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When estimating the average causal effect in observational studies, researchers have to tackle both self-selection of treatment and outcome modeling. This is difficult because the parametric form of the outcome model is often unknown and there exists a large number of covariates. In this work, we present a semiparametric strategy for estimating the average causal effect by regressing on the propensity score. Furthermore, we show that regression error terms usually depend on the propensity score as well, which could cause heteroscedastic variances, and thus construct a refined estimator to improve the estimation efficiency. Both estimators are shown to be consistent and asymptotically normally distributed, with the latter one having a smaller asymptotic variance. The simulation studies indicate that our methods compare favorably with many competing estimators. Our methods are easy to implement and avoid hazardous impact due to extreme weights as often seen in weighting estimators. They can also be extended to handle subgroup effects with known structure. We apply the proposed methods to data from the Ohio Medicaid Assessment Survey 2012, estimating the effect of having health insurance on self-reported health status for a population with subsidized insurance plan choices under the Affordable Care Act.

This article discusses regression analysis of mixed interval-censored failure time data. Such data frequently occur across a variety of settings, including clinical trials, epidemiologic investigations, and many other biomedical studies with a follow-up component. For example, mixed failure times are commonly found in the two largest studies of long-term survivorship after childhood cancer, the datasets that motivated this work. However, most existing methods for failure time data consider only right-censored or only interval-censored failure times, not the more general case where times may be mixed. Additionally, among regression models developed for mixed interval-censored failure times, the proportional hazards formulation is generally assumed. It is well-known that the proportional hazards model may be inappropriate in certain situations, and alternatives are needed to analyze mixed failure time data in such cases. To fill this need, we develop a maximum likelihood estimation procedure for the proportional odds regression model with mixed interval-censored data. We show that the resulting estimators are consistent and asymptotically Gaussian. An extensive simulation study is performed to assess the finite-sample properties of the method, and this investigation indicates that the proposed method works well for many practical situations. We then apply our approach to examine the impact of age at cranial radiation therapy on risk of growth hormone deficiency in long-term survivors of childhood cancer.

Matching is a routinely used technique to balance covariates and thereby alleviate confounding bias in causal inference with observational data. Most of the matching literatures involve the estimating of propensity score with parametric model, which heavily depends on the model specification. In this paper, we employ machine learning and matching techniques to learn the average causal effect. By comparing a variety of machine learning methods in terms of propensity score under extensive scenarios, we find that the ensemble methods, especially generalized random forests, perform favorably with others. We apply all the methods to the data of tropical storms that occurred on the mainland of China since 1949.

Due to the lack of fault signals and the variability of working conditions in engineering practice, there is still a gap between the conventional deep learning fault diagnosis models and the practical application. Aiming at the problem of few-shot fault diagnosis in variable conditions, we propose a novel few-shot transfer learning method based on meta-learning and graph convolutional network for machinery fault diagnosis. The 2D convolution module is used to extract latent features. Then the extracted features and their labels are combined as the nodes, and the similarity between the nodes is used as the connection relationship between the nodes, so as to realize the construction of the graph sample. Subsequently, graph samples are input into the graph convolutional network to evaluate the similarity and complete the classification of faults. Crucially, the idea of metric-based meta-learning is integrated into the graph convolutional network to set tasks and extraction methods. Finally, the analysis and comparison of the diagnostic accuracy under different sample capacity and transfer conditions were demonstrated. The results show that the method can achieve 97.25% diagnostic accuracy with only a few samples in the scene of variable working conditions.

