Causal inference with longitudinal data subject to irregular assessment times.

Data collected in the context of usual care present a rich source of longitudinal data for research, but often require analyses that simultaneously enable causal inferences from observational data while handling irregular and informative assessment times. An inverse-weighting approach to this was recently proposed, and handles the case where the assessment times are at random (ie, conditionally independent of the outcome process given the observed history). In this paper, we extend the inverse-weighting approach to handle a special case of assessment not at random, where assessment and outcome processes are conditionally independent given past observed covariates and random effects. We use multiple outputation to accomplish the same purpose as inverse-weighting, and apply it to the Liang semi-parametric joint model. Moreover, we develop an alternative joint model that does not require covariates for the outcome model to be known at times where there is no assessment of the outcome. We examine the performance of these methods through simulation and illustrate them through a study of the causal effect of wheezing on time spent playing outdoors among children aged 2-9 years and enrolled in the TargetKids! study.

Longitudinal mediation analysis of time-to-event endpoints in the presence of competing risks.

This proposal is motivated by an analysis of the English Longitudinal Study of Ageing (ELSA), which aims to investigate the role of loneliness in explaining the negative impact of hearing loss on dementia. The methodological challenges that complicate this mediation analysis include the use of a time-to-event endpoint subject to competing risks, as well as the presence of feedback relationships between the mediator and confounders that are both repeatedly measured over time. To account for these challenges, we introduce path-specific effect proportional (cause-specific) hazard models. These extend marginal structural proportional (cause-specific) hazard models to enable effect decomposition on either the cause-specific hazard ratio scale or the cumulative incidence function scale. We show that under certain ignorability assumptions, the path-specific direct and indirect effects indexing this model are identifiable from the observed data. We next propose an inverse probability weighting approach to estimate these effects. On the ELSA data, this approach reveals little evidence that the total effect of hearing loss on dementia is mediated through the feeling of loneliness, with a non-statistically significant indirect effect equal to 1.01 (hazard ratio (HR) scale; 95% confidence interval (CI) 0.99 to 1.05).

Restricted mean survival time as a function of restriction time.

Restricted mean survival time (RMST) is a clinically interpretable and meaningful survival metric that has gained popularity in recent years. Several methods are available for regression modeling of RMST, most based on pseudo-observations or what is essentially an inverse-weighted complete-case analysis. No existing RMST regression method allows for the covariate effects to be expressed as functions over time. This is a considerable limitation, in light of the many hazard regression methods that do accommodate such effects. To address this void in the literature, we propose RMST methods that permit estimating time-varying effects. In particular, we propose an inference framework for directly modeling RMST as a continuous function of L. Large-sample properties are derived. Simulation studies are performed to evaluate the performance of the methods in finite sample sizes. The proposed framework is applied to kidney transplant data obtained from the Scientific Registry of Transplant Recipients.

Clustered longitudinal data subject to irregular observation.

Data collected longitudinally as part of usual health care is becoming increasingly available for research, and is often available across several centres. Because the frequency of follow-up is typically determined by the patient's health, the timing of measurements may be related to the outcome of interest. Failure to account for the informative nature of the observation process can result in biased inferences. While methods for accounting for the association between observation frequency and outcome are available, they do not currently account for clustering within centres. We formulate a semi-parametric joint model to include random effects for centres as well as subjects. We also show how inverse-intensity weighted GEEs can be adapted to account for clustering, comparing stratification, frailty models, and covariate adjustment to account for clustering in the observation process. The finite-sample performance of the proposed methods is evaluated through simulation and the methods illustrated using a study of the relationship between outdoor play and air quality in children aged 2-9 living in the Greater Toronto Area.

Assessing the effects of maternal HIV infection on pregnancy outcomes using cross-sectional data in Malawi.

