Structural Nested Mean Models Research Articles

Time-varying effect moderation using the structural nested mean model: estimation using inverse-weighted regression with residuals.

This article considers the problem of examining time-varying causal effect moderation using observational, longitudinal data in which treatment, candidate moderators, and possible confounders are time varying. The structural nested mean model (SNMM) is used to specify the moderated time-varying causal effects of interest in a conditional mean model for a continuous response given time-varying treatments and moderators. We present an easy-to-use estimator of the SNMM that combines an existing regression-with-residuals (RR) approach with an inverse-probability-of-treatment weighting (IPTW) strategy. The RR approach has been shown to identify the moderated time-varying causal effects if the time-varying moderators are also the sole time-varying confounders. The proposed IPTW+RR approach provides estimators of the moderated time-varying causal effects in the SNMM in the presence of an additional, auxiliary set of known and measured time-varying confounders. We use a small simulation experiment to compare IPTW+RR versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the IPTW+RR approach. This article clarifies the distinction between time-varying moderators and time-varying confounders. We illustrate the methodology in a case study to assess if time-varying substance use moderates treatment effects on future substance use.

Impact of time to start treatment following infection with application to initiating HAART in HIV-positive patients.

We estimate how the effect of antiretroviral treatment depends on the time from HIV-infection to initiation of treatment, using observational data. A major challenge in making inferences from such observational data arises from biases associated with the nonrandom assignment of treatment, for example bias induced by dependence of time of initiation on disease status. To address this concern, we develop a new class of Structural Nested Mean Models (SNMMs) to estimate the impact of time of initiation of treatment after infection on an outcome measured a fixed duration after initiation, compared to the effect of not initiating treatment. This leads to a SNMM that models the effect of multiple dosages of treatment on a time-dependent outcome, in contrast to most existing SNNMs, which focus on the effect of one dosage of treatment on an outcome measured at the end of the study. Our identifying assumption is that there are no unmeasured confounders. We illustrate our methods using the observational Acute Infection and Early Disease Research Program (AIEDRP) Core01 database on HIV. The current standard of care in HIV-infected patients is Highly Active Anti-Retroviral Treatment (HAART); however, the optimal time to start HAART has not yet been identified. The new class of SNNMs allows estimation of the dependence of the effect of 1 year of HAART on the time between estimated date of infection and treatment initiation, and on patient characteristics. Results of fitting this model imply that early use of HAART substantially improves immune reconstitution in the early and acute phase of HIV-infection.

Subgroups Analysis when Treatment and Moderators are Time-varying

Prevention scientists are often interested in understanding characteristics of participants that are predictive of treatment effects because these characteristics can be used to inform the types of individuals who benefit more or less from treatment or prevention programs. Often, effect moderation questions are examined using subgroups analysis or, equivalently, using covariate × treatment interactions in the context of regression analysis. This article focuses on conceptualizing and examining causal effect moderation in longitudinal settings in which both treatment and the putative moderators are time-varying. Studying effect moderation in the time-varying setting helps identify which individuals will benefit more or less from additional treatment services on the basis of both individual characteristics and their evolving outcomes, symptoms, severity, and need. Examining effect moderation in these longitudinal settings, however, is difficult because moderators of future treatment may themselves be affected by prior treatment (for example, future moderators may be mediators of prior treatment). This article introduces moderated intermediate causal effects in the time-varying setting, describes how they are part of Robins' Structural Nested Mean Model, discusses two problems with using a traditional regression approach to estimate these effects, and describes a new approach (a two-stage regression estimator) to estimate these effects. The methodology is illustrated using longitudinal data to examine the time-varying effects of receiving community-based substance abuse treatment as a function of time-varying severity (or need).

Estimation of HIV treatment-efficacy by combining structural nested mean models with pharmacokinetic models of antiretroviral drug exposure

The aim of treating HIV-1-infected patients is to achieve and maintain suppression of viral load (VL). Achievement of this aim is thwarted by variable adherence to prescribed anti-retroviral drugs. Variable adherence to an antiretroviral regimen creates variability in the patient's internal exposure to the drugs. Structural nested mean models (SNMMs) enabled us to estimate, during the initial phase of treatment, the relationship between variable internal exposure and VL, accounting for measured time-varying confounders and feedback relations using an antiretroviral regimen containing lopinavir/ritonavir (LPV/RTV, LPV/r). Our final SNMM predicts that the short term effect of treatment is modified by the most recent past VL, with higher initial VL's being associated with larger treatment-induced reductions in VL for a given internal exposure to the drugs. Variation in internal exposure to LPV/r in the interquartile interval (P25%-P75%) only slightly affects the overall reduction in VL, supporting the conclusion that the relatively long duration of action of LPV/r lessens the impact on VL of the most frequently recurring intermittent lapses in dosing.

