Jessica G. Young

The parametric g-formula to estimate the effect of highly active antiretroviral therapy on incident AIDS or death

The parametric g-formula can be used to contrast the distribution of potential outcomes under arbitrary treatment regimes. Like g-estimation of structural nested models and inverse probability weighting of marginal structural models, the parametric g-formula can appropriately adjust for measured time-varying confounders that are affected by prior treatment. However, there have been few implementations of the parametric g-formula to date. Here, we apply the parametric g-formula to assess the impact of highly active antiretroviral therapy on time to acquired immune deficiency syndrome (AIDS) or death in two US-based human immunodeficiency virus cohorts including 1498 participants. These participants contributed approximately 7300 person-years of follow-up (49% exposed to highly active antiretroviral therapy) during which 382 events occurred and 259 participants were censored because of dropout. Using the parametric g-formula, we estimated that antiretroviral therapy substantially reduces the hazard of AIDS or death (hazard ratio = 0.55; 95% confidence limits [CL]: 0.42, 0.71). This estimate was similar to one previously reported using a marginal structural model, 0.54 (95% CL: 0.38, 0.78). The 6.5-year difference in risk of AIDS or death was 13% (95% CL: 8%, 18%). Results were robust to assumptions about temporal ordering, and extent of history modeled, for time-varying covariates. The parametric g-formula is a viable alternative to inverse probability weighting of marginal structural models and g-estimation of structural nested models for the analysis of complex longitudinal data.

Relation between three classes of structural models for the effect of a time-varying exposure on survival

Standard methods for estimating the effect of a time-varying exposure on survival may be biased in the presence of time-dependent confounders themselves affected by prior exposure. This problem can be overcome by inverse probability weighted estimation of Marginal Structural Cox Models (Cox MSM), g-estimation of Structural Nested Accelerated Failure Time Models (SNAFTM) and g-estimation of Structural Nested Cumulative Failure Time Models (SNCFTM). In this paper, we describe a data generation mechanism that approximately satisfies a Cox MSM, an SNAFTM and an SNCFTM. Besides providing a procedure for data simulation, our formal description of a data generation mechanism that satisfies all three models allows one to assess the relative advantages and disadvantages of each modeling approach. A simulation study is also presented to compare effect estimates across the three models.

Structural Nested Cumulative Failure Time Models to Estimate the Effects of Interventions

In the presence of time-varying confounders affected by prior treatment, standard statistical methods for failure time analysis may be biased. Methods that correctly adjust for this type of covariate include the parametric g-formula, inverse probability weighted estimation of marginal structural Cox proportional hazards models, and g-estimation of structural nested accelerated failure time models. In this article, we propose a novel method to estimate the causal effect of a time-dependent treatment on failure in the presence of informative right-censoring and time-dependent confounders that may be affected by past treatment: g-estimation of structural nested cumulative failure time models (SNCFTMs). An SNCFTM considers the conditional effect of a final treatment at time m on the outcome at each later time k by modeling the ratio of two counterfactual cumulative risks at time k under treatment regimes that differ only at time m. Inverse probability weights are used to adjust for informative censoring. We also present a procedure that, under certain “no-interaction” conditions, uses the g-estimates of the model parameters to calculate unconditional cumulative risks under nondynamic (static) treatment regimes. The procedure is illustrated with an example using data from a longitudinal cohort study, in which the “treatments” are healthy behaviors and the outcome is coronary heart disease.

Comparative effectiveness of immediate antiretroviral therapy versus CD4-based initiation in HIV-positive individuals in high-income countries: observational cohort study