BACKGROUND: Several studies have shown that maternal HIV infection is associated with adverse pregnancy outcomes such as low birth weight and perinatal mortality. However, the association is conflicted with the effect of antiretroviral therapy (ART) on the pregnancy outcomes and it remains unexamined. If the association is confirmed then it would guide policy makers towards more effective prevention of mother to child HIV transmission interventions. Using methods for matching possible confounders, the objectives of the study were to assess the effect of maternal HIV infection on birth weight and perinatal mortality and to investigate the effect of ART on these two pregnancy outcomes in HIV-infected women. METHODS: Data on 4111 and 4759 children, born within five years of the 2010 and 2015-16 Malawi Demographic and Health Surveys (MDHS) respectively, whose mothers had an HIV test result, were analysed. A best balancing method was chosen from a set of covariate balance methods namely, the 1:1 nearest neighbour (NN) matching, matching on the propensity score (PS) and inverse weighting on the PS. HIV and ART data were only available in the MDHS 2010, permitting an assessment of the moderating effect of ART on the association between maternal HIV infection and birth weight and perinatal mortality. RESULTS: The overall average birth weight was 3227.9g (95% CI: 3206.4, 3249.5) in 2010 and 3226.4g (95%: 3205.6, 3247.2) in 2015-16 and perinatal mortality was 3.8% (95%: 3.2, 4.3) in 2010 and 3.5% (95%: 2.8, 3.8) in 2015-16. The prevalence of HIV among the mothers was 11.1% (95%: 10.1, 12.0) and 9.2% (95% CI: 8.4, 10.1) in 2010 and 2015-16, respectively. In 2010, maternal HIV infection was negatively associated with birth weight (mean= -25.3g, 95% CI:(-95.5, -7.4)) and in 2015-16 it was positively associated with birth weight (mean= 116.3g, 95% CI:(27.8, 204.7)). Perinatal mortality was higher in infants of HIV-infected mothers compared to infants of HIV-uninfected mothers (OR = 1.5, 95% CI:(1.1 - 3.1)) in 2010, while there was no difference in the rate in 2015-16 (OR = 1.0, 95% CI:(0.4, 1.6)). ART was not associated with birth weight, however, it was associated with perinatal mortality (OR=3.9, 95% CI:(1.1, 14.8)). CONCLUSION: The study has found that maternal HIV infection had an adverse effect on birth weight and perinatal mortality in 2010. Birth weight was not dependent on ART uptake but perinatal mortality was higher among infants of HIV-infected mothers who were not on ART. The higher birth weight among HIV-infected mothers and similarity in perinatal mortality with HIV-uninfected mothers in 2015-16 may be indicative of successes of interventions within the PMTCT program in Malawi.

Causal comparative effectiveness analysis of dynamic continuous-time treatment initiation rules with sparsely measured outcomes and death.

Evidence supporting the current World Health Organization recommendations of early antiretroviral therapy (ART) initiation for adolescents is inconclusive. We leverage a large observational data and compare, in terms of mortality and CD4 cell count, the dynamic treatment initiation rules for human immunodeficiency virus-infected adolescents. Our approaches extend the marginal structural model for estimating outcome distributions under dynamic treatment regimes, developed in Robins et al. (2008), to allow the causal comparisons of both specific regimes and regimes along a continuum. Furthermore, we propose strategies to address three challenges posed by the complex data set: continuous-time measurement of the treatment initiation process; sparse measurement of longitudinal outcomes of interest, leading to incomplete data; and censoring due to dropout and death. We derive a weighting strategy for continuous-time treatment initiation, use imputation to deal with missingness caused by sparse measurements and dropout, and define a composite outcome that incorporates both death and CD4 count as a basis for comparing treatment regimes. Our analysis suggests that immediate ART initiation leads to lower mortality and higher median values of the composite outcome, relative to other initiation rules.

Using a monotone single-index model to stabilize the propensity score in missing data problems and causal inference.

The augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems. An important component of this method is the propensity score. Popular parametric models for the propensity score include the logistic, probit, and complementary log-log models. A common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables. To avoid the need to choose a model, we model the propensity score via a semiparametric single-index model, in which the score is an unknown monotonic nondecreasing function of the given single index. Under this new model, the augmented inverse weighting estimator (AIWE) of the mean of the response is asymptotically linear, semiparametrically efficient, and more robust than existing estimators. Moreover, we have made a surprising observation. The inverse probability weighting and AIWEs based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model. A heuristic explanation of this phenomenon is provided. A real-data example is used to illustrate the proposed methods.

Nonparametric estimation of transition probabilities for a general progressive multi-state model under cross-sectional sampling.

Nonparametric estimation of the transition probability matrix of a progressive multi-state model is considered under cross-sectional sampling. Two different estimators adapted to possibly right-censored and left-truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub-samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left-truncation times associated with the cross-sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs).

Tobit regression for modeling mean survival time using data subject to multiple sources of censoring.