Structural Nested Mean Models for Assessing Time‐Varying Effect Moderation

This article considers the problem of assessing causal effect moderation in longitudinal settings in which treatment (or exposure) is time varying and so are the covariates said to moderate its effect. Intermediate causal effects that describe time-varying causal effects of treatment conditional on past covariate history are introduced and considered as part of Robins' structural nested mean model. Two estimators of the intermediate causal effects, and their standard errors, are presented and discussed: The first is a proposed two-stage regression estimator. The second is Robins' G-estimator. The results of a small simulation study that begins to shed light on the small versus large sample performance of the estimators, and on the bias-variance trade-off between the two estimators are presented. The methodology is illustrated using longitudinal data from a depression study.

Estimating Optimal Dynamic Regimes: Correcting Bias under the Null

A dynamic regime provides a sequence of treatments that are tailored to patient-specific characteristics and outcomes. In 2004 James Robins proposed g-estimation using structural nested mean models for making inference about the optimal dynamic regime in a multi-interval trial. The method provides clear advantages over traditional parametric approaches. Robins' g-estimation method always yields consistent estimators, but these can be asymptotically biased under a given structural nested mean model for certain longitudinal distributions of the treatments and covariates, termed exceptional laws. In fact, under the null hypothesis of no treatment effect, every distribution constitutes an exceptional law under structural nested mean models which allow for interaction of current treatment with past treatments or covariates. This paper provides an explanation of exceptional laws and describes a new approach to g-estimation which we call Zeroing Instead of Plugging In (ZIPI). ZIPI provides nearly identical estimators to recursive g-estimators at non-exceptional laws while providing substantial reduction in the bias at an exceptional law when decision rule parameters are not shared across intervals.

The intensity-score approach to adjusting for confounding.

In a recent article on the efficacy of antihypertensive therapy, Berlowitz et al. (1998, New England Journal of Medicine 339, 1957-1963) introduced an ad hoc method of adjusting for serial confounding assessed via an intensity score, which records cumulative differences over time between therapy actually received and therapy predicted by prior medical history. Outcomes are subsequently regressed on the intensity score and baseline covariates to determine whether intense treatment or exposure predicts a favorable response. We use a structural nested mean model to derive conditions sufficient for interpreting the Berlowitz results causally. We also consider a modified approach that scales the intensity at each time by the inverse expected treatment given prior medical history. This leads to a simple, two-step implementation of G-estimation if we assume a nonstandard but useful structural nested mean model in which subjects less likely to receive treatment are more likely to benefit from it. These modeling assumptions apply, for example, to health services research contexts in which differential access to care is a primary concern. They are also plausible in our analysis of the causal effect of potent antiretroviral therapy on change in CD4 cell count, because men in the sample who are less likely to initiate treatment when baseline CD4 counts are high are more likely to experience large positive changes. We further extend the methods to accomodate repeated outcomes and time-varying effects of time-varying exposures.

The Effect of Treatment Compliance in a Placebo-Controlled Trial: Regression with Unpaired Data

SUMMARY The causal effect of a treatment is estimated at different levels of treatment compliance, in a placebo-controlled trial on the reduction of blood pressure. The structural nested mean model makes no direct assumptions on selected treatment compliance levels and placebo prognosis but relies on the randomization assumption and a parametric form for causal effects. It can be seen as a regression model for unpaired data, where pre- and post-randomization covariables are treated differently. The causal parameters are found as solutions to estimating equations involving estimated placebo response and treatment compliance based on base-line covariates for all subjects. Our example considers a linear effect of the percentage of prescribed dose taken on achieved diastolic blood pressure reduction. We propose an exploration of structural model checks. In the example, this reveals an interaction between the causal effect of active dose taken and the base-line body weight of the patient.

Correcting for non-compliance in randomized trials using structural nested mean models

In a randomized trial designed to study the effect of a treatment of interest on the evolution of the mean of a time-dependent outcome variable, subjects are assigned to a treatment regime, or, equivalently, a treatment protocol. Unfortunately, subjects often fail to comply with their assigned regime. From a public health point of view, the causal parameter of interest will often be a function of the treatment differences that would have been observed hadcontrary to fact, all subjects remained on protocol. This paper considers the identification and estimation of these treatment differences based on a new class of structural models, the multivariate structural nested mean models, when reliable estimates of each subject's actual treatment are available. Estimates of “actual treatment” might, for example, be obtained by measuring the amount of “active drug” in the subject's blood or urine at each follow-up visit or by pill counting techniques. In addition, we discuss a natural extension of our methods to ob...