Study Design in Causal Models

The causal assumptions, the study design and the data are the elements required for scientific inference in empirical research. The research is adequately communicated only if all of these elements and their relations are described precisely. Causal models with design describe the study design and the missing‐data mechanism together with the causal structure and allow the direct application of causal calculus in the estimation of the causal effects. The flow of the study is visualized by ordering the nodes of the causal diagram in two dimensions by their causal order and the time of the observation. Conclusions on whether a causal or observational relationship can be estimated from the collected incomplete data can be made directly from the graph. Causal models with design offer a systematic and unifying view to scientific inference and increase the clarity and speed of communication. Examples on the causal models for a case–control study, a nested case–control study, a clinical trial and a two‐stage case–cohort study are presented.     

Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies

Testing the existence of a quantitative trait locus (QTL) effect is an important task in QTL mapping studies. Most studies concentrate on the case where the phenotype distributions of different QTL groups follow normal distributions with the same unknown variance. In this paper we make a more general assumption that the phenotype distributions come from a location-scale distribution family. We derive the limiting distribution of the likelihood ratio test (LRT) for the existence of the QTL effect in both location and scale in genetic backcross studies. We further identify an explicit representation for this limiting distribution. As a complement, we study the limiting distribution of the LRT and its explicit representation for the existence of the QTL effect in the location only. The asymptotic properties of the LRTs under a local alternative are also investigated. Simulation studies are used to evaluate the asymptotic results, and a real-data example is included for illustration.     

THE POTENTIAL FOR BIAS IN PRINCIPAL CAUSAL EFFECT ESTIMATION WHEN TREATMENT RECEIVED DEPENDS ON A KEY COVARIATE

Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of the "complier average causal effect" (CACE) derive from observations in the two treatment arms with different covariate distributions. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop posterior checks that characterize the extent to which incorporating the pretreatment covariate endangers estimation of the CACE. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule both possible randomized treatment assignments based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received.     

Principal component analysis of canine hip dysplasia phenotypes and their statistical power for genome-wide association mapping

The aims of this study were to undertake principal component analysis (PCA) of hip dysplasia (HD) and to examine the power of the principal components (PCs) in genome-wide association studies. A cohort of 278 dogs for PCA and that of 369 dogs for genotyping were used. The distraction index (DI), the dorsolateral subluxation (DLS) score, the Norberg angle (NA), and the extended-hip radiographic (EHR) score were used for the PCA. One thousand single-nucleotide polymorphisms (SNPs) (of 23,500) were used to simulate genetic locus sharing between the HD phenotypes and 1000 SNPs were used to calculate the genetic mapping power of the PCs. The DI and the DLS score (first group) reflected hip laxity and the NA and the EHR score (second group) reflected the congruency between the femoral head and acetabulum. The average hip measurements of the two groups reflected in the first PC captured 55% of total radiographic variation. The first four PCs captured 90% of the total variation. The PCs had higher statistical mapping power to detect pleiotropic quantitative trait loci (QTL) than the raw phenotypes. The PCA demonstrated for the first time that HD can be reduced mathematically into simpler components essential for its genetic dissection. Genes that contribute jointly to all four radiographic hip phenotypes can be detected by mapping their first four PCs, while those contributing to individual phenotypes can be mapped by association with the individual raw phenotype.     

The Effects of Detrending in Granger Causality Tests

Nonstationary time series are frequently detrended in empirical investigations by regressing the series on time or a function of time. The effects of the detrending on the tests for causal relationships in the sense of Granger are investigated using quarterly U.S. data. The causal relationships between nominal or real GNP and M1, inferred from the Granger–Sims tests, are shown to depend very much on, among other factors, whether or not series are detrended. Detrending tends to remove or weaken causal relationships, and conversely, failure to detrend tends to introduce or enhance causal relationships. The study suggests that we need a more robust test or a better definition of causality.     

CAUSAL EFFECTS OF TREATMENTS FOR INFORMATIVE MISSING DATA DUE TO PROGRESSION/DEATH

In longitudinal clinical trials, when outcome variables at later time points are only defined for patients who survive to those times, the evaluation of the causal effect of treatment is complicated. In this paper, we describe an approach that can be used to obtain the causal effect of three treatment arms with ordinal outcomes in the presence of death using a principal stratification approach. We introduce a set of flexible assumptions to identify the causal effect and implement a sensitivity analysis for non-identifiable assumptions which we parameterize parsimoniously. Methods are illustrated on quality of life data from a recent colorectal cancer clinical trial.     