Mean survival time is often of inherent interest in medical and epidemiologic studies. In the presence of censoring and when covariate effects are of interest, Cox regression is the strong default, but mostly due to convenience and familiarity. When survival times are uncensored, covariate effects can be estimated as differences in mean survival through linear regression. Tobit regression can validly be performed through maximum likelihood when the censoring times are fixed (ie, known for each subject, even in cases where the outcome is observed). However, Tobit regression is generally inapplicable when the response is subject to random right censoring. We propose Tobit regression methods based on weighted maximum likelihood which are applicable to survival times subject to both fixed and random censoring times. Under the proposed approach, known right censoring is handled naturally through the Tobit model, with inverse probability of censoring weighting used to overcome random censoring. Essentially, the re-weighting data are intended to represent those that would have been observed in the absence of random censoring. We develop methods for estimating the Tobit regression parameter, then the population mean survival time. A closed form large-sample variance estimator is proposed for the regression parameter estimator, with a semiparametric bootstrap standard error estimator derived for the population mean. The proposed methods are easily implementable using standard software. Finite-sample properties are assessed through simulation. The methods are applied to a large cohort of patients wait-listed for kidney transplantation.

Modeling survival distribution as a function of time to treatment discontinuation: A dynamic treatment regime approach.

We consider estimating the effect that discontinuing a beneficial treatment will have on the distribution of a time to event clinical outcome, and in particular assessing whether there is a period of time over which the beneficial effect may continue after discontinuation. There are two major challenges. The first is to make a distinction between mandatory discontinuation, where by necessity treatment has to be terminated and optional discontinuation which is decided by the preference of the patient or physician. The innovation in this article is to cast the intervention in the form of a dynamic regime "terminate treatment optionally at time v unless a mandatory treatment-terminating event occurs prior to v" and consider estimating the distribution of time to event as a function of treatment regime v. The second challenge arises from biases associated with the nonrandom assignment of treatment regimes, because, naturally, optional treatment discontinuation is left to the patient and physician, and so time to discontinuation may depend on the patient's disease status. To address this issue, we develop dynamic-regime Marginal Structural Models and use inverse probability of treatment weighting to estimate the impact of time to treatment discontinuation on a time to event outcome, compared to the effect of not discontinuing treatment. We illustrate our methods using the IMPROVE-IT data on cardiovascular disease.

Inverse probability weighted Cox regression for doubly truncated data.

Doubly truncated data arise when event times are observed only if they fall within subject-specific, possibly random, intervals. While non-parametric methods for survivor function estimation using doubly truncated data have been intensively studied, only a few methods for fitting regression models have been suggested, and only for a limited number of covariates. In this article, we present a method to fit the Cox regression model to doubly truncated data with multiple discrete and continuous covariates, and describe how to implement it using existing software. The approach is used to study the association between candidate single nucleotide polymorphisms and age of onset of Parkinson's disease.

Modeling the causal effect of treatment initiation time on survival: Application to HIV/TB co-infection.

The timing of antiretroviral therapy (ART) initiation for HIV and tuberculosis (TB) co-infected patients needs to be considered carefully. CD4 cell count can be used to guide decision making about when to initiate ART. Evidence from recent randomized trials and observational studies generally supports early initiation but does not provide information about effects of initiation time on a continuous scale. In this article, we develop and apply a highly flexible structural proportional hazards model for characterizing the effect of treatment initiation time on a survival distribution. The model can be fitted using a weighted partial likelihood score function. Construction of both the score function and the weights must accommodate censoring of the treatment initiation time, the outcome, or both. The methods are applied to data on 4903 individuals with HIV/TB co-infection, derived from electronic health records in a large HIV care program in Kenya. We use a model formulation that flexibly captures the joint effects of ART initiation time and ART duration using natural cubic splines. The model is used to generate survival curves corresponding to specific treatment initiation times; and to identify optimal times for ART initiation for subgroups defined by CD4 count at time of TB diagnosis. Our findings potentially provide 'higher resolution' information about the relationship between ART timing and mortality, and about the differential effect of ART timing within CD4 subgroups.

Modeling restricted mean survival time under general censoring mechanisms.

Restricted mean survival time (RMST) is often of great clinical interest in practice. Several existing methods involve explicitly projecting out patient-specific survival curves using parameters estimated through Cox regression. However, it would often be preferable to directly model the restricted mean for convenience and to yield more directly interpretable covariate effects. We propose generalized estimating equation methods to model RMST as a function of baseline covariates. The proposed methods avoid potentially problematic distributional assumptions pertaining to restricted survival time. Unlike existing methods, we allow censoring to depend on both baseline and time-dependent factors. Large sample properties of the proposed estimators are derived and simulation studies are conducted to assess their finite sample performance. We apply the proposed methods to model RMST in the absence of liver transplantation among end-stage liver disease patients. This analysis requires accommodation for dependent censoring since pre-transplant mortality is dependently censored by the receipt of a liver transplant.

Doubly robust estimator for net survival rate in analyses of cancer registry data.

Cancer population studies based on cancer registry databases are widely conducted to address various research questions. In general, cancer registry databases do not collect information on cause of death. The net survival rate is defined as the survival rate if a subject would not die for any causes other than cancer. This counterfactual concept is widely used for the analyses of cancer registry data. Perme, Stare, and Estève (2012) proposed a nonparametric estimator of the net survival rate under the assumption that the censoring time is independent of the survival time and covariates. Kodre and Perme (2013) proposed an inverse weighting estimator for the net survival rate under the covariate-dependent censoring. An alternative approach to estimating the net survival rate under covariate-dependent censoring is to apply a regression model for the conditional net survival rate given covariates. In this article, we propose a new estimator for the net survival rate. The proposed estimator is shown to be doubly robust in the sense that it is consistent at least one of the regression models for survival time and for censoring time. We examine the theoretical and empirical properties of our proposed estimator by asymptotic theory and simulation studies. We also apply the proposed method to cancer registry data for gastric cancer patients in Osaka, Japan.

Methods for Contrasting Gap Time Hazard Functions: Application to Repeat Liver Transplantation.

In studies featuring a sequence of ordered events, gap times between successive events are often of interest. Despite the rich literature in this area, very few methods for comparing gap times have been developed. We propose methods for estimating a hazard ratio connecting the first and second gap times. Specifically, a two-stage procedure is developed based on estimating equations. At the first stage, a proportional hazards model is fitted for the first gap time. Weighted estimating equations are then solved at the second stage to estimate the hazard ratio between the first and second gap times. The proposed estimator has a closed form and, being analogous to a standardized mortality ratio, is easy to interpret. Large sample properties of the proposed estimators are derived, with simulation studies used to evaluate finite sample characteristics. Extension of the approach to accommodate a piecewise constant hazard ratio is considered. The proposed methods are applied to contrast repeat (second) versus primary (first) liver transplants with respect to graft failure, based on national registry data.

A joint latent class analysis for adjusting survival bias with application to a trauma transfusion study.

There is no clear classification rule to rapidly identify trauma patients who are severely hemorrhaging and may need substantial blood transfusions. Massive transfusion (MT), defined as the transfusion of at least 10 units of red blood cells within 24 h of hospital admission, has served as a conventional surrogate that has been used to develop early predictive algorithms and establish criteria for ordering an MT protocol from the blood bank. However, the conventional MT rule is a poor proxy, because it is likely to misclassify many severely hemorrhaging trauma patients as they could die before receiving the 10th red blood cells transfusion. In this article, we propose to use a latent class model to obtain a more accurate and complete metric in the presence of early death. Our new approach incorporates baseline patient information from the time of hospital admission, by combining respective models for survival time and usage of blood products transfused within the framework of latent class analysis. To account for statistical challenges, caused by induced dependent censoring inherent in 24-h sums of transfusions, we propose to estimate an improved standard via a pseudo-likelihood function using an expectation-maximization algorithm with the inverse weighting principle. We evaluated the performance of our new standard in simulation studies and compared with the conventional MT definition using actual patient data from the Prospective Observational Multicenter Major Trauma Transfusion study. Copyright © 2015 John Wiley & Sons, Ltd.

Semiparametric Contrasts of Cumulative Pre-Treatment Mortality in the Presence of Dependent Censoring.

In clinical settings, the necessity of treatment is often measured in terms of the patient's prognosis in the absence of treatment. Along these lines, it is often of interest to compare subgroups of patients (e.g., based on underlying diagnosis) with respect to pre-treatment survival. Such comparisons may be complicated by at least two important issues. First, mortality contrasts by subgroup may differ over follow-up time, as opposed to being constant, and may follow a form that is difficult to model parametrically. Moreover, in settings where the proportional hazards assumption fails, investigators tend to be more interested in cumulative (as opposed to instantaneous) effects on mortality. Second, pre-treatment death is censored by the receipt of treatment and in settings where treatment assignment depends on time-dependent factors that also affect mortality, such censoring is likely to be informative. We propose semiparametric methods for contrasting subgroup-specific cumulative mortality in the presence of dependent censoring. The proposed estimators are based on the cumulative hazard function, with pre-treatment mortality assumed to follow a stratified Cox model. No functional form is assumed for the nature of the non-proportionality. Asymptotic properties of the proposed estimators are derived, and simulation studies show that the proposed methods are applicable to practical sample sizes. The methods are then applied to contrast pre-transplant mortality for acute versus chronic End-Stage Liver Disease patients.