RKHS-based covariate balancing for survival causal effect estimation.

Survival causal effect estimation based on right-censored data is of key interest in both survival analysis and causal inference. Propensity score weighting is one of the most popular methods in the literature. However, since it involves the inverse of propensity score estimates, its practical performance may be very unstable, especially when the covariate overlap is limited between treatment and control groups. To address this problem, a covariate balancing method is developed in this paper to estimate the counterfactual survival function. The proposed method is nonparametric and balances covariates in a reproducing kernel Hilbert space (RKHS) via weights that are counterparts of inverse propensity scores. The uniform rate of convergence for the proposed estimator is shown to be the same as that for the classical Kaplan-Meier estimator. The appealing practical performance of the proposed method is demonstrated by a simulation study as well as two real data applications to study the causal effect of smoking on survival time of stroke patients and that of endotoxin on survival time for female patients with lung cancer respectively.

On a simple estimation of the proportional odds model under right truncation.

Retrospective sampling can be useful in epidemiological research for its convenience to explore an etiological association. One particular retrospective sampling is that disease outcomes of the time-to-event type are collected subject to right truncation, along with other covariates of interest. For regression analysis of the right-truncated time-to-event data, the so-called proportional reverse-time hazards model has been proposed, but the interpretation of its regression parameters tends to be cumbersome, which has greatly hampered its application in practice. In this paper, we instead consider the proportional odds model, an appealing alternative to the popular proportional hazards model. Under the proportional odds model, there is an embedded relationship between the reverse-time hazard function and the usual hazard function. Building on this relationship, we provide a simple procedure to estimate the regression parameters in the proportional odds model for the right truncated data. Weighted estimations are also studied.

Model selection among Dimension-Reduced generalized Cox models.

Conventional semiparametric hazards regression models rely on the specification of particular model formulations, such as proportional-hazards feature and single-index structures. Instead of checking these modeling assumptions one-by-one, we proposed a class of dimension-reduced generalized Cox models, and then a consistent model selection procedure among this class to select covariates with proportional-hazards feature and a proper model formulation for non-proportional-hazards covariates. In this class, the non-proportional-hazards covariates are treated in a nonparametric manner, and a partial sufficient dimension reduction is introduced to reduce the curse of dimensionality. A semiparametric efficient estimation is proposed to estimate these models. Based on the proposed estimation, we further constructed a cross-validation type criterion to consistently select the correct model among this class. Most importantly, this class of hazards regression models contains the fully nonparametric hazards regression model as the most saturated submodel, and hence no further model diagnosis is required. Overall speaking, this model selection approach is more effective than performing a sequence of conventional model checking. The proposed method is illustrated by simulation studies and a data example.

Maternal Gestational Weight Gain in Relation to Antidepressant Continuation in Pregnancy.

OBJECTIVE: Both excessive and inadequate gestational weight gain (GWG) are associated with adverse health outcomes for the woman and her child. Antidepressant use in pregnancy could affect GWG, based on evidence in nonpregnant women that some antidepressants may cause weight gain and others weight loss. Previous studies of antidepressant use and GWG were small with limited ability to account for confounding, including by maternal mental health status and severity. We assessed the association of antidepressant continuation in pregnancy with GWG among women using antidepressants before pregnancy. STUDY DESIGN: Our retrospective cohort study included singleton livebirths from 2001 to 2014 within Kaiser Permanente Washington, an integrated health care system. Data were obtained from electronic health records and linked Washington State birth records. Among women with ≥1 antidepressant fill within 6 months before pregnancy, women who filled an antidepressant during pregnancy were considered "continuers;" women without a fill were "discontinuers." We calculated mean differences in GWG and relative risks (RR) of inadequate and excessive weight gain based on Institute of Medicine guidelines. Using inverse probability of treatment weighting with generalized estimating equations, we addressed differences in maternal characteristics, including mental health conditions. RESULTS: Among the 2,887 births, 1,689 (59%) were to women who continued antidepressants in pregnancy and 1,198 (42%) were to discontinuers. After accounting for confounding, continuers had similar weight gain to those who discontinued (mean difference: 1.3 lbs, 95% confidence interval [CI]: -0.1 to 2.8 lbs) and similar risks of inadequate and excessive GWG (RR: 0.95, 95% CI: 0.80-1.14 and RR: 1.06, 95% CI: 0.98-1.14, respectively). Findings were comparable for specific antidepressants and trimesters of exposure. CONCLUSION: We did not find evidence that continuation of antidepressants in pregnancy led to differences in GWG. KEY POINTS: · Antidepressant use is associated with weight change in nonpregnant populations.. · Prior evidence on whether antidepressant use in pregnancy affects gestational weight gain is sparse.. · We accounted for confounding by characteristics such as mental health conditions and their severity.. · We found no association between pregnancy antidepressant continuation and gestational weight gain..

