Contrasting treatment-specific survival using double-robust estimators

Transporting survival of an HIV clinical trial to the external target populations

Due to the heterogeneity of the randomized controlled trial (RCT) and external target populations, the estimated treatment effect from the RCT is not directly applicable to the target population. For example, the patient characteristics of the ACTG 175 HIV trial are significantly different from that of the three external target populations of interest: US early-stage HIV patients, Thailand HIV patients, and southern Ethiopia HIV patients. This paper considers several methods to transport the treatment effect from the ACTG 175 HIV trial to the target populations beyond the trial population. Most transport methods focus on continuous and binary outcomes; on the contrary, we derive and discuss several transport methods for survival outcomes: an outcome regression method based on a Cox proportional hazard (PH) model, an inverse probability weighting method based on the models for treatment assignment, sampling score, and censoring, and a doubly robust method that combines both methods, called the augmented calibration weighting (ACW) method. However, as the PH assumption was found to be incorrect for the ACTG 175 trial, the methods that depend on the PH assumption may lead to the biased quantification of the treatment effect. To account for the violation of the PH assumption, we extend the ACW method with the linear spline-based hazard regression model that does not require the PH assumption. Applying the aforementioned methods for transportability, we explore the effect of PH assumption, or the violation thereof, on transporting the survival results from the ACTG 175 trial to various external populations.

Unanchored Population-Adjusted Indirect Comparison Methods for Time-to-Event Outcomes Using Inverse Odds Weighting, Regression Adjustment, and Doubly Robust Methods With Either Individual Patient or Aggregate Data

OBJECTIVES

Several methods for unanchored population-adjusted indirect comparisons (PAICs) are available. Exploring alternative adjustment methods, depending on the available individual patient data (IPD) and the aggregate data (AD) in the external study, may help minimize bias in unanchored indirect comparisons. However, methods for time-to-event outcomes are not well understood. This study provides an overview and comparison of methods using a case study to increase familiarity. A recent method is applied to marginalize conditional hazard ratios, which allows for the comparisons of methods, and a doubly robust method is proposed.

METHODS

The following PAIC methods were compared through a case study in third-line small cell lung cancer, comparing nivolumab with standard of care based on a single-arm phase II trial (CheckMate 032) and real-world study (Flatiron) in terms of overall survival: IPD-IPD analyses using inverse odds weighting, regression adjustment, and a doubly robust method; IPD-AD analyses using matching-adjusted indirect comparison, simulated treatment comparison, and a doubly robust method.

RESULTS

Nivolumab extended survival versus standard of care with hazard ratios ranging from 0.63 (95% CI 0.44-0.90) in naive comparisons (identical estimates for IPD-IPD and IPD-AD analyses) to 0.69 (95% CI 0.44-0.98) in the IPD-IPD analyses using regression adjustment. Regression-based and doubly robust estimates yielded slightly wider confidence intervals versus the propensity score-based analyses.

CONCLUSIONS

The proposed doubly robust approach for time-to-event outcomes may help to minimize bias due to model misspecification. However, all methods for unanchored PAIC rely on the strong assumption that all prognostic covariates have been included.

Multiply robust causal inference of the restricted mean survival time difference

The hazard ratio (HR) remains the most frequently employed metric in assessing treatment effects on survival times. However, the difference in restricted mean survival time (RMST) has become a popular alternative to the HR when the proportional hazards assumption is considered untenable. Moreover, independent of the proportional hazards assumption, many comparative effectiveness studies aim to base contrasts on survival probability rather than on the hazard function. Causal effects based on RMST are often estimated via inverse probability of treatment weighting (IPTW). However, this approach generally results in biased results when the assumed propensity score model is misspecified. Motivated by the need for more robust techniques, we propose an empirical likelihood-based weighting approach that allows for specifying a set of propensity score models. The resulting estimator is consistent when the postulated model set contains a correct model; this property has been termed multiple robustness. In this report, we derive and evaluate a multiply robust estimator of the causal between-treatment difference in RMST. Simulation results confirm its robustness. Compared with the IPTW estimator from a correct model, the proposed estimator tends to be less biased and more efficient in finite samples. Additional simulations reveal biased results from a direct application of machine learning estimation of propensity scores. Finally, we apply the proposed method to evaluate the impact of intrapartum group B streptococcus antibiotic prophylaxis on the risk of childhood allergic disorders using data derived from electronic medical records from the Children's Hospital of Philadelphia and census data from the American Community Survey.

