Censored Responses Research Articles

Model-Based Causal Feature Selection for General Response Types

Discovering causal relationships from observational data is a fundamental yet challenging task. Invariant causal prediction (ICP, Peters, Bühlmann, and Meinshausen) is a method for causal feature selection which requires data from heterogeneous settings and exploits that causal models are invariant. ICP has been extended to general additive noise models and to nonparametric settings using conditional independence tests. However, the latter often suffer from low power (or poor Type I error control) and additive noise models are not suitable for applications in which the response is not measured on a continuous scale, but reflects categories or counts. Here, we develop transformation-model (tram) based ICP, allowing for continuous, categorical, count-type, and uninformatively censored responses (these model classes, generally, do not allow for identifiability when there is no exogenous heterogeneity). As an invariance test, we propose tram-GCM based on the expected conditional covariance between environments and score residuals with uniform asymptotic level guarantees. For the special case of linear shift trams, we also consider tram-Wald, which tests invariance based on the Wald statistic. We provide an open-source R package tramicp and evaluate our approach on simulated data and in a case study investigating causal features of survival in critically ill patients. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Mixtures of factor analysers with censored responses and external covariates: An application to educational data from Peru.

Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures of factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

Youth Misuse of Fire: Measuring the Risk of Firesetting Behaviour Using Explicit and Implicit Methods

Accelerated shifts in global climate have increased the threat from intentionally lit fires, especially within wildfire prone communities. A considerable proportion of intentionally lit fires are set by adolescents with high levels of fire interest. A persistent issue within the literature is difficulty with reliably assessing fire interest, as existing self-report measures are highly susceptible to censored responses. The current study investigated whether fire interest could be effectively measured using attentional bias tasks. The sample consisted of 86 participants (10–17 years; M = 13.65, SD = 1.81) allocated into three firesetter classifications: minor firesetter (n = 24), serious firesetter (n = 28), and non-firesetter (n = 34). All participants completed a series of questionnaires and two modified Stroop tasks aimed at measuring implicit fire interest. The findings showed no association between explicit and implicit measures of fire interest. However, serious firesetters scored significantly higher than other firesetter classifications on both explicit and implicit measures. Additionally, both explicit fire interest and performance on the Lexical Fire-Stroop emerged as significant predictors of firesetting behaviour. Collectively, these results illustrate the Stroop paradigm may be an effective tool to measure implicit fire interest within a community sample, and potential improvements are discussed. The current study detected a surprisingly high frequency of self-reported firesetters within a community sample and significant incongruency between parental and child reported firesetting behaviour, demonstrating the importance of continued research in this area.

Smoothed simulated pseudo-maximum likelihood estimation for nonlinear mixed effects models with censored responses.

Nonlinear mixed effects models have been widely applied to analyses of data that arise from biological, agricultural, and environmental sciences. Estimation of and inference on parameters in nonlinear mixed effects models are often based on the specification of a likelihood function. Maximizing this likelihood function can be complicated by the specification of the random effects distribution, especially in the presence of multiple random effects. The implementation of nonlinear mixed effects models can be further complicated by left-censored responses, representing measurements from bioassays where the exact quantification below a certain threshold is not possible. Motivated by the need to characterize the nonlinear human immunodeficiency virus RNA viral load trajectories after the interruption of antiretroviral therapy, we propose a smoothed simulated pseudo-maximum likelihood estimation approach to fit nonlinear mixed effects models in the presence of left-censored observations. We establish the consistency and asymptotic normality of the resulting estimators. We develop testing procedures for the correlation among random effects and for testing the distributional assumptions on random effects against a specific alternative. In contrast to the existing variants of expectation-maximization approaches, the proposed methods offer flexibility in the specification of the random effects distribution and convenience in making inference about higher-order correlation parameters. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies and illustrate them on a combined dataset from six AIDS Clinical Trials Group treatment interruption studies.

Optimal Model Averaging for Semiparametric Partially Linear Models with Censored Data

In the past few decades, model averaging has received extensive attention, and has been regarded as a feasible alternative to model selection. However, this work is mainly based on parametric model framework and complete dataset. This paper develops a frequentist model-averaging estimation for semiparametric partially linear models with censored responses. The nonparametric function is approximated by B-spline, and the weights in model-averaging estimator are picked up via minimizing a leave-one-out cross-validation criterion. The resulting model-averaging estimator is proved to be asymptotically optimal in the sense of achieving the lowest possible squared error. A simulation study demonstrates that the method in this paper is superior to traditional model-selection and model-averaging methods. Finally, as an illustration, the proposed procedure is further applied to analyze two real datasets.