BACKGROUND Recommendations have differed nationally and internationally with respect to the best time to start antiretroviral therapy (ART). We compared effectiveness of three strategies for initiation of ART in high-income countries for HIV-positive individuals who do not have AIDS: immediate initiation, initiation at a CD4 count less than 500 cells per μL, and initiation at a CD4 count less than 350 cells per μL. METHODS We used data from the HIV-CAUSAL Collaboration of cohort studies in Europe and the USA. We included 55,826 individuals aged 18 years or older who were diagnosed with HIV-1 infection between January, 2000, and September, 2013, had not started ART, did not have AIDS, and had CD4 count and HIV-RNA viral load measurements within 6 months of HIV diagnosis. We estimated relative risks of death and of death or AIDS-defining illness, mean survival time, the proportion of individuals in need of ART, and the proportion of individuals with HIV-RNA viral load less than 50 copies per mL, as would have been recorded under each ART initiation strategy after 7 years of HIV diagnosis. We used the parametric g-formula to adjust for baseline and time-varying confounders. FINDINGS Median CD4 count at diagnosis of HIV infection was 376 cells per μL (IQR 222-551). Compared with immediate initiation, the estimated relative risk of death was 1·02 (95% CI 1·01-1·02) when ART was started at a CD4 count less than 500 cells per μL, and 1·06 (1·04-1·08) with initiation at a CD4 count less than 350 cells per μL. Corresponding estimates for death or AIDS-defining illness were 1·06 (1·06-1·07) and 1·20 (1·17-1·23), respectively. Compared with immediate initiation, the mean survival time at 7 years with a strategy of initiation at a CD4 count less than 500 cells per μL was 2 days shorter (95% CI 1-2) and at a CD4 count less than 350 cells per μL was 5 days shorter (4-6). 7 years after diagnosis of HIV, 100%, 98·7% (95% CI 98·6-98·7), and 92·6% (92·2-92·9) of individuals would have been in need of ART with immediate initiation, initiation at a CD4 count less than 500 cells per μL, and initiation at a CD4 count less than 350 cells per μL, respectively. Corresponding proportions of individuals with HIV-RNA viral load less than 50 copies per mL at 7 years were 87·3% (87·3-88·6), 87·4% (87·4-88·6), and 83·8% (83·6-84·9). INTERPRETATION The benefits of immediate initiation of ART, such as prolonged survival and AIDS-free survival and increased virological suppression, were small in this high-income setting with relatively low CD4 count at HIV diagnosis. The estimated beneficial effect on AIDS is less than in recently reported randomised trials. Increasing rates of HIV testing might be as important as a policy of early initiation of ART. FUNDING National Institutes of Health.

Identification, estimation and approximation of risk under interventions that depend on the natural value of treatment using observational data

Abstract Robins et al. (2004, Comparative Quantification of Health Risks: Global and Regional Burden of Disease Attributable to Selected Major Risk Factors. Geneva: World Health Organization) introduced the extended g-formula to estimate from observational data the risk of failure under hypothetical interventions wherein a subject’s treatment at time k is assigned based on the natural value of treatment at k; that is, the value of treatment that would have been observed at k were the intervention discontinued right before k. Several authors have parametrically applied the extended g-formula to estimate long-term failure risk under hypothetical interventions on time-varying behaviors in observational studies. For example, Taubman et al. (2009, Intervening on risk factors for coronary heart disease: an application of the parametric g-formula. International Journal of Epidemiology, 380(6):1599–1611) used this approach to estimate the 20-year risk of coronary heart disease in the Nurses’ Health Study under the hypothetical intervention “If a subject’s natural value of exercise by the end of day k is less than 30 minutes, set her exercise on day k to exactly 30 minutes; otherwise, do not intervene on her on that day”. Non-parametrically, the extended g-formula differs from the (non-extended) g-formula of Robins (1986, A new approach to causal inference in mortality studies with a sustained exposure period: application to the healthy worker survivor effect. Mathematical Modelling, 7:1393–1512) in that it is a function of (i) a user-specified intervention depending on the natural value of treatment and (ii) the distribution of natural treatment itself. Richardson and Robins (2013, http://www.csss.washington.edu/Papers/) recently defined a sufficient condition such that the extended g-formula may identify risk under an intervention that depends on the natural value of treatment, provided this expression is well-defined. In this paper, we complement this result by showing that the extended g-formula associated with an intervention depending on the natural value of treatment is algebraically equivalent to the (non-extended) g-formula associated with a particular random dynamic regime that does not depend on this value. Using previous results for random dynamic regimes, we show that this equivalence immediately gives a sufficient positivity condition that guarantees the extended g-formula is well-defined as well as semi-parametric alternatives to the parametric extended g-formula for estimation. Finally, given a hypothetical intervention that depends on the natural value of treatment, we define a plausible (implementable) approximation to this hypothetical intervention along with an untestable assumption that gives exact equivalence.