Women's beliefs about what causes obesity: variation by race/ethnicity and acculturation in a Washington State sample.

Objective: Individuals' beliefs about the causes of multifactorial health conditions (causal attributions) shape how they conceptualize and respond to health threats and are therefore important for health promotion. Studies of racial/ethnic and cultural variation in obesity causal beliefs, however, are scarce. To address this gap, this study described beliefs about the underlying causes of obesity (genetic inheritance, diet, and physical activity) in Hispanic and non-Hispanic White women participating in a longitudinal cohort study in South King County, Washington State (n = 1,002).Design: Analysis of baseline survey data. Self-reported obesity causal beliefs were compared by race/ethnicity and acculturation indicators (survey language and nativity) using marginal effect estimates generated from multinomial logistic regression models.Results: Hispanic women had a higher probability of not believing 'at all' in inheritance and physical activity as causes of obesity - an absolute increase of 33% and 5% over non-Hispanic White women, respectively. Both acculturation indicators were also associated with a higher probability of not believing 'at all' in inheritance as a cause of obesity, though Hispanic women who completed the survey in English and were born in the United States had genetic causal beliefs similar to non-Hispanic White women. Behavioral attributions did not vary by acculturation indicators in Hispanic women.Conclusions: Differences in obesity casual beliefs, particularly genetic attributions, exist and may be important for developing and delivering effective obesity-related health promotion interventions. Identifying the determinants and public health consequences of cultural variation in obesity attributions should be the focus of future research.

Sufficient dimension reduction with simultaneous estimation of effective dimensions for time-to-event data.

When there is not enough scientific knowledge to assume a particular regression model, sufficient dimension reduction is a flexible yet parsimonious nonparametric framework to study how covariates are associated with an outcome. We propose a novel estimator of low-dimensional composite scores, which can summarize the contribution of covariates on a right-censored survival outcome. The proposed estimator determines the degree of dimension reduction adaptively from data; it estimates the structural dimension, the central subspace and a rate-optimal smoothing bandwidth parameter simultaneously from a single criterion. The methodology is formulated in a counting process framework. Further, the estimation is free of the inverse probability weighting employed in existing methods, which often leads to instability in small samples. We derive the large sample properties for the estimated central subspace with data-adaptive structural dimension and bandwidth. The estimation can be easily implemented by a forward selection algorithm, and this implementation is justified by asymptotic convexity of the criterion in working dimensions. Numerical simulations and two real examples are given to illustrate the proposed method.

Semiparametric regression analysis of length-biased interval-censored data.

In prevalent cohort design, subjects who have experienced an initial event but not the failure event are preferentially enrolled and the observed failure times are often length-biased. Moreover, the prospective follow-up may not be continuously monitored and failure times are subject to interval censoring. We study the nonparametric maximum likelihood estimation for the proportional hazards model with length-biased interval-censored data. Direct maximization of likelihood function is intractable, thus we develop a computationally simple and stable expectation-maximization algorithm through introducing two layers of data augmentation. We establish the strong consistency, asymptotic normality and efficiency of the proposed estimator and provide an inferential procedure through profile likelihood. We assess the performance of the proposed methods through extensive simulations and apply the proposed methods to the Massachusetts Health Care Panel Study.

Simple and fast overidentified rank estimation for right-censored length-biased data and backward recurrence time.

Length-biased survival data subject to right-censoring are often collected from a prevalent cohort. However, informative right censoring induced by the sampling design creates challenges in methodological development. While certain conditioning arguments could circumvent the problem of informative censoring, related rank estimation methods are typically inefficient because the marginal likelihood of the backward recurrence time is not ancillary. Under a semiparametric accelerated failure time model, an overidentified set of log-rank estimating equations is constructed based on the left-truncated right-censored data and backward recurrence time. Efficient combination of the estimating equations is simplified by exploiting an asymptotic independence property between two sets of estimating equations. A fast algorithm is studied for solving non-smooth, non-monotone estimating equations. Simulation studies confirm that the overidentified rank estimator can have a substantially improved estimation efficiency compared to just-identified rank estimators. The proposed method is applied to a dementia study for illustration.

ESTIMATION OF A MONOTONE DENSITY IN S-SAMPLE BIASED SAMPLING MODELS.

