the virus. Our results indicate that the effective number of HCV infections in Egypt underwent rapid exponential growth between 1930 and 1955. The timing and speed of this spread provides quantitative genetic evidence that the Egyptian HCV epidemic was initiated and propagated by extensive antischistosomiasis injection campaigns. Although our results show that HCV transmission has since decreased, we conclude that HCV is likely to remain prevalent in Egypt for several decades. Our combined population genetic and epidemiological analysis provides detailed estimates of historical changes in Egyptian HCV prevalence. Because our results are consistent with a demographic scenario specified a priori, they also provide an objective test of inference methods based on the coalescent process.     

The compliance score as a regressor in randomized trials

The compliance score in randomized trials is a measure of the effect of randomization on treatment received. It is in principle a group-level pretreatment variable and so can be used where individual-level measures of treatment received can produce misleading inferences. The interpretation of models with the compliance score as a regressor of interest depends on the link function. Using the identity link can lead to valid inference about the effects of treatment received even in the presence of nonrandom noncompliance; such inference is more problematic for nonlinear links. We illustrate these points with data from two randomized trials.     

Insights on bias and information in group-level studies

Ecological and aggregate data studies are examples of group-level studies. Even though the link between the predictors and outcomes is not preserved in these studies, inference about individual-level exposure effects is often a goal. The disconnection between the level of inference and the level of analysis expands the array of potential biases that can invalidate the inference from group-level studies. While several sources of bias, specifically due to measurement error and confounding, may be more complex in group-level studies, two sources of bias, cross-level and model specification bias, are a direct consequence of the disconnection. With the goal of aligning inference from individual versus group-level studies, I discuss the interplay between exposure and study design. I specify the additional assumptions necessary for valid inference, specifically that the between- and within-group exposure effects are equal. Then cross-level inference is possible. However, all the information in the group-level analysis comes from between-group comparisons. Models where the group-level analysis provides even a small percentage of information about the within-group exposure effect are most susceptible to model specification bias. Model specification bias can be even more serious when the group-level model isn't derived from an individual-level model.     

Should we take measurements at an intermediate design point?

It is well known that, for estimating a linear treatment effect with constant variance, the optimal design divides the units equally between the two extremes of the design space. If the dose-response relation may be nonlinear, however, intermediate measurements may be useful in order to estimate the effects of partial treatments. We consider the decision of whether to gather data at an intermediate design point: do the gains from learning about nonlinearity outweigh the loss in efficiency in estimating the linear effect? Under reasonable assumptions about nonlinearity, we find that, unless sample size is very large, the design with no interior measurements is best, because with moderate total sample sizes, any nonlinearity in the dose-response will be difficult to detect. We discuss in the context of a simplified version of the problem that motivated this work-a study of pest-control treatments intended to reduce asthma symptoms in children.