Conditions for Non-confounding and Collapsibility without Knowledge of Completely Constructed Causal Diagrams

In this paper, we discuss several concepts in causal inference in terms of causal diagrams proposed by Pearl (1993 , 1995a , b ), and we give conditions for non-confounding, homogeneity and collapsibility for causal effects without knowledge of a completely constructed causal diagram. We first introduce the concepts of non-confounding, conditional non-confounding, uniform non-confounding, homogeneity, collapsibility and strong collapsibility for causal effects, then we present necessary and sufficient conditions for uniform non-confounding, homegeneity and collapsibilities, and finally we show sufficient conditions for non-confounding, conditional non-confounding and uniform non-confounding.     

Graphs for Margins of Bayesian Networks

Directed acyclic graph (DAG) models—also called Bayesian networks—are widely used in probabilistic reasoning, machine learning and causal inference. If latent variables are present, then the set of possible marginal distributions over the remaining (observed) variables is generally not represented by any DAG. Larger classes of mixed graphical models have been introduced to overcome this; however, as we show, these classes are not sufficiently rich to capture all the marginal models that can arise. We introduce a new class of hyper‐graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG. We show that each distinct marginal of a DAG model is represented by at least one mDAG and provide graphical results towards characterizing equivalence of these models. Finally, we show that mDAGs correctly capture the marginal structure of causally interpreted DAGs under interventions on the observed variables.     

Optimizing a control plan using a structural equation model with an application to statistical process analysis

In the case where non-experimental data are available from an industrial process and a directed graph for how various factors affect a response variable is known based on a substantive understanding of the process, we consider a problem in which a control plan involving multiple treatment variables is conducted in order to bring a response variable close to a target value with variation reduction. Using statistical causal analysis with linear (recursive and non-recursive) structural equation models, we configure an optimal control plan involving multiple treatment variables through causal parameters. Based on the formulation, we clarify the causal mechanism for how the variance of a response variable changes when the control plan is conducted. The results enable us to evaluate the effect of a control plan on the variance of a response variable from non-experimental data and provide a new application of linear structural equation models to engineering science.     

On the Estimation Accuracy of Causal Effects using Supplementary Variables

This paper focuses on a situation in which a set of treatments is associated with a response through a set of supplementary variables in linear models as well as discrete models. Under the situation, we demonstrate that the causal effect can be estimated more accurately from the set of supplementary variables. In addition, we show that the set of supplementary variables can include selection variables and proxy variables as well. Furthermore, we propose selection criteria for supplementary variables based on the estimation accuracy of causal effects. From graph structures based on our results, we can judge certain situations under which the causal effect can be estimated more accurately by supplementary variables and reliably evaluate the causal effects from observed data.     

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.     

Estimation of Causal Odds of Concordance using the Aalen Additive Model

A simple summary of a treatment effect is attractive, which is part of the explanation of the success of the Cox model when analysing time‐to‐event data since the relative risk measure is such a convenient summary measure. In practice, however, the Cox model may fail to give a reasonable fit, very often because of time‐changing treatment effect. The Aalen additive hazards model may be a good alternative as time‐changing effects are easily modelled within this model, but results are then evidently more complicated to communicate. In such situations, the odds of concordance measure (OC) is a convenient way of communicating results, and recently Martinussen & Pipper (2012) showed how a variant of the OC measure may be estimated based on the Aalen additive hazards model. In this study, we propose an estimator that should be preferred in observational studies as it always estimates the causal effect on the chosen scale, only assuming that there are no un‐measured confounders. The resulting estimator is shown to be consistent and asymptotically normal, and an estimator of its limiting variance is provided. Two real applications are provided.     

Predictive Inference,Causal Reasoning,and Model Assessment in Nonparametric Bayesian Analysis: A Case Study

This paper continuesour earlier analysis of a data set on acute ear infections insmall children, presented in Andreev and Arjas (1998). The maingoal here is to provide a method, based on the use of predictivedistributions, for assessing the possible causal influence whichthe type of day care will have on the incidence of ear infections.A closely related technique is used for the assessment of thenonparametric Bayesian intensity model applied in the paper.Two graphical methods, supported by formal tests, are suggestedfor this purpose.     

Did the Military Interventions in the Mexican Drug War Increase Violence?