We study the nonparametric estimation of a decreasing density function g 0 in a general s-sample biased sampling model with weight (or bias) functions wi for i = 1, …, s. The determination of the monotone maximum likelihood estimator gn and its asymptotic distribution, except for the case when s = 1, has been long missing in the literature due to certain non-standard structures of the likelihood function, such as non-separability and a lack of strictly positive second order derivatives of the negative of the log-likelihood function. The existence, uniqueness, self-characterization, consistency of gn and its asymptotic distribution at a fixed point are established in this article. To overcome the barriers caused by non-standard likelihood structures, for instance, we show the tightness of gn via a purely analytic argument instead of an intrinsic geometric one and propose an indirect approach to attain the n -rate of convergence of the linear functional ∫ wi gn.

Joint modeling of longitudinal, recurrent events and failure time data for survivor's population.

Recurrent events together with longitudinal measurements are commonly observed in follow-up studies where the observation is terminated by censoring or a primary failure event. In this article, we developed a joint model where the dependence of longitudinal measurements, recurrent event process and time to failure event is modeled through rescaling the time index. The general idea is that the trajectories of all biology processes of subjects in the survivors' population are elongated or shortened by the rate identified from a model for the failure event. To avoid making disputing assumptions on recurrent events or biomarkers after the failure event (such as death), the model is constructed on the basis of survivors' population. The model also possesses a specific feature that, by aligning failure events as time origins, the backward-in-time model of recurrent events and longitudinal measurements shares the same parameter values with the forward time model. The statistical properties, simulation studies and real data examples are conducted. The proposed method can be generalized to analyze left-truncated data.

Reproducibility and relative validity of food group intake in a food frequency questionnaire developed for Nepalese diet.

We developed a food frequency questionnaire (FFQ) designed to measure the dietary practices of adult Nepalese. The present study examined the validity and reproducibility of the FFQ. To evaluate the reproducibility of the FFQ, 116 subjects completed two 115-item FFQ across a four-month interval. Six 24-h dietary recalls were collected (1 each month) to assess the validity of the FFQ. Seven major food groups and 23 subgroups were clustered from the FFQ based on macronutrient composition. Spearman correlation coefficients evaluating reproducibility for all food groups were greater than 0.5, with the exceptions of oil. The correlations varied from 0.41 (oil) to 0.81 (vegetables). All crude spearman coefficients for validity were greater than 0.5 except for dairy products, pizzas/pastas and sausage/burgers. The FFQ was found to be reliable and valid for ranking the intake of food groups for Nepalese dietary intake.

Acceleration of Expectation-Maximization algorithm for length-biased right-censored data.

Vardi's Expectation-Maximization (EM) algorithm is frequently used for computing the nonparametric maximum likelihood estimator of length-biased right-censored data, which does not admit a closed-form representation. The EM algorithm may converge slowly, particularly for heavily censored data. We studied two algorithms for accelerating the convergence of the EM algorithm, based on iterative convex minorant and Aitken's delta squared process. Numerical simulations demonstrate that the acceleration algorithms converge more rapidly than the EM algorithm in terms of number of iterations and actual timing. The acceleration method based on a modification of Aitken's delta squared performed the best under a variety of settings.

Nonparametric inference for the joint distribution of recurrent marked variables and recurrent survival time.

Time between recurrent medical events may be correlated with the cost incurred at each event. As a result, it may be of interest to describe the relationship between recurrent events and recurrent medical costs by estimating a joint distribution. In this paper, we propose a nonparametric estimator for the joint distribution of recurrent events and recurrent medical costs in right-censored data. We also derive the asymptotic variance of our estimator, a test for equality of recurrent marker distributions, and present simulation studies to demonstrate the performance of our point and variance estimators. Our estimator is shown to perform well for a wide range of levels of correlation, demonstrating that our estimators can be employed in a variety of situations when the correlation structure may be unknown in advance. We apply our methods to hospitalization events and their corresponding costs in the second Multicenter Automatic Defibrillator Implantation Trial (MADIT-II), which was a randomized clinical trial studying the effect of implantable cardioverter-defibrillators in preventing ventricular arrhythmia.

Rank-based testing of equal survivorship based on cross-sectional survival data with or without prospective follow-up.

Existing linear rank statistics cannot be applied to cross-sectional survival data without follow-up since all subjects are essentially censored. However, partial survival information are available from backward recurrence times and are frequently collected from health surveys without prospective follow-up. Under length-biased sampling, a class of linear rank statistics is proposed based only on backward recurrence times without any prospective follow-up. When follow-up data are available, the proposed rank statistic and a conventional rank statistic that utilizes follow-up information from the same sample are shown to be asymptotically independent. We discuss four ways to combine these two statistics when follow-up is present. Simulations show that all combined statistics have substantially improved power compared with conventional rank statistics, and a Mantel-Haenszel test performed the best among the proposal statistics. The method is applied to a cross-sectional health survey without follow-up and a study of Alzheimer's disease with prospective follow-up.

Reader reaction: Instrumental variable additive hazards models with exposure-dependent censoring.

Li, Fine, and Brookhart (2015) presented an extension of the two-stage least squares (2SLS) method for additive hazards models which requires an assumption that the censoring distribution is unrelated to the endogenous exposure variable. We present another extension of 2SLS that can address this limitation.

Testing concordance of instrumental variable effects in generalized linear models with application to Mendelian randomization.

Instrumental variable regression is one way to overcome unmeasured confounding and estimate causal effect in observational studies. Built on structural mean models, there has been considerable work recently developed for consistent estimation of causal relative risk and causal odds ratio. Such models can sometimes suffer from identification issues for weak instruments. This hampered the applicability of Mendelian randomization analysis in genetic epidemiology. When there are multiple genetic variants available as instrumental variables, and causal effect is defined in a generalized linear model in the presence of unmeasured confounders, we propose to test concordance between instrumental variable effects on the intermediate exposure and instrumental variable effects on the disease outcome, as a means to test the causal effect. We show that a class of generalized least squares estimators provide valid and consistent tests of causality. For causal effect of a continuous exposure on a dichotomous outcome in logistic models, the proposed estimators are shown to be asymptotically conservative. When the disease outcome is rare, such estimators are consistent because of the log-linear approximation of the logistic function. Optimality of such estimators relative to the well-known two-stage least squares estimator and the double-logistic structural mean model is further discussed.

Can we make smart choices between OLS and contaminated IV methods?

In the outcomes research and comparative effectiveness research literature, there are strong cautionary tales on the use of instrumental variables (IVs) that may influence the newly initiated to shun this premier tool for casual inference without properly weighing their advantages. It has been recommended that IV methods should be avoided if the instrument is not econometrically perfect. The fact that IVs can produce better results than naïve regression, even in nonideal circumstances, remains underappreciated. In this paper, we propose a diagnostic criterion and related software that can be used by an applied researcher to determine the plausible superiority of IV over an ordinary least squares (OLS) estimator, which does not address the endogeneity of a covariate in question. Given a reasonable lower bound for the bias arising out of an OLS estimator, the researcher can use our proposed diagnostic tool to confirm whether the IV at hand can produce a better estimate (i.e., with lower mean square error) of the true effect parameter than the OLS, without knowing the true level of contamination in the IV.

A note about the identifiability of causal effect estimates in randomized trials with non-compliance.

We show that assumptions that are sufficient for estimating an average treatment effect in randomized trials with non-compliance restrict the subgroup means for always takers, compliers, defiers and never takers to a two dimensional linear subspace of a four dimensional space. Implications and specials cases are examplified.

Longitudinal Relationship Between Brain Atrophy Patterns, Cognitive Decline, and Cerebrospinal Fluid Biomarkers in Alzheimer's Disease Explored by Orthonormal Projective Non-Negative Matrix Factorization.

Background: Longitudinal magnetic resonance imaging (MRI) has been proposed for tracking the progression of Alzheimer's disease (AD) through the assessment of brain atrophy. Objective: Detection of brain atrophy patterns in patients with AD as the longitudinal disease tracker. Methods: We used a refined version of orthonormal projective non-negative matrix factorization (OPNMF) to identify six distinct spatial components of voxel-wise volume loss in the brains of 83 subjects with AD from the ADNI3 cohort relative to healthy young controls from the ABIDE study. We extracted non-negative coefficients representing subject-specific quantitative measures of regional atrophy. Coefficients of brain atrophy were compared to subjects with mild cognitive impairment and controls, to investigate the cross-sectional and longitudinal associations between AD biomarkers and regional atrophy severity in different groups. We further validated our results in an independent dataset from ADNI2. Results: The six non-overlapping atrophy components represent symmetric gray matter volume loss primarily in frontal, temporal, parietal and cerebellar regions. Atrophy in these regions was highly correlated with cognition both cross-sectionally and longitudinally, with medial temporal atrophy showing the strongest correlations. Subjects with elevated CSF levels of TAU and PTAU and lower baseline CSF Aß42 values, demonstrated a tendency toward a more rapid increase of atrophy. Conclusions: The present study has applied a transferable method to characterize the imaging changes associated with AD through six spatially distinct atrophy components and correlated these atrophy patterns with cognitive changes and CSF biomarkers cross-sectionally and longitudinally, which may help us better understand the underlying pathology of AD.