A model selection approach for the identification of quantitative trait loci in experimental crosses

Summary. We consider the problem of identifying the genetic loci (called quantitative trait loci (QTLs)) contributing to variation in a quantitative trait, with data on an experimental cross. A large number of different statistical approaches to this problem have been described; most make use of multiple tests of hypotheses, and many consider models allowing only a single QTL. We feel that the problem is best viewed as one of model selection. We discuss the use of model selection ideas to identify QTLs in experimental crosses. We focus on a back-cross experiment, with strictly additive QTLs, and concentrate on identifying QTLs, considering the estimation of their effects and precise locations of secondary importance. We present the results of a simulation study to compare the performances of the more prominent methods.     

一种协整时间序列的动态因果效应估计与推断方法

为了进一步规避经典面板数据模型因果推断方法中对照样本异质性的问题,以及中断时间序列方法可能存在的“伪回归”问题和“二阶矩平稳”等条件的限制,本文借助时间序列的协整理论,并结合误差修正模型和结构突变检验方法提出了一种基于协整时间序列的实验设计方法,扩展了政策因果效应估计与推断方法。该方法将传统的趋势平稳过程中断时间序列扩展到随机趋势过程,不仅可以推断和估计处理效应,而且解决了政策效应的暂时性和持续性识别问题;另外,协整时间序列的因果效应推断方法更适用于不存在有效对照样本的政策因果效应分析。此外,本文评估了上海市和重庆市的房地产税试点政策,研究发现,长期来看试点政策对两市的商品房价格增长具有抑制作用,但政策效应表现出显著的差异性,上海市的试点政策对抑制房价上涨的力度大、起效快速,但重庆市的房产税政策存在较长期的时滞。     

A Bayesian Approach to Modelling Reticulation Events with Application to the Ribosomal Protein Gene rps11 of Flowering Plants

Traditional phylogenetic inference assumes that the history of a set of taxa can be explained by a tree. This assumption is often violated as some biological entities can exchange genetic material giving rise to non‐treelike events often called reticulations. Failure to consider these events might result in incorrectly inferred phylogenies. Phylogenetic networks provide a flexible tool which allows researchers to model the evolutionary history of a set of organisms in the presence of reticulation events. In recent years, a number of methods addressing phylogenetic network parameter estimation have been introduced. Some of them are based on the idea that a phylogenetic network can be defined as a directed acyclic graph. Based on this definition, we propose a Bayesian approach to the estimation of phylogenetic network parameters which allows for different phylogenies to be inferred at different parts of a multiple DNA alignment. The algorithm is tested on simulated data and applied to the ribosomal protein gene rps11 data from five flowering plants, where reticulation events are suspected to be present. The proposed approach can be applied to a wide variety of problems which aim at exploring the possibility of reticulation events in the history of a set of taxa.     

Inference of Genetic Networks from Time Course Expression Data Using Functional Regression with Lasso Penalty

Statistical inference of genetic regulatory networks is essential for understanding temporal interactions of regulatory elements inside the cells. In this work, we propose to infer the parameters of the ordinary differential equations using the techniques from functional data analysis (FDA) by regarding the observed time course expression data as continuous-time curves. For networks with a large number of genes, we take advantage of the sparsity of the networks by penalizing the linear coefficients with a L ₁ norm. The ability of the algorithm to infer network structure is demonstrated using the cell-cycle time course data for Saccharomyces cerevisiae.     

Asymptotic test of mixture model and its applications to QTL interval mapping

Quantitative trait loci (QTL) mapping has been a standard means in identifying genetic regions harboring potential genes underlying complex traits. Likelihood ratio test (LRT) has been commonly applied to assess the significance of a genetic locus in a mixture model content. Given the time constraint in commonly used permutation tests to assess the significance of LRT in QTL mapping, we study the behavior of the LRT statistic in mixture model when the proportions of the distributions are unknown. We found that the asymptotic null distribution is stationary Gaussian process after suitable transformation. The result can be applied to one-parameter exponential family mixture model. Under certain condition, such as in a backcross mapping model, the tail probability of the supremum of the process is calculated and the threshold values can be determined by solving the distribution function. Simulation studies were performed to evaluate the asymptotic results.     

Gene Pathways Discovery in Asbestos-Related Diseases using Local Causal Discovery Algorithm

To learn about the progression of a complex disease, it is necessary to understand the physiology and function of many genes operating together in distinct interactions as a system. In order to significantly advance our understanding of the function of a system, we need to learn the causal relationships among its modeled genes. To this end, it is desirable to compare experiments of the system under complete interventions of some genes, e.g., knock-out of some genes, with experiments of the system without interventions. However, it is expensive and difficult (if not impossible) to conduct wet lab experiments of complete interventions of genes in animal models, e.g., a mouse model. Thus, it will be helpful if we can discover promising causal relationships among genes with observational data alone in order to identify promising genes to perturb in the system that can later be verified in wet laboratories. While causal Bayesian networks have been actively used in discovering gene pathways, most of the algorithms that discover pairwise causal relationships from observational data alone identify only a small number of significant pairwise causal relationships, even with a large dataset. In this article, we introduce new causal discovery algorithms—the Equivalence Local Implicit latent variable scoring Method (EquLIM) and EquLIM with Markov chain Monte Carlo search algorithm (EquLIM-MCMC)—that identify promising causal relationships even with a small observational dataset.     

BAYESIAN MODEL SEARCH AND MULTILEVEL INFERENCE FOR SNP ASSOCIATION STUDIES

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations, MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally "validated" in independent studies. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.     

Multiple Interval Mapping for Quantitative Trait Loci via EM Algorithm in the Presence of Crossover Interference

The rapid advance in molecular biology has made feasible systematic studies of mapping quantitative trait loci (QTL) in experiment organisms. The method of multiple interval mapping provides an appropriate way for mapping QTL using genetic makers. However, crossover interference has not been considered sufficiently in the current QTL mapping in which no crossover interference is assumed, and the length of maker interval is always kept fixed. In this article, we consider the issue of statistical inference in multiple interval mapping for QTL when crossover interference is present. The marker interval can be chosen appropriately in our method without keeping the maker interval lengths fixed in advance, and the asymptotic variance–covariance matrix of the MLEs is also derived. Two simulations are performed to evaluate the proposed method and show the impact of crossover interference to QTL mapping.     

A Bayesian nonparametric causal model

Typically, in the practice of causal inference from observational studies, a parametric model is assumed for the joint population density of potential outcomes and treatment assignments, and possibly this is accompanied by the assumption of no hidden bias. However, both assumptions are questionable for real data, the accuracy of causal inference is compromised when the data violates either assumption, and the parametric assumption precludes capturing a more general range of density shapes (e.g., heavier tail behavior and possible multi-modalities). We introduce a flexible, Bayesian nonparametric causal model to provide more accurate causal inferences. The model makes use of a stick-breaking prior, which has the flexibility to capture any multi-modalities, skewness and heavier tail behavior in this joint population density, while accounting for hidden bias. We prove the asymptotic consistency of the posterior distribution of the model, and illustrate our causal model through the analysis of small and large observational data sets.     

Analysis of the Threshold Values of Semantic Structure Analysis in Identifying Causal Relationships

This study uses a semantic structure analysis (SSA) method to construct the causal relationships among the criteria from survey data. The literatures provide a predetermined threshold value when the SSA is applied without explanation, but we use a Monte Carlo simulation based on the raw data to determine the threshold values with the significant levels of 0.05 and 0.10 for constructing the causal relationships. The results show that the causal relationships among the criteria using the suggested threshold value are too complicated, while the causal relationships by the simulated threshold values are relatively easy to be understood and used practically.     

On robust causality nonresponse testing in duration studies under the Cox model

High survey nonresponse in unemployment duration studies may have a strong effect on inference if the so called causal mechanism is present. A robust method of testing the causal nonresponse is proposed for data sets where survey information can be combined with complete administrative records. It is assumed that population distribution follows approximately the Cox regression model. Formal justification of the method and a comparative simulation study are included.     

Analysis of bivariate binary data with possible chances of wrong ascertainment

In familial data, ascertainment correction is often necessary to decipher genetic bases of complex human diseases. This is because families usually are not drawn at random or are not selected according to well-defined rules. While there has been much progress in identifying genes associated with a certain phenotype, little attention has been paid so far for familial studies on exploring common genetic influences on different phenotypes of interest. In this study, we develop a powerful bivariate analytical approach that can be used for a complex situation with paired binary traits. In addition, our model has been framed to accommodate the possibility of imperfect diagnosis as traits may be wrongly observed. Thus, the primary focus is to see whether a particular gene jointly influences both phenotypes. We examine the plausibility of this theory in a sample of families ascertained on the basis of at least one affected individual. We propose a bivariate binary mixed model that provides a novel and flexible way to account for wrong ascertainment in families collected with multiple cases. A hierarchical Bayesian analysis using Markov Chain Monte Carlo (MCMC) method has been carried out to investigate the effect of covariates on the disease status. Results based on simulated data indicate that estimates of the parameters are biased when classification errors and/or ascertainment are ignored.