Partly interval censored data frequently occur in many areas including clinical trials, epidemiology research, and medical follow-up studies. When data come from observational studies, we need to carefully adjust for the confounding bias in order to estimate the true treatment effect. Pair matching designs are popular for removing confounding bias without parametric assumptions. With time-to-event outcomes, there are some literature for hypothesis testing with paired right censored data, but not for interval censored data. O’Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the Prentice-Wilcoxon scores. Akritas proposed the Akritas test and established its asymptotic properties. We extend Akritas test to partly interval censored data. We estimate the survival distribution function by nonparametric maximum likelihood estimation (NPMLE), and prove the asymptotic validity of the new test. To improve our test under small sample size or extreme distributions, we also propose a modified version using the rank of the score difference. Simulation results indicate that our proposed methods have very good performance.

Genetic pleiotropy occurs when a single gene influences two or more seemingly unrelated phenotypic traits. It is significant to detect pleiotropy and understand its causes. However, most current st...

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...

In this paper, we are interested in exploring the dynamic causal relationships among two sets of three variables in different quarters. One set is futures sugar closing price in Zhengzhou futures exchange market (ZC), spot sugar price in Zhengzhou (ZS) and futures sugar closing price in New York futures exchange market(NC) and the other includes futures sugar opening price in Zhengzhou (ZO), ZS and NC. For each quarter, we first use Bayesian model selection to obtain the optimal causal graph with the highest BD scores and then use Bayesian model averaging approach to explore the causal relationship between every two variables. From the real data analysis, the two conclusions almost coincide, which shows that the two methods are practical.

This paper discusses the transformed linear regression with non-normal error distributions, a problem that often occurs in many areas such as economics and social sciences as well as medical studies. The linear transformation model is an important tool in survival analysis partly due to its flexibility. In particular, it includes the Cox model and the proportional odds model as special cases when the error follows the extreme value distribution and the logistic distribution, respectively. Despite the popularity and generality of linear transformation models, however, there is no general theory on the maximum likelihood estimation of the regression parameter and the transformation function. One main difficulty for this is that the transformation function near the tails diverges to infinity and can be quite unstable. It affects the accuracy of the estimation of the transformation function and regression parameters. In this paper, we develop the maximum likelihood estimation approach and provide the near optimal conditions on the error distribution under which the consistency and asymptotic normality of the resulting estimators can be established. Extensive numerical studies suggest that the methodology works well, and an application to the data on a typhoon forecast is provided.

High-throughput sequencing technologies have enabled large-scale studies of the role of the human microbiome in health conditions and diseases. Microbial community level association test, as a critical step to establish the connection between overall microbiome composition and an outcome of interest, has now been routinely performed in many studies. However, current microbiome association tests all focus on a single outcome. It has become increasingly common for a microbiome study to collect multiple, possibly related, outcomes to maximize the power of discovery. As these outcomes may share common mechanisms, jointly analyzing these outcomes can amplify the association signal and improve statistical power to detect potential associations. We propose the multivariate microbiome regression-based kernel association test (MMiRKAT) for testing association between multiple continuous outcomes and overall microbiome composition, where the kernel used in MMiRKAT is based on Bray-Curtis or UniFrac distance. MMiRKAT directly regresses all outcomes on the microbiome profiles via a semiparametric kernel machine regression framework, which allows for covariate adjustment and evaluates the association via a variance-component score test. Because most of the current microbiome studies have small sample sizes, a novel small-sample correction procedure is implemented in MMiRKAT to correct for the conservativeness of the association test when the sample size is small or moderate. The proposed method is assessed via simulation studies and an application to a real data set examining the association between host gene expression and mucosal microbiome composition. We demonstrate that MMiRKAT is more powerful than large sample based multivariate kernel association test, while controlling the type I error. A free implementation of MMiRKAT in R language is available at http://research.fhcrc.org/wu/en.html.

This paper studies semiparametric regression analysis of panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and reliability experiments, for example. To explore the nonlinear interactions between covariates, we propose a class of partially linear models with possibly varying coefficients for the mean function of the counting processes with panel count data. The functional coefficients are estimated by B-spline function approximations. The estimation procedures are based on maximum pseudo-likelihood and likelihood approaches and they are easy to implement. The asymptotic properties of the resulting estimators are established, and their finite-sample performance is assessed by Monte Carlo simulation studies. We also demonstrate the value of the proposed method by the analysis of a cancer data set, where the new modeling approach provides more comprehensive information than the usual proportional mean model.

This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series. We construct a partial correlation graph at first which is an undirected graph. For every undirected edge in the partial correlation graph, the measures of linear feedback between two time series can help us decide its direction, then we obtain the mixed graph. Using this method, we construct a mixed graph for futures sugar prices in Zhengzhou (ZF), spot sugar prices in Zhengzhou (ZS) and futures sugar prices in New York (NF). The result shows that there is a bi-directional causality between ZF and ZS, an unidirectional causality from NF to ZF, but no causality between NF and ZS.

This paper studies a monotone constrained varying-coefficient partially linear model with errors in variables using a monotone B-spline approach based on adjusted least squares. The proposed estimator is consistent, asymptotically normal, and performs well in numerical studies.

In recent years the analysis of interval-censored failure time data has attracted a great deal of attention and such data arise in many fields including demographical studies, economic and financial studies, epidemiological studies, social sciences, and tumorigenicity experiments. This is especially the case in medical studies such as clinical trials. In this article, we discuss regression analysis of one type of such data, Case I interval-censored data, in the presence of left-truncation. For the problem, the additive hazards model is employed and the maximum likelihood method is applied for estimations of unknown parameters. In particular, we adopt the sieve estimation approach that approximates the baseline cumulative hazard function by linear functions. The resulting estimates of regression parameters are shown to be consistent and efficient and have an asymptotic normal distribution. An illustrative example is provided.

We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estimation of the covariate effect. The proposed estimator is asymptotically normal. Simulation studies are presented to show that the proposed method performs well with finite samples, and the proposed method is applied to a real data set.

When a single gene influences more than one trait, known as pleiotropy, it is important to detect pleiotropy to improve the biological understanding of a gene. This can lead to improved screening, diagnosis, and treatment of diseases. Yet, most current multivariate methods to evaluate pleiotropy test the null hypothesis that none of the traits are associated with a variant; departures from the null could be driven by just one associated trait. A formal test of pleiotropy should assume a null hypothesis that one or fewer traits are associated with a genetic variant. We recently developed statistical methods to analyze pleiotropy for quantitative traits having a multivariate normal distribution. We now extend this approach to traits that can be modeled by generalized linear models, such as analysis of binary, ordinal, or quantitative traits, or a mixture of these types of traits. Based on methods from estimating equations, we developed a new test for pleiotropy. We then extended the testing framework to a sequential approach to test the null hypothesis that [Formula: see text] traits are associated, given that the null of [Formula: see text] associated traits was rejected. This provides a testing framework to determine the number of traits associated with a genetic variant, as well as which traits, while accounting for correlations among the traits. By simulations, we illustrate the Type-I error rate and power of our new methods, describe how they are influenced by sample size, the number of traits, and the trait correlations, and apply the new methods to a genome-wide association study of multivariate traits measuring symptoms of major depression. Our new approach provides a quantitative assessment of pleiotropy, enhancing current analytic practice.

In many clinical studies, patients may be asked to report their medication adherence, presence of side effects, substance use, and hospitalization information during the study period. However, the exact occurrence time of these recurrent events may not be available due to privacy protection, recall difficulty, or incomplete medical records. Instead, the only available information is whether the events of interest have occurred during the past period. In this paper, we call these incomplete recurrent events as repeated current status data. Currently, there are no valid standard methods for this kind of data. We propose to use the Andersen-Gill proportional intensity assumption to analyze such data. Specifically, we propose a maximum sieve likelihood approach for inference and we show that the proposed estimators for regression coefficients are consistent, asymptotically normal and attain semiparametric efficiency bounds. Simulation studies show that the proposed approach performs well with small sample sizes. Finally, our method is applied to study medication adherence in a clinical trial on non-psychotic major depressive disorder.

Time-to-event data are very common in observational studies. Unlike randomized experiments, observational studies suffer from both observed and unobserved confounding biases. To adjust for observed confounding in survival analysis, the commonly used methods are the Cox proportional hazards (PH) model, the weighted logrank test, and the inverse probability of treatment weighted Cox PH model. These methods do not rely on fully parametric models, but their practical performances are highly influenced by the validity of the PH assumption. Also, there are few methods addressing the hidden bias in causal survival analysis. We propose a strategy to test for survival function differences based on the matching design and explore sensitivity of the P-values to assumptions about unmeasured confounding. Specifically, we apply the paired Prentice-Wilcoxon (PPW) test or the modified PPW test to the propensity score matched data. Simulation studies show that the PPW-type test has higher power in situations when the PH assumption fails. For potential hidden bias, we develop a sensitivity analysis based on the matched pairs to assess the robustness of our finding, following Rosenbaum's idea for nonsurvival data. For a real data illustration, we apply our method to an observational cohort of chronic liver disease patients from a Mayo Clinic study. The PPW test based on observed data initially shows evidence of a significant treatment effect. But this finding is not robust, as the sensitivity analysis reveals that the P-value becomes nonsignificant if there exists an unmeasured confounder with a small impact.

Linear transformation models provide a class of flexible models for regression analysis of failure time data and several methods have been proposed for fitting them to right-censored failure time data (Chen, 2002; Cheng et al., 1995; Yin and Zeng, 2006). This article considers the fitting of these models to current status data, a special type of interval-censored failure time data. We derive the maximum likelihood estimates and their information bound and establish the efficiency of the estimates. Simulation studies show that the approach is appropriate for practical use and an application is given to illustrate the approach.

We consider a general semiparametric hazards regression model that encompasses Cox’s proportional hazards model and the accelerated failure time model for survival analysis. To overcome the nonexistence of the maximum likelihood, we derive a kernel-smoothed profile likelihood function, and prove that the resulting estimates of the regression parameters are consistent and achieve semiparametric efficiency. In addition, we develop penalized structure selection techniques to determine which covariates constitute the accelerate failure time model and which covariates constitute the proportional hazards model. The proposed method is able to estimate the model structure consistently and model parameters efficiently. Furthermore, variance estimation is straightforward. The proposed estimation performs well in simulation studies and is applied to the analysis of a real data set. Copyright

This paper discusses multivariate interval-censored failure time data observed when several correlated survival times of interest exist and only interval censoring is available for each survival time. Such data occur in many fields, for instance, studies of the development of physical symptoms or diseases in several organ systems. A marginal inference approach was used to create a linear transformation model and applied to bivariate interval-censored data arising from a diabetic retinopathy study and an AIDS study. The results of simulation studies that were conducted to evaluate the performance of the presented approach suggest that it performs well. The Canadian Journal of Statistics 41: 275–290; 2013 © 2013 Statistical Society of Canada Cet article traite des donnees multivariees se presentant lorsque plusieurs temps de survie d'interet sont correles et qu'ils sont censures par intervalle. De telles donnees surviennent dans plusieurs domaines, notamment dans les etudes sur le developpement de symptomes physiques ou de maladies dans plusieurs systemes organiques. Les auteurs proposent une methode d'inference marginale pour definir un modele de transformation lineaire qu'ils ont applique a des donnees bivariees censurees par intervalle provenant d'une etude sur la retinopathie diabetique et d'une etude sur le SIDA. Les etudes de simulation realisees en vue d'evaluer la performance de l'approche proposee ont produit des resultats concluants. La revue canadienne de statistique 41: 275–290; 2013 © 2013 Societe statistique du Canada

In this article, we consider a linear model in which the covariates are measured with errors. We propose a t-type corrected-loss estimation of the covariate effect, when the measurement error follows the Laplace distribution. The proposed estimator is asymptotically normal. In practical studies, some outliers that diminish the robustness of the estimation occur. Simulation studies show that the estimators are resistant to vertical outliers and an application of 6-minute walk test is presented to show that the proposed method performs well.

High-throughput sequencing technologies have enabled large-scale studies of the role of the human microbiome in health conditions and diseases. Microbial community level association test, as a critical step to establish the connection between overall microbiome composition and an outcome of interest, has now been routinely performed in many studies. However, current microbiome association tests all focus on a single outcome. It has become increasingly common for a microbiome study to collect multiple, possibly related, outcomes to maximize the power of discovery. As these outcomes may share common mechanisms, jointly analyzing these outcomes can amplify the association signal and improve statistical power to detect potential associations. We propose the multivariate microbiome regression-based kernel association test (MMiRKAT) for testing association between multiple continuous outcomes and overall microbiome composition, where the kernel used in MMiRKAT is based on Bray-Curtis or UniFrac distance. MMiRKAT directly regresses all outcomes on the microbiome profiles via a semiparametric kernel machine regression framework, which allows for covariate adjustment and evaluates the association via a variance-component score test. Because most of the current microbiome studies have small sample sizes, a novel small-sample correction procedure is implemented in MMiRKAT to correct for the conservativeness of the association test when the sample size is small or moderate. The proposed method is assessed via simulation studies and an application to a real data set examining the association between host gene expression and mucosal microbiome composition. We demonstrate that MMiRKAT is more powerful than large sample based multivariate kernel association test, while controlling the type I error. A free implementation of MMiRKAT in R language is available at http://research.fhcrc.org/wu/en.html.

Clustered interval-censored failure time data occur when the failure times of interest are clustered into small groups and known only to lie in certain intervals. A number of methods have been proposed for regression analysis of clustered failure time data, but most of them apply only to clustered right-censored data. In this paper, a sieve estimation procedure is proposed for fitting a Cox frailty model to clustered interval-censored failure time data. In particular, a two-step algorithm for parameter estimation is developed and the asymptotic properties of the resulting sieve maximum likelihood estimators are established. The finite sample properties of the proposed estimators are investigated through a simulation study and the method is illustrated by the data arising from a lymphatic filariasis study.

Event history studies occur in many fields including economics, medical studies, and social science. In such studies concerning some recurrent events, two types of data have been extensively discussed in the literature. One is recurrent event data that arise if study subjects are monitored or observed continuously. In this case, the observed information provides the times of all occurrences of the recurrent events of interest. The other is panel count data, which occur if the subjects are monitored or observed only periodically. This can happen if the continuous observation is too expensive or not practical, and in this case, only the numbers of occurrences of the events between subsequent observation times are available. In this paper, we discuss a third type of data, which is a mixture of recurrent event and panel count data and for which there exists little literature. For regression analysis of such data, we present a marginal mean model and propose an estimating equation-based approach for estimation of regression parameters. We conduct a simulation study to assess the finite sample performance of the proposed methodology, and the results indicate that it works well for practical situations. Finally, we apply it to a motivating study on childhood cancer survivors. Copyright © 2012 John Wiley & Sons, Ltd.

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments (Keiding, 1991; Sun, 2006) and several approaches have been proposed for the additive hazards model with univariate current status data (Lin et al., 1998; Martinussen and Scheike, 2002). For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

In this paper, we are interested in investigating the causal relationships among futures sugar prices in the Zhengzhou futures exchange market (ZF), the spot sugar prices in Zhengzhou (ZS) and the futures sugar prices in New York futures exchange market (NF). A useful tool called Bayesian network is introduced to analyze the problem. Since there are only three variables in our Bayesian network, the algorithm is straightforward: we display all the 25 possible network structures and adopt certain scoring metrics to evaluate them. We applied five different scoring metrics in total. Firstly, for each metric, we obtained 24 scores, each calculated from one of the 24 possible structures i.e. a Directed Acyclic Graph (DAG). Then we eliminated the network structure which represents the independence of the three variables according to our prior knowledge concerning the futures sugar market. After that, the optimal network structure which implies the causal relationships was selected according to the corresponding scoring metric. Finally, after comparing the results from different scoring metrics, we obtained the relatively affirmative conclusion that ZS causes ZF from both the Bayesian Dirichlet (BD) metric, Bayesian Dirichlet-Akaike Information Criterion (BD-AIC) metric, Bayesian Dirichlet-Bayesian Information Criterion (BD-BIC) metric and Bayesian Information Criterion (BIC) metric. The conclusions that NF causes ZF and ZF causes ZS from the Akaike Information Criterion (AIC) metric and ZF causes ZS from the BIC metric were useful and significant to our investigation.

In many longitudinal studies, observation times as well as censoring times may be correlated with longitudinal responses. This paper considers a multiplicative random effects model for the longitudinal response where these correlations may exist and a joint modeling approach is proposed via a shared latent variable. For inference about regression parameters, estimating equation approaches are developed and asymptotic properties of the proposed estimators are established. The finite sample behavior of the methods is examined through simulation studies and an application to a data set from a bladder cancer study is provided for illustration.

A maximum likelihood method with spline smoothing is proposed for linear transformation models with varying coefficients. The estimation and inference procedures are computationally easy. Under some regularity conditions, the estimators are proved to be consistent and asymptotically normal. A simulation study using the Stanford transplant data is presented to show that the proposed method performs well with a finite sample and is easy to use in practice. Copyright 2010, Oxford University Press.

Recurrent event data occur in many clinical and observational studies (Cook and Lawless, Analysis of recurrent event data, 2007) and in these situations, there may exist a terminal event such as death that is related to the recurrent event of interest (Ghosh and Lin, Biometrics 56:554-562, 2000; Wang et al., J Am Stat Assoc 96:1057-1065, 2001; Huang and Wang, J Am Stat Assoc 99:1153-1165, 2004; Ye et al., Biometrics 63:78-87, 2007). In addition, sometimes there may exist more than one type of recurrent events, that is, one faces multivariate recurrent event data with some dependent terminal event (Chen and Cook, Biostatistics 5:129-143, 2004). It is apparent that for the analysis of such data, one has to take into account the dependence both among different types of recurrent events and between the recurrent and terminal events. In this paper, we propose a joint modeling approach for regression analysis of the data and both finite and asymptotic properties of the resulting estimates of unknown parameters are established. The methodology is applied to a set of bivariate recurrent event data arising from a study of leukemia patients.

Variable selection is an important issue in all regression analyses, and in this paper we discuss this in the context of regression analysis of panel count data. Panel count data often occur in long-term studies that concern occurrence rate of a recurrent event, and their analysis has recently attracted a great deal of attention. However, there does not seem to exist any established approach for variable selection with respect to panel count data. For the problem, we adopt the idea behind the non-concave penalized likelihood approach and develop a non-concave penalized estimating function approach. The proposed methodology selects variables and estimates regression coefficients simultaneously, and an algorithm is presented for this process. We show that the proposed procedure performs as well as the oracle procedure in that it yields the estimates as if the correct submodel were known. Simulation studies are conducted for assessing the performance of the proposed approach and suggest that it works well for practical situations. An illustrative example from a cancer study is provided.

In many situations, longitudinal responses may be correlated with observation times as well as censoring time. This paper considers the regression analysis of longitudinal data where these correlations may exist under biased sampling, and a joint modeling approach that uses some latent variables to characterize the correlations is proposed. For inference about regression parameters, estimating equation approaches are developed and asymptotic properties of the proposed estimators are established. The finite sample behavior of the methods is examined through simulation studies, and an application to a data set from a bladder cancer study is provided for illustration.

This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.