Parametric mediational g-formula approach to mediation analysis with time-varying exposures, mediators, and confounders

The assessment of direct and indirect effects with time-varying mediators and confounders is a common but challenging problem, and standard mediation analysis approaches are generally not applicable in this context. The mediational g-formula was recently proposed to address this problem, paired with a semiparametric estimation approach to evaluate longitudinal mediation effects empirically. In this article, we develop a parametric estimation approach to the mediational g-formula, including a feasible algorithm implemented in a freely available SAS macro. In the Framingham Heart Study data, we apply this method to estimate the interventional analogues of natural direct and indirect effects of smoking behaviors sustained over a 10-year period on blood pressure when considering weight change as a time-varying mediator. Compared with not smoking, smoking 20 cigarettes per day for 10 years was estimated to increase blood pressure by 1.2 mm Hg (95% CI: −0.7, 2.7). The direct effect was estimated to increase blood pressure by 1.5 mm Hg (95% CI: −0.3, 2.9), and the indirect effect was −0.3 mm Hg (95% CI: −0.5, −0.1), which is negative because smoking which is associated with lower weight is associated in turn with lower blood pressure. These results provide evidence that weight change in fact partially conceals the detrimental effects of cigarette smoking on blood pressure. Our study represents, to our knowledge, the first application of the parametric mediational g-formula in an epidemiologic cohort study (see video abstract at, http://links.lww.com/EDE/B159.)

Predicting smoking cessation and its relapse in HIV-infected patients: the Swiss HIV Cohort Study

The aim of the study was to assess whether prospective follow‐up data within the Swiss HIV Cohort Study can be used to predict patients who stop smoking; or among smokers who stop, those who start smoking again.

Weight Loss and Coronary Heart Disease: Sensitivity Analysis for Unmeasured Confounding by Undiagnosed Disease.

Background: Evidence for the effect of weight loss on coronary heart disease (CHD) or mortality has been mixed. The effect estimates can be confounded due to undiagnosed diseases that may affect weight loss. Methods: We used data from the Nurses’ Health Study to estimate the 26-year risk of CHD under several hypothetical weight loss strategies. We applied the parametric g-formula and implemented a novel sensitivity analysis for unmeasured confounding due to undiagnosed disease by imposing a lag time for the effect of weight loss on chronic disease. Several sensitivity analyses were conducted. Results: The estimated 26-year risk of CHD did not change under weight loss strategies using lag times from 0 to 18 years. For a 6-year lag time, the risk ratios of CHD for weight loss compared with no weight loss ranged from 1.00 (0.99, 1.02) to 1.02 (0.99, 1.05) for different degrees of weight loss with and without restricting the weight loss strategy to participants with no major chronic disease. Similarly, no protective effect of weight loss was estimated for mortality risk. In contrast, we estimated a protective effect of weight loss on risk of type 2 diabetes. Conclusion: We estimated that maintaining or losing weight after becoming overweight or obese does not reduce the risk of CHD or death in this cohort of middle-age US women. Unmeasured confounding, measurement error, and model misspecification are possible explanations but these did not prevent us from estimating a beneficial effect of weight loss on diabetes.

The rate of recovery in renal function when patients with HIV infection discontinue treatment with tenofovir

Tenofovir is associated with reduced renal function. It is not clear whether patients can be expected to fully recover their renal function if tenofovir is discontinued.

Comparing the Effectiveness of Dynamic Treatment Strategies Using Electronic Health Records: An Application of the Parametric g‐Formula to Anemia Management Strategies

OBJECTIVE To compare the effectiveness of dynamic anemia management strategies by applying the parametric g-formula to electronic health records. DATA SOURCE/STUDY SETTING Patients with end-stage renal disease from the US Renal Data System who had congestive heart failure or ischemic heart disease and were undergoing hemodialysis in outpatient dialysis facilities between 2006 and 2010. STUDY DESIGN We explicitly emulated a target trial of three ‎erythropoietin dosing strategies (aimed at achieving a low, middle, or high hematocrit) and estimated the observational analog of the per-protocol effect. RESULTS Of 156,945 eligible patients, 41,970 died during the 18-month follow-up. Compared to the low-hematocrit strategy, the estimated risk of death was 4.6 (95% CI 4.4-4.9) percentage points higher under the high-hematocrit strategy and 1.8 (95% CI 1.7-1.9) percentage points higher under the mid-hematocrit strategy. The corresponding risk differences for a composite outcome of death and myocardial infarction were similar. CONCLUSION An explicit emulation of a target trial using electronic health records, combined with the parametric g-formula, allowed comparison of real-world dynamic strategies that have not been compared in randomized trials.