Multiply robust estimator for the difference in survival functions using pseudo-observations

BACKGROUND

When estimating the causal effect on survival outcomes in observational studies, it is necessary to adjust confounding factors due to unbalanced covariates between treatment and control groups. There is no study on multiple robust method for estimating the difference in survival functions. In this study, we propose a multiply robust (MR) estimator, allowing multiple propensity score models and outcome regression models, to provide multiple protection.

METHOD

Based on the previous MR estimator (Han 2014) and pseudo-observation approach, we proposed a new MR estimator for estimating the difference in survival functions. The proposed MR estimator based on the pseudo-observation approach has several advantages. First, the proposed estimator has a small bias when any PS and OR models were correctly specified. Second, the proposed estimator considers the advantage pf the pseudo-observation approach, which avoids proportional hazards assumption. A Monte Carlo simulation study was performed to evaluate the performance of the proposed estimator. And the proposed estimator was used to estimate the effect of chemotherapy on triple-negative breast cancer (TNBC) in real data.

RESULTS

The simulation studies showed that the bias of the proposed estimator was small, and the coverage rate was close to 95% when any model for propensity score or outcome regression is correctly specified regardless of whether the proportional hazard assumption holds, finite sample size and censoring rate. And the simulation results also showed that even though the propensity score models are misspecified, the bias of the proposed estimator was still small when there is a correct model in candidate outcome regression models. And we applied the proposed estimator in real data, finding that chemotherapy could improve the prognosis of TNBC.

CONCLUSIONS

The proposed estimator, allowing multiple propensity score and outcome regression models, provides multiple protection for estimating the difference in survival functions. The proposed estimator provided a new choice when researchers have a "difficult time" choosing only one model for their studies.

External Beam Radiation Therapy With or Without Brachytherapy Boost in Men With Very-High-Risk Prostate Cancer: A Large Multicenter International Consortium Analysis

PURPOSE

Very-high-risk (VHR) prostate cancer (PC) is an aggressive subgroup with high risk of distant disease progression. Systemic treatment intensification with abiraterone or docetaxel reduces PC-specific mortality (PCSM) and distant metastasis (DM) in men receiving external beam radiation therapy (EBRT) with androgen deprivation therapy (ADT). Whether prostate-directed treatment intensification with the addition of brachytherapy (BT) boost to EBRT with ADT improves outcomes in this group is unclear.

METHODS AND MATERIALS

This cohort study from 16 centers across 4 countries included men with VHR PC treated with either dose-escalated EBRT with ≥24 months of ADT or EBRT + BT boost with ≥12 months of ADT. VHR was defined by National Comprehensive Cancer Network (NCCN) criteria (clinical T3b-4, primary Gleason pattern 5, or ≥2 NCCN high-risk features), and results were corroborated in a subgroup of men who met Systemic Therapy in Advancing or Metastatic Prostate Cancer: Evaluation of Drug Efficacy (STAMPEDE) trials inclusion criteria (≥2 of the following: clinical T3-4, Gleason 8-10, or PSA ≥40 ng/mL). PCSM and DM between EBRT and EBRT + BT were compared using inverse probability of treatment weight-adjusted Fine-Gray competing risk regression.

RESULTS

Among the entire cohort, 270 underwent EBRT and 101 EBRT + BT. After a median follow-up of 7.8 years, 6.7% and 5.9% of men died of PC and 16.3% and 9.9% had DM after EBRT and EBRT + BT, respectively. There was no significant difference in PCSM (sHR, 1.47 [95% CI, 0.57-3.75]; P = .42) or DM (sHR, 0.72, [95% CI, 0.30-1.71]; P = .45) between EBRT + BT and EBRT. Results were similar within the STAMPEDE-defined VHR subgroup (PCSM: sHR, 1.67 [95% CI, 0.48-5.81]; P = .42; DM: sHR, 0.56 [95% CI, 0.15-2.04]; P = .38).

CONCLUSIONS

In this VHR PC cohort, no difference in clinically meaningful outcomes was observed between EBRT alone with ≥24 months of ADT compared with EBRT + BT with ≥12 months of ADT. Comparative analyses in men treated with intensified systemic therapy are warranted.

A comparison of different methods to adjust survival curves for confounders

Treatment specific survival curves are an important tool to illustrate the treatment effect in studies with time-to-event outcomes. In non-randomized studies, unadjusted estimates can lead to biased depictions due to confounding. Multiple methods to adjust survival curves for confounders exist. However, it is currently unclear which method is the most appropriate in which situation. Our goal is to compare forms of inverse probability of treatment weighting, the G-Formula, propensity score matching, empirical likelihood estimation and augmented estimators as well as their pseudo-values based counterparts in different scenarios with a focus on their bias and goodness-of-fit. We provide a short review of all methods and illustrate their usage by contrasting the survival of smokers and non-smokers, using data from the German Epidemiological Trial on Ankle-Brachial-Index. Subsequently, we compare the methods using a Monte-Carlo simulation. We consider scenarios in which correctly or incorrectly specified models for describing the treatment assignment and the time-to-event outcome are used with varying sample sizes. The bias and goodness-of-fit is determined by taking the entire survival curve into account. When used properly, all methods showed no systematic bias in medium to large samples. Cox regression based methods, however, showed systematic bias in small samples. The goodness-of-fit varied greatly between different methods and scenarios. Methods utilizing an outcome model were more efficient than other techniques, while augmented estimators using an additional treatment assignment model were unbiased when either model was correct with a goodness-of-fit comparable to other methods. These "doubly-robust" methods have important advantages in every considered scenario.

Doubly robust estimation of the hazard difference for competing risks data

We consider the conditional treatment effect for competing risks data in observational studies. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to (1) the assumed propensity score for treatment and the censoring model, and (2) the outcome models for the competing risks. An important property regarding the estimators is rate double robustness, in addition to the classical model double robustness. Rate double robustness enables the use of machine learning and nonparametric methods in order to estimate the nuisance parameters, while preserving the root-n $$ n $$ asymptotic normality of the estimated treatment effect for inferential purposes. We study the performance of the estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life drinking behavior on late life cognitive outcomes. The approaches developed in this article are implemented in the R package "HazardDiff".

Doubly robust estimators for generalizing treatment effects on survival outcomes from randomized controlled trials to a target population

In the presence of heterogeneity between the randomized controlled trial (RCT) participants and the target population, evaluating the treatment effect solely based on the RCT often leads to biased quantification of the real-world treatment effect. To address the problem of lack of generalizability for the treatment effect estimated by the RCT sample, we leverage observational studies with large samples that are representative of the target population. This article concerns evaluating treatment effects on survival outcomes for a target population and considers a broad class of estimands that are functionals of treatment-specific survival functions, including differences in survival probability and restricted mean survival times. Motivated by two intuitive but distinct approaches, i.e., imputation based on survival outcome regression and weighting based on inverse probability of sampling, censoring, and treatment assignment, we propose a semiparametric estimator through the guidance of the efficient influence function. The proposed estimator is doubly robust in the sense that it is consistent for the target population estimands if either the survival model or the weighting model is correctly specified and is locally efficient when both are correct. In addition, as an alternative to parametric estimation, we employ the nonparametric method of sieves for flexible and robust estimation of the nuisance functions and show that the resulting estimator retains the root-n consistency and efficiency, the so-called rate-double robustness. Simulation studies confirm the theoretical properties of the proposed estimator and show that it outperforms competitors. We apply the proposed method to estimate the effect of adjuvant chemotherapy on survival in patients with early-stage resected non-small cell lung cancer.

Doubly-robust methods for differences in restricted mean lifetimes using pseudo-observations

In clinical studies or trials comparing survival times between two treatment groups, the restricted mean lifetime (RML), defined as the expectation of the survival from time 0 to a prespecified time-point, is often the quantity of interest that is readily interpretable to clinicians without any modeling restrictions. It is well known that if the treatments are not randomized (as in observational studies), covariate adjustment is necessary to account for treatment imbalances due to confounding factors. In this article, we propose a simple doubly-robust pseudo-value approach to effectively estimate the difference in the RML between two groups (akin to a metric for estimating average causal effects), while accounting for confounders. The proposed method combines two general approaches: (a) group-specific regression models for the time-to-event and covariate information, and (b) inverse probability of treatment assignment weights, where the RMLs are replaced by the corresponding pseudo-observations for survival outcomes, thereby mitigating the estimation complexities in presence of censoring. The proposed estimator is double-robust, in the sense that it is consistent if at least one of the two working models remains correct. In addition, we explore the potential of available machine learning algorithms in causal inference to reduce possible bias of the causal estimates in presence of a complex association between the survival outcome and covariates. We conduct extensive simulation studies to assess the finite-sample performance of the pseudo-value causal effect estimators. Furthermore, we illustrate our methodology via application to a dataset from a breast cancer cohort study. The proposed method is implementable using the R package drRML, available in GitHub.

Survival Augmented Patient Preference Incorporated Reinforcement Learning to Evaluate Tailoring Variables for Personalized Healthcare

In this paper, we consider personalized treatment decision strategies in the management of chronic diseases, such as chronic kidney disease, which typically consists of sequential and adaptive treatment decision making. We investigate a two-stage treatment setting with a survival outcome that could be right censored. This can be formulated through a dynamic treatment regime (DTR) framework, where the goal is to tailor treatment to each individual based on their own medical history in order to maximize a desirable health outcome. We develop a new method, Survival Augmented Patient Preference incorporated reinforcement Q-Learning (SAPP-Q-Learning) to decide between quality of life and survival restricted at maximal follow-up. Our method incorporates the latent patient preference into a weighted utility function that balances between quality of life and survival time, in a Q-learning model framework. We further propose a corresponding m-out-of-n Bootstrap procedure to accurately make statistical inferences and construct confidence intervals on the effects of tailoring variables, whose values can guide personalized treatment strategies.

Estimating heterogeneous survival treatment effect in observational data using machine learning

Methods for estimating heterogeneous treatment effect in observational data have largely focused on continuous or binary outcomes, and have been relatively less vetted with survival outcomes. Using flexible machine learning methods in the counterfactual framework is a promising approach to address challenges due to complex individual characteristics, to which treatments need to be tailored. To evaluate the operating characteristics of recent survival machine learning methods for the estimation of treatment effect heterogeneity and inform better practice, we carry out a comprehensive simulation study presenting a wide range of settings describing confounded heterogeneous survival treatment effects and varying degrees of covariate overlap. Our results suggest that the nonparametric Bayesian Additive Regression Trees within the framework of accelerated failure time model (AFT-BART-NP) consistently yields the best performance, in terms of bias, precision, and expected regret. Moreover, the credible interval estimators from AFT-BART-NP provide close to nominal frequentist coverage for the individual survival treatment effect when the covariate overlap is at least moderate. Including a nonparametrically estimated propensity score as an additional fixed covariate in the AFT-BART-NP model formulation can further improve its efficiency and frequentist coverage. Finally, we demonstrate the application of flexible causal machine learning estimators through a comprehensive case study examining the heterogeneous survival effects of two radiotherapy approaches for localized high-risk prostate cancer.

Comparison of Multimodal Therapies and Outcomes Among Patients With High-Risk Prostate Cancer With Adverse Clinicopathologic Features

IMPORTANCE

The optimal management strategy for high-risk prostate cancer and additional adverse clinicopathologic features remains unknown.

OBJECTIVE

To compare clinical outcomes among patients with high-risk prostate cancer after definitive treatment.

DESIGN, SETTING, AND PARTICIPANTS

This retrospective cohort study included patients with high-risk prostate cancer (as defined by the National Comprehensive Cancer Network [NCCN]) and at least 1 adverse clinicopathologic feature (defined as any primary Gleason pattern 5 on biopsy, clinical T3b-4 disease, ≥50% cores with biopsy results positive for prostate cancer, or NCCN ≥2 high-risk features) treated between 2000 and 2014 at 16 tertiary centers. Data were analyzed in November 2020.

EXPOSURES

Radical prostatectomy (RP), external beam radiotherapy (EBRT) with androgen deprivation therapy (ADT), or EBRT plus brachytherapy boost (BