Structural Cox Proportional Hazards Models Research Articles

Overall survival (OS) of metastatic renal cell carcinoma (mRCC) patients corrected for crossover using inverse probability of censoring weights (IPCW) and rank preserving structural failure time (RPSFT) models: Two analyses from the RECORD-1 trial.

4595 Background: The phase III, double-blind, placebo-controlled RECORD-1 trial (NCT00410124) evaluated everolimus (EVE) in VEGF receptor-tyrosine kinase inhibitor (VEGFr-TKI) refractory mRCC. An updated intent-to-treat OS analysis favored EVE (hazard ratio [HR]=0.87, 95% CI: 0.65- 1.15, p=0.162), but was likely null biased as a result of crossover of ∼80% of placebo (PLB) patients to EVE treatment. These 2 validated and independentmethods were used to correct OS for crossover and estimate true survival benefit of a therapy vs PLB had there been no crossover. Methods: RPSFT postulates a structural model where each day on EVE (whether randomized to EVE or after crossover) prolongs survival by a multiplicative factor. The RPSFT method respects randomization and provides a crossover-corrected estimate. The weighted marginal structural IPCW Cox proportional hazards model uses pooled logistic regressions to estimate weights equal to the inverse probability of not crossing over (ie, the probability of PLB patients remaining not censored) and applies these to the final Cox model, resulting in a HR measure of effect. Multiple models were examined using alternate methods to segment time to identify baseline and time-dependent covariates for inclusion. Results: RPSFT estimated survival time was 1.9-fold longer (95% CI: 0.5-8.5) with EVE vs PLB (ie, hypothetical PLB without crossover). A corrected PLB Kaplan-Meier curve estimated OS at 10.0 mo (observed was 14.4 mo). OS for patients randomized to EVE was 14.8 mo. OS HR estimates from multiple IPCW Cox models were robust and indicated a benefit for EVE. Estimated HRs ranged from 0.44-0.55 and most estimated treatment effects were statistically significant. Point estimates from the RPSFT and IPCW methods are intuitively comparable as the former suggests a roughly 2 times longer survival on EVE and the latter suggest a roughly 50% reduction in death risk. Conclusions: Both independent crossover correction methods suggest that EVE was associated with an OS benefit in VEGFr-TKI refractory mRCC patients in RECORD-1. Author Disclosure Employment or Leadership Position Consultant or Advisory Role Stock Ownership Honoraria Research Funding Expert Testimony Other Remuneration Analytica International, Novartis Analytica International, Novartis Novartis, sanofi-aventis Wyeth GlaxoSmithKline, Novartis, Pfizer

Effect of pulmonary tuberculosis on mortality in patients receiving HAART

To estimate the effect of ongoing treatment for pulmonary tuberculosis (PTB) at time of initiation of HAART on subsequent risk of death. Evaluation of an open cohort of 7512 patients who initiated HAART between April 2004 and March 2007 in the Themba Lethu Clinic in Johannesburg, South Africa. Mortality hazard ratios were estimated using marginal structural Cox proportional hazards models to control for bias due to both confounding and loss to follow-up. Extensive sensitivity and secondary analyses were performed. Although the crude hazard ratio for mortality in HAART-treated patients comparing those with and without treated PTB was 1.71 (95% confidence interval 1.31-2.23), the adjusted hazard ratio was 1.06 (95% confidence interval 0.75-1.49), indicating no difference in mortality risk. Similar effects were found when we considered different durations of time between initiation of PTB treatment and HAART, and sensitivity analysis confirmed main results. Secondary analysis suggested that individuals with PTB and other risk factors for death might be at particularly high risk of death during HAART treatment. The increase in death that we observed among individuals with PTB at the time of HAART initiation appears not to be due to the to the presence of PTB, but instead to confounding factors such as low CD4 cell count, low BMI, and WHO stage IV disease. These results further demonstrate that initiation of HAART soon after initiation of PTB treatment is not likely to put patients at higher risk of death.

Sensitivity analysis for unmeasured confounding in a marginal structural Cox proportional hazards model

Sensitivity analysis for unmeasured confounding should be reported more often, especially in observational studies. In the standard Cox proportional hazards model, this requires substantial assumptions and can be computationally difficult. The marginal structural Cox proportional hazards model (Cox proportional hazards MSM) with inverse probability weighting has several advantages compared to the standard Cox model, including situations with only one assessment of exposure (point exposure) and time-independent confounders. We describe how simple computations provide sensitivity for unmeasured confounding in a Cox proportional hazards MSM with point exposure. This is achieved by translating the general framework for sensitivity analysis for MSMs by Robins and colleagues to survival time data. Instead of bias-corrected observations, we correct the hazard rate to adjust for a specified amount of unmeasured confounding. As an additional bonus, the Cox proportional hazards MSM is robust against bias from differential loss to follow-up. As an illustration, the Cox proportional hazards MSM was applied in a reanalysis of the association between smoking and depression in a population-based cohort of Norwegian adults. The association was moderately sensitive for unmeasured confounding.

Effect of discontinuing antiretroviral therapy on survival of women initiated on highly active antiretroviral therapy.

To estimate the effect of discontinuing antiretroviral therapy (ART) on survival, among women who initiated highly active antiretroviral therapy (HAART). A multicenter cohort study. A total of 951 HAART-initiated women were followed for total mortality between 1995 and 2002. The relative hazard (RH) of death attributable to discontinuing all ART was estimated using an inverse probability of treatment-weighted marginal structural Cox proportional hazards model, as well as standard Cox models. Three hundred and forty-three out of 951 women discontinued all ART during the 3187 person-years of follow-up, and 116 died. The RH of death attributable to discontinuation was 1.97 [95% confidence interval (CI) 1.17, 3.31] from the marginal structural Cox model. A RH of 1.49 (95% CI 0.94, 2.35) was observed using the same set of covariates in a standard Cox model. An increased risk of mortality for those HAART initiators who discontinued ART was observed using a marginal structural Cox model. This increased risk was independent of measured treatment failure, and was greatly attenuated in a standard Cox model with time-varying covariates.

Methotrexate and mortality in patients with rheumatoid arthritis: a prospective study

Methotrexate is the most frequent choice of disease-modifying antirheumatic therapy for rheumatoid arthritis. Although results of studies have shown the efficacy of such drugs, including methotrexate, on rheumatoid arthritis morbidity measures, their effect on mortality in patients with the disease remains unknown. Our aim was to prospectively assess the effect on mortality of methotrexate in a cohort of patients with rheumatoid arthritis. Our cohort included 1240 patients with rheumatoid arthritis seen at the Wichita Arthritis Center, an outpatient rheumatology facility. Patients' details were entered into a computerised database at the time of their first clinic visit. We also obtained and recorded demographic, clinical, laboratory, and self-reported data at each follow-up visit (average interval 3.5 months). We estimated the mortality hazard ratio of methotrexate with a marginal structural Cox proportional hazards model. 191 individuals died during follow-up. Patients who began treatment with methotrexate (n=588) had worse prognostic factors for mortality. After adjustment for this confounding by indication, the mortality hazard ratio for methotrexate use compared with no methotrexate use was 0.4 (95% CI 0.2-0.8). Other conventional disease-modifying antirheumatic drugs did not have a significant effect on mortality. The hazard ratio of methotrexate use for cardiovascular death was 0.3 (0.2-0.7), whereas that for non-cardiovascular deaths was 0.6 (0.2-1.2). Our data indicate that methotrexate may provide a substantial survival benefit, largely by reducing cardiovascular mortality. This survival benefit of methotrexate would set a standard against which new disease-modifying antirheumatic drugs could be compared.

Marginal Structural Models to Estimate the Joint Causal Effect of Nonrandomized Treatments

Even in the absence of unmeasured confounding factors or model misspecification, standard methods for estimating the causal effect of time-varying treatments on survival are biased when (a) there exists a time-dependent risk factor for survival that also predicts subsequent treatment, and (b) past treatment history predicts subsequent risk factor level. In contrast, methods based on marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. MSMs are a new class of causal models whose parameters are estimated using a new class of estimators—inverse-probability-of-treatment weighted estimators. We use a marginal structural Cox proportional hazards model to estimate the joint effect of zidovudine (AZT) and prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of HIV-positive men in the Multicenter AIDS Cohort Study, an observational study of homosexual men. We obtained an estimated causal mortality rate (hazard) ratio of .67 (conservative 95% confidence interval .46-.98) for AZT and of 1.14 (.79, 1.64) for prophylaxis therapy. These estimates will be consistent for the true causal rate ratios when the functional forms chosen for our models are correct and data have been obtained on all time-independent and time-dependent covariates that predict both subsequent treatment and mortality.

Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men.

Standard methods for survival analysis, such as the time-dependent Cox model, may produce biased effect estimates when there exist time-dependent confounders that are themselves affected by previous treatment or exposure. Marginal structural models are a new class of causal models the parameters of which are estimated through inverse-probability-of-treatment weighting; these models allow for appropriate adjustment for confounding. We describe the marginal structural Cox proportional hazards model and use it to estimate the causal effect of zidovudine on the survival of human immunodeficiency virus-positive men participating in the Multicenter AIDS Cohort Study. In this study, CD4 lymphocyte count is both a time-dependent confounder of the causal effect of zidovudine on survival and is affected by past zidovudine treatment. The crude mortality rate ratio (95% confidence interval) for zidovudine was 3.6 (3.0-4.3), which reflects the presence of confounding. After controlling for baseline CD4 count and other baseline covariates using standard methods, the mortality rate ratio decreased to 2.3 (1.9-2.8). Using a marginal structural Cox model to control further for time-dependent confounding due to CD4 count and other time-dependent covariates, the mortality rate ratio was 0.7 (95% conservative confidence interval = 0.6-1.0). We compare marginal structural models with previously proposed causal methods.