We analyze publicly available data to estimate the causal effects of military interventions on the homicide rates in certain problematic regions in Mexico. We use the Rubin causal model to compare the post-intervention homicide rate in each intervened region to the hypothetical homicide rate for that same year had the military intervention not taken place. Because the effect of a military intervention is not confined to the municipality subject to the intervention, a nonstandard definition of units is necessary to estimate the causal effect of the intervention under the standard no-interference assumption of stable-unit treatment value assumption (SUTVA). Donor pools are created for each missing potential outcome under no intervention, thereby allowing for the estimation of unit-level causal effects. A multiple imputation approach accounts for uncertainty about the missing potential outcomes.     

Causal Proportional Hazards Models and Time-constant Exposure in Randomized Clinical Trials

The last decade saw enormous progress in the development of causal inference tools to account for noncompliance in randomized clinical trials. With survival outcomes, structural accelerated failure time (SAFT) models enable causal estimation of effects of observed treatments without making direct assumptions on the compliance selection mechanism. The traditional proportional hazards model has however rarely been used for causal inference. The estimator proposed by Loeys and Goetghebeur (2003, Biometrics vol. 59 pp. 100–105) is limited to the setting of all or nothing exposure. In this paper, we propose an estimation procedure for more general causal proportional hazards models linking the distribution of potential treatment-free survival times to the distribution of observed survival times via observed (time-constant) exposures. Specifically, we first build models for observed exposure-specific survival times. Next, using the proposed causal proportional hazards model, the exposure-specific survival distributions are backtransformed to their treatment-free counterparts, to obtain – after proper mixing – the unconditional treatment-free survival distribution. Estimation of the parameter(s) in the causal model is then based on minimizing a test statistic for equality in backtransformed survival distributions between randomized arms.     

微观计量经济学中的实验设计法——期望“计量经济（学）设计与分析”的出现

 摘　　要:本文论述了实验设计思想在微观计量经济分析中的重要作用。从实验设计三大原理局部控制、随机化和重复出发，重新诠释微观计量经济学（特别是“因果链”分析）中有关方法论的问题，预期实验经济学和微观计量经济学将通过实验设计的思想方法而互相促进，并期望“计量经济（学）设计与分析”一类读物的出现。     

Model-based clustering,classification, and discriminant analysis of data with mixed type

We propose a mixture of latent variables model for the model-based clustering, classification, and discriminant analysis of data comprising variables with mixed type. This approach is a generalization of latent variable analysis, and model fitting is carried out within the expectation-maximization framework. Our approach is outlined and a simulation study conducted to illustrate the effect of sample size and noise on the standard errors and the recovery probabilities for the number of groups. Our modelling methodology is then applied to two real data sets and their clustering and classification performance is discussed. We conclude with discussion and suggestions for future work.     

Bayesian assessment of times to diagnosis in breast cancer screening

Breast cancer is one of the diseases with the most profound impact on health in developed countries and mammography is the most popular method for detecting breast cancer at a very early stage. This paper focuses on the waiting period from a positive mammogram until a confirmatory diagnosis is carried out in hospital. Generalized linear mixed models are used to perform the statistical analysis, always within the Bayesian reasoning. Markov chain Monte Carlo algorithms are applied for estimation by simulating the posterior distribution of the parameters and hyperparameters of the model through the free software WinBUGS.     

Parameter estimation for three-parameter generalized Pareto distribution by weighted non linear least squares

Generalized Pareto distribution (GPD) is widely used to model exceedances over thresholds. In this paper, we propose a new method, called weighted non linear least squares (WNLS), to estimate the parameters of the three-parameter GPD. Some asymptotic results of the proposed method are provided. An extensive simulation is carried out to evaluate the finite sample behaviour of the proposed method and to compare the behaviour with other methods suggested in the literature. The simulation results show that WNLS outperforms other methods in general situations. Finally, the WNLS is applied to analysis the real-life data.     

Covariate selection for estimating the causal effect of control plans by using causal diagrams

Summary. Consider a case where cause–effect relationships between variables can be described by a causal path diagram and the corresponding linear structural equation model. The paper proposes a graphical selection criterion for covariates to estimate the causal effect of a control plan. For designing the control plan, it is essential to determine both covariates that are used for control and covariates that are used for identification. The selection of covariates used for control is only constrained by the requirement that the covariates be non-descendants of a treatment variable. However, the selection of covariates used for identification is dependent on the selection of covariates used for control and is not unique. In the paper, the difference between covariates that are used for identification is evaluated on the basis of the asymptotic variance of the estimated causal effect of an effective control plan. Furthermore, the results can be also described in terms of a graph structure.     

Inference for proportional hazard model with propensity score

Since the publication of the seminal paper by Cox (1972), proportional hazard model has become very popular in regression analysis for right censored data. In observational studies, treatment assignment may depend on observed covariates. If these confounding variables are not accounted for properly, the inference based on the Cox proportional hazard model may perform poorly. As shown in Rosenbaum and Rubin (1983), under the strongly ignorable treatment assignment assumption, conditioning on the propensity score yields valid causal effect estimates. Therefore we incorporate the propensity score into the Cox model for causal inference with survival data. We derive the asymptotic property of the maximum partial likelihood estimator when the model is correctly specified. Simulation results show that our method performs quite well for observational data. The approach is applied to a real dataset on the time of readmission of trauma patients. We also derive the asymptotic property of the maximum partial likelihood estimator with a robust variance estimator, when the model is incorrectly specified.     

双重广义线性模型在车损险费率厘定中的应用

双重广义线模型是对广义线性模型的扩展,其对反应变量的均值与散度参数同时建立模型,提高了模型运用的灵活性与适应性。将双重广义线性模型应用到车损险费率厘定中,既考虑了费率期望值与费率因子之间的关系,又考虑了变量的分散程度与费率因子之间的关系,并以欧洲一家保险公司的汽车保险损失数据为样本进行实证研究,把无索赔优待等级、地区、车型与年均行驶里程数作为费率因子,建立了费率厘定模型。结果表明,所得到费率结构合理,符合实际。     

On causality test for time series of counts based on poisson ingarch models with application to crime and temperature data

In this study, we consider the causality test for the integer-valued time series. Using the mean equation of Poisson INGARCH models, we construct a regression that includes exogenous variables. The test is then constructed based on the least squares estimator and is shown to follow a chi-square distribution under the null of no causal relationships. A simulation study and real data analysis using the crime and temperature data in Chicago are provided for illustration.     

Estimation in large cross random-effect models by data augmentation

Estimation in mixed linear models is, in general, computationally demanding, since applied problems may involve extensive data sets and large numbers of random effects. Existing computer algorithms are slow and/or require large amounts of memory. These problems are compounded in generalized linear mixed models for categorical data, since even approximate methods involve fitting of a linear mixed model within steps of an iteratively reweighted least squares algorithm. Only in models in which the random effects are hierarchically nested can the computations for fitting these models to large data sets be carried out rapidly. We describe a data augmentation approach to these computational difficulties in which we repeatedly fit an overlapping series of submodels, incorporating the missing terms in each submodel as 'offsets'. The submodels are chosen so that they have a nested random-effect structure, thus allowing maximum exploitation of the computational efficiency which is available in this case. Examples of the use of the algorithm for both metric and discrete responses are discussed, all calculations being carried out using macros within the MLwiN program.     

Impact of missing data on type 1 error rates in non‐inferiority trials

In this paper, a simulation study is conducted to systematically investigate the impact of different types of missing data on six different statistical analyses: four different likelihood‐based linear mixed effects models and analysis of covariance (ANCOVA) using two different data sets, in non‐inferiority trial settings for the analysis of longitudinal continuous data. ANCOVA is valid when the missing data are completely at random. Likelihood‐based linear mixed effects model approaches are valid when the missing data are at random. Pattern‐mixture model (PMM) was developed to incorporate non‐random missing mechanism. Our simulations suggest that two linear mixed effects models using unstructured covariance matrix for within‐subject correlation with no random effects or first‐order autoregressive covariance matrix for within‐subject correlation with random coefficient effects provide well control of type 1 error (T1E) rate when the missing data are completely at random or at random. ANCOVA using last observation carried forward imputed data set is the worst method in terms of bias and T1E rate. PMM does not show much improvement on controlling T1E rate compared with other linear mixed effects models when the missing data are not at random but is markedly inferior when the missing data are at random. Copyright © 2009 John Wiley & Sons, Ltd.     

Interval-valued data regression using partial linear model

Semi-parametric modelling of interval-valued data is of great practical importance, as exampled by applications in economic and financial data analysis. We propose a flexible semi-parametric modelling of interval-valued data by integrating the partial linear regression model based on the Center & Range method, and investigate its estimation procedure. Furthermore, we introduce a test statistic that allows one to decide between a parametric linear model and a semi-parametric model, and approximate its null asymptotic distribution based on wild Bootstrap method to obtain the critical values. Extensive simulation studies are carried out to evaluate the performance of the proposed methodology and the new test. Moreover, several empirical data sets are analysed to document its practical applications.