Multivariate linear mixed models with censored and nonignorable missing outcomes, with application to AIDS studies.

The analysis of multivariate longitudinal data could encounter some complications due to censorship induced by detection limits of the assay and nonresponse occurring when participants missed scheduled visits intermittently or discontinued participation. This paper establishes a generalization of the multivariate linear mixed model that can accommodate censored responses and nonignorable missing outcomes simultaneously. To account for the nonignorable missingness, the selection approach which decomposes the joint distribution as a marginal distribution for the primary outcome variables and a model describing the missing process conditional on the hypothetical complete data is used. A computationally feasible Monte Carlo expectation conditional maximization algorithm is developed for parameter estimation with the maximum likelihood (ML) method. Furthermore, a general information-based approach is presented to assess the variability of ML estimators. The techniques for the prediction of censored responses and imputation of missing outcomes are also discussed. The methodology is motivated and exemplified by a real dataset concerning HIV-AIDS clinical trials. A simulation study is conducted to examine the performance of the proposed method compared with other traditionalapproaches.

Extending multivariate Student's- semiparametric mixed models for longitudinal data with censored responses and heavy tails.

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Distributional anchor regression

Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and in general requires strong assumptions on the data generating process (DGP). In a causally inspired perspective on OOD generalization, the test data arise from a specific class of interventions on exogenous random variables of the DGP, called anchors. Anchor regression models, introduced by Rothenhäusler et al. (J R Stat Soc Ser B 83(2):215–246, 2021. https://doi.org/10.1111/rssb.12398), protect against distributional shifts in the test data by employing causal regularization. However, so far anchor regression has only been used with a squared-error loss which is inapplicable to common responses such as censored continuous or ordinal data. Here, we propose a distributional version of anchor regression which generalizes the method to potentially censored responses with at least an ordered sample space. To this end, we combine a flexible class of parametric transformation models for distributional regression with an appropriate causal regularizer under a more general notion of residuals. In an exemplary application and several simulation scenarios we demonstrate the extent to which OOD generalization is possible.

Food-Away-from-Home Expenditure in Mexico during the COVID-19 Pandemic: A Micro-Econometric Analysis

Disruptive events such as the coronavirus disease 2019 (COVID-19) pandemic have the potential to reshape even the most basic human systems and behaviors, including those related to food production, acquisition, and consumption. This paper provides an in-depth analysis of how the pandemic has changed the ratio of food-away-from-home (FAFH) expenditure to income in Mexico, as well as participation in this market. In 2020, household participation in FAFH expenditures declined in all income deciles and regions, but the impact on household shares is far from uniform. Using a detailed national database of household income and expenditures (N = 87,274), an Engel curve of the Working-Lesser functional form for FAFH including 19 independent variables was estimated using the Heckman method appropriate for censored response data. The results provide statistically significant estimates for income, which both increases the probability of participation in this expenditure and has a negative relationship with its budget share. The number of older adults and the exposure to food insecurity during the pandemic similarly limit participation and increase the budget share. In addition, remittances encourage participation and decrease the budget share. The corrected conditional income elasticity for FAFH is 0.4609; the sign and magnitude indicate that FAFH behaved as a necessary good in Mexico for the proportion of households that maintained spending during the lockdown conditions (about one-third of the sample). An increase or decrease in income will lead to a corresponding change in FAFH expenditure, but the change will be less than proportional.

Scalable algorithms for semiparametric accelerated failure time models in high dimensions.

Semiparametric accelerated failure time (AFT) models are a useful alternative to Cox proportional hazards models, especially when the assumption of constant hazard ratios is untenable. However, rank-based criteria for fitting AFT models are often nondifferentiable, which poses a computational challenge in high-dimensional settings. In this article, we propose a new alternating direction method of multipliers algorithm for fitting semiparametric AFT models by minimizing a penalized rank-based loss function. Our algorithm scales well in both the number of subjects and number of predictors, and can easily accommodate a wide range of popular penalties. To improve the selection of tuning parameters, we propose a new criterion which avoids some common problems in cross-validation with censored responses. Through extensive simulation studies, we show that our algorithm and software is much faster than existing methods (which can only be applied to special cases), and we show that estimators which minimize a penalized rank-based criterion often outperform alternative estimators which minimize penalized weighted least squares criteria. Application to nine cancer datasets further demonstrates that rank-based estimators of semiparametric AFT models are competitive with estimators assuming proportional hazards in high-dimensional settings, whereas weighted least squares estimators are often not. A software package implementing the algorithm, along with a set of auxiliary functions, is available for download at github.com/ajmolstad/penAFT.

Multiparameter one‐sided tests for nonlinear mixed effects models with censored responses

Nonlinear mixed-effects (NLME) models are commonly used in longitudinal studies such as pharmacokinetics and HIV viral dynamics studies. NLME models are often derived based on underlying data-generating mechanisms, therefore the parameters in these models often have natural physical interpretations that may suggest reasonable constraints on certain parameters. For example, the HIV viral decay rates for populations receiving anti-HIV treatments may be reasonably expected to be nonnegative. Hypothesis testing for these parameters should incorporate practically reasonable constraints to increase statistical power. Motivated from HIV viral dynamic models, in this article we propose multiparameter one-sided or constrained tests for NLME models with censored responses, for example, viral dynamic models with viral loads subject to lower detection limits. We propose approximate likelihood-based tests that are computationally efficient. We evaluate the tests via simulations and show that the proposed tests are more powerful than the corresponding two-sided or unrestricted tests. We apply the proposed tests to two AIDS datasets with new findings.

On moments of folded and truncated multivariate Student-t distributions based on recurrence relations

The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that involve the density of multivariate Student-t distributions. The proposed techniques allow for fast computation of arbitrary-order product moments of folded and truncated multivariate Student-t distributions and offer explicit expressions of low-order moments of folded and truncated multivariate Student-t distributions. A real data example containing positive censored responses is applied to illustrate the effectiveness and importance of the proposed methods. An R MomTrunc package is developed and publicly available on the CRAN repository.

A quantile-slicing approach for sufficient dimension reduction with censored responses.

Sufficient dimension reduction (SDR) that effectively reduces the predictor dimension in regression has been popular in high-dimensional data analysis. Under the presence of censoring, however, most existing SDR methods suffer. In this article, we propose a new algorithm to perform SDR with censored responses based on the quantile-slicing scheme recently proposed by Kim etal. First, we estimate the conditional quantile function of the true survival time via the censored kernel quantile regression (Shin etal.) and then slice the data based on the estimated censored regression quantiles instead of the responses. Both simulated and real data analysis demonstrate promising performance of the proposed method.

Linear censored regression models with skew scale mixtures of normal distributions

A special source of difficulty in the statistical analysis is the possibility that some subjects may not have a complete observation of the response variable. Such incomplete observation of the response variable is called censoring. Censorship can occur for a variety of reasons, including limitations of measurement equipment, design of the experiment, and non-occurrence of the event of interest until the end of the study. In the presence of censoring, the dependence of the response variable on the explanatory variables can be explored through regression analysis. In this paper, we propose to examine the censorship problem in context of the class of asymmetric, i.e., we have proposed a linear regression model with censored responses based on skew scale mixtures of normal distributions. We develop a Monte Carlo EM (MCEM) algorithm to perform maximum likelihood inference of the parameters in the proposed linear censored regression models with skew scale mixtures of normal distributions. The MCEM algorithm has been discussed with an emphasis on the skew-normal, skew Student-t-normal, skew-slash and skew-contaminated normal distributions. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset.

Quantile regression for survival data with covariates subject to detection limits.

With advances in biomedical research, biomarkers are becoming increasingly important prognostic factors for predicting overall survival, while the measurement of biomarkers is often censored due to instruments' lower limits of detection. This leads to two types of censoring: random censoring in overall survival outcomes and fixed censoring in biomarker covariates, posing new challenges in statistical modeling and inference. Existing methods for analyzing such data focus primarily on linear regression ignoring censored responses or semiparametric accelerated failure time models with covariates under detection limits (DL). In this paper, we propose a quantile regression for survival data with covariates subject to DL. Comparing to existing methods, the proposed approach provides a more versatile tool for modeling the distribution of survival outcomes by allowing covariate effects to vary across conditional quantiles of the survival time and requiring no parametric distribution assumptions for outcome data. To estimate the quantile process of regression coefficients, we develop a novel multiple imputation approach based on another quantile regression for covariates under DL, avoiding stringent parametric restrictions on censored covariates as often assumed in the literature. Under regularity conditions, we show that the estimation procedure yields uniformly consistent and asymptotically normal estimators. Simulation results demonstrate the satisfactory finite-sample performance of the method. We also apply our method to the motivating data from a study of genetic and inflammatory markers ofSepsis.

Bayesian analysis of multivariate linear mixed models with censored and intermittent missing responses.

Multivariate longitudinal data usually exhibit complex features such as the presence of censored responses due to detection limits of the assay and unavoidable missing values arising when participants make irregular visits that lead to intermittently recorded characteristics. A generalization of the multivariate linear mixed model constructed by taking into account impacts of censored and intermittent missing responses simultaneously, which is named as the MLMM-CM, has been recently proposed for more precisely analyzing such kinds of data. This paper aims at presenting a fully Bayesian sampling-based approach to the MLMM-CM for addressing the uncertainties of censored and missing responses as well as unknown parameters. Two widely accepted Bayesian computational techniques based on the Markov chain Monte Carlo and the inverse Bayes formulas coupled with the Gibbs (IBF-Gibbs) schemes are developed for carrying out posterior inference of the model. The proposed methodology is illustrated through a simulation study and a real-data example from the Adult AIDS Clinical Trials Group 388 study. Numerical results show empirically that the proposed Bayesian methodology performs satisfactorily and offers reliable posterior inference.

High-dimensional single-index models with censored responses.

In this article, we study the estimation of high-dimensional single index models when the response variable is censored. We hybrid the estimation methods for high-dimensional single-index models (but without censorship) and univariate nonparametric models with randomly censored responses to estimate the index parameters and the link function and apply the proposed methods to analyze a genomic dataset from a study of diffuse large B-cell lymphoma. We evaluate the finite sample performance of the proposed procedures via simulation studies and establish large sample theories for the proposed estimators of the index parameter and the nonparametric link function under certain regularity conditions.

Multivariate-t linear mixed models with censored responses, intermittent missing values and heavy tails.

Multivariate longitudinal data arisen in medical studies often exhibit complex features such as censored responses, intermittent missing values, and atypical or outlying observations. The multivariate-t linear mixed model (MtLMM) has been recognized as a powerful tool for robust modeling of multivariate longitudinal data in the presence of potential outliers or fat-tailed noises. This paper presents a generalization of MtLMM, called the MtLMM-CM, to properly adjust for censorship due to detection limits of the assay and missingness embodied within multiple outcome variables recorded at irregular occasions. An expectation conditional maximization either (ECME) algorithm is developed to compute parameter estimates using the maximum likelihood (ML) approach. The asymptotic standard errors of the ML estimators of fixed effects are obtained by inverting the empirical information matrix according to Louis' method. The techniques for the estimation of random effects and imputation of missing responses are also investigated. The proposed methodology is illustrated on two real-world examples from HIV-AIDS studies and a simulation study under a variety of scenarios.

Practical Causal Analysis for the Treatment Timing Effect on Doubly Censored Duration: Effect of Fertility on Work Span

Summary We present a practical causal framework to estimate the effects of a treatment and its timing on a doubly censored response. We then apply the methodology to find the effect of fertility on work duration where, not just fertility itself, but the timing of fertility should matter greatly. Since fertility and its decision of timing are chosen by the individual, it is likely to be endogenous. We use a populationwide data set over mothers with two children to address the endogeneity issue by using the first two children’s same-sex instrument in a ‘control function’ setting. We find that having a third child reduces the average labour market work duration, and that the magnitude of the effect increases monotonically with the waiting time between the second and third children. Moreover, the negative effect varies substantially over education and second-birth age, being stronger for mothers with higher education and lower second-birth age.

Estimation in additive models with fixed censored responses

ABSTRACTWe propose a new estimation method to estimate the nonparametric functions in additive models, where the response is subject to fixed censoring. Under some regularity conditions, we show that the proposed estimator is uniformly consistent with certain convergence rates. The simulation study shows that the proposed estimator performs well in finite sample sizes. We also analyze a dataset from an HIV study for an illustration.