Bounds on the average causal effects in randomized trials with noncompliance by covariate adjustment

In randomized trials with noncompliance, causal effects cannot be identified without strong assumptions. Therefore, several authors have considered bounds on the causal effects. Applying an idea of VanderWeele ( 2008 ), Chiba ( 2009 ) gave bounds on the average causal effects in randomized trials with noncompliance using the information on the randomized assignment, the treatment received and the outcome under monotonicity assumptions about covariates. But he did not consider any observed covariates. If there are some observed covariates such as age, gender, and race in a trial, we propose new bounds using the observed covariate information under some monotonicity assumptions similar to those of VanderWeele and Chiba. And we compare the three bounds in a real example.     

Covariate selection strategies for causal inference: Classification and comparison

When causal effects are to be estimated from observational data, we have to adjust for confounding. A central aim of covariate selection for causal inference is therefore to determine a set that is sufficient for confounding adjustment, but other aims such as efficiency or robustness can be important as well. In this paper, we review six general approaches to covariate selection that differ in the targeted type of adjustment set. We discuss and illustrate their advantages and disadvantages using causal diagrams. Moreover, the approaches and different ways of implementing them are compared empirically in an extensive simulation study. We conclude that there are considerable differences between the approaches but none of them is uniformly best, with performance depending on the chosen adjustment method as well as the true confounding structure. Any prior structural knowledge on the causal relations is helpful to choose the most appropriate method.     

Identification of causal effects with latent confounding and classical additive errors in treatment

In this paper, we discuss the identifiability and estimation of causal effects of a continuous treatment on a binary response when the treatment is measured with errors and there exists a latent categorical confounder associated with both treatment and response. Under some widely used parametric models, we first discuss the identifiability of the causal effects and then propose an approach for estimation and inference. Our approach can eliminate the biases induced by latent confounding and measurement errors by using only a single instrumental variable. Based on the identification results, we give guidelines for determining the existence of a latent categorical confounder and for selecting the number of levels of the latent confounder. We apply the proposed approach to a data set from the Framingham Heart Study to evaluate the effect of the systolic blood pressure on the coronary heart disease.     

Dealing with limited overlap in estimation of average treatment effects

Estimation of average treatment effects under unconfounded orignorable treatment assignment is often hampered by lack ofoverlap in the covariate distributions between treatment groups.This lack of overlap can lead to imprecise estimates, and canmake commonly used estimators sensitive to the choice of specification.In such cases researchers have often used ad hoc methods fortrimming the sample. We develop a systematic approach to addressinglack of overlap. We characterize optimal subsamples for whichthe average treatment effect can be estimated most precisely.Under some conditions, the optimal selection rules depend solelyon the propensity score. For a wide range of distributions,a good approximation to the optimal rule is provided by thesimple rule of thumb to discard all units with estimated propensityscores outside the range [0.1,0.9].     

Fixed and random effects selection in linear and logistic models

We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed effect coefficients or nonzero random effects variance, while allowing uncertainty in the model selection process. Default priors are proposed for the variance components and an efficient parameter expansion Gibbs sampler is developed for posterior computation. The approach is illustrated using simulated data and an epidemiologic example.     

Fixation probability with multiple alleles and projected average allelic effect on selection

The first-order effect of selection on the probability of fixation of an allele, with respect to an intensity of selection s>0 in a diploid population of fixed finite size N, undergoing discrete, non-overlapping generations, is shown to be given by the sum of the average effects of that allele on the coefficient of selection in the current generation and all future generations, given the population state in the current generation. This projected average allelic effect is a weighted sum of average allelic effects in allozygous and autozygous offspring in the initial generation, with weights given in terms of expected coalescence times, under neutrality, for the lineages of two or three gametes chosen at random in the same generation. This is shown in the framework of multiple alleles at one locus, with genotypic values determining either viability or fertility differences, and with either multinomial or exchangeable reproduction schemes. In the limit of weak selection in a large population such that Ns tends to zero, the initial average allelic effects in allozygous offspring and autozygous offspring have the same weight on the fixation probability only in the domain of application of the Kingman coalescent. With frequency-dependent selection in a linear-game-theoretic context with two phenotypes determined by additive gene action, the first-order effect on the fixation probability is a combination of two effects of frequency-independent selection, one in a haploid population, the other in a diploid population. In the domain of application of the Kingman coalescent as the population size goes to infinity and Ns to zero, the first effect is three times more important than the second effect. This explains the one-third law of evolutionary dynamics in this domain, and shows how this law can be extended beyond this domain.     

Imputation and variable selection in linear regression models with missing covariates

Across multiply imputed data sets, variable selection methods such as stepwise regression and other criterion-based strategies that include or exclude particular variables typically result in models with different selected predictors, thus presenting a problem for combining the results from separate complete-data analyses. Here, drawing on a Bayesian framework, we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates. One approach, which we call "impute, then select" (ITS) involves initially performing multiple imputation and then applying Bayesian variable selection to the multiply imputed data sets. A second strategy is to conduct Bayesian variable selection and missing data imputation simultaneously within one Gibbs sampling process, which we call "simultaneously impute and select" (SIAS). The methods are implemented and evaluated using the Bayesian procedure known as stochastic search variable selection for multivariate normal data sets, but both strategies offer general frameworks within which different Bayesian variable selection algorithms could be used for other types of data sets. A study of mental health services utilization among children in foster care programs is used to illustrate the techniques. Simulation studies show that both ITS and SIAS outperform complete-case analysis with stepwise variable selection and that SIAS slightly outperforms ITS.     

Accounting for uncertainty in the tree topology has little effect on the decision-theoretic approach to model selection in phylogeny estimation

Currently available methods for model selection used in phylogenetic analysis are based on an initial fixed-tree topology. Once a model is picked based on this topology, a rigorous search of the tree space is run under that model to find the maximum-likelihood estimate of the tree (topology and branch lengths) and the maximum-likelihood estimates of the model parameters. In this paper, we propose two extensions to the decision-theoretic (DT) approach that relax the fixed-topology restriction. We also relax the fixed-topology restriction for the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) methods. We compare the performance of the different methods (the relaxed, restricted, and the likelihood-ratio test [LRT]) using simulated data. This comparison is done by evaluating the relative complexity of the models resulting from each method and by comparing the performance of the chosen models in estimating the true tree. We also compare the methods relative to one another by measuring the closeness of the estimated trees corresponding to the different chosen models under these methods. We show that varying the topology does not have a major impact on model choice. We also show that the outcome of the two proposed extensions is identical and is comparable to that of the BIC, Extended-BIC, and DT. Hence, using the simpler methods in choosing a model for analyzing the data is more computationally feasible, with results comparable to the more computationally intensive methods. Another outcome of this study is that earlier conclusions about the DT approach are reinforced. That is, LRT, Extended-AIC, and AIC result in more complicated models that do not contribute to the performance of the phylogenetic inference, yet cause a significant increase in the time required for data analysis.     

Standard errors for EM estimates in generalized linear models with random effects

A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss-Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations.     

An exploration of fixed and random effects selection for longitudinal binary outcomes in the presence of nonignorable dropout

We explore a Bayesian approach to selection of variables that represent fixed and random effects in modeling of longitudinal binary outcomes with missing data caused by dropouts. We show via analytic results for a simple example that nonignorable missing data lead to biased parameter estimates. This bias results in selection of wrong effects asymptotically, which we can confirm via simulations for more complex settings. By jointly modeling the longitudinal binary data with the dropout process that possibly leads to nonignorable missing data, we are able to correct the bias in estimation and selection. Mixture priors with a point mass at zero are used to facilitate variable selection. We illustrate the proposed approach using a clinical trial for acute ischemic stroke.     

glmm.hp: an R package for computing individual effect of predictors in generalized linear mixed models

glmm.hp:一个计算广义线性混合模型中单个预测变量效应的R包 广义线性混合效应模型(GLMMs)是当代生态学研究中广泛应用的数据分析模型。然而,确定GLMMs中共线性的预测变量(固定效应)对响应变量的相对重要性是个挑战。基于适用于多元分析的‘平均共享方差’的算法,我们开发一个新的R包glmm.hp来分解GLMMs中由固定效应解释的边际(marginal)R²。我们论述了该软件包的工作原理并通过模拟数据集演示了该软件包的使用。glmm.hp 包的输出结果为每个预测变量将获得一个独自的(individual)边际R²,且它们的总和刚好等于模型总的边际R²。总之,我们相信glmm.hp包将有助于解释GLMMs 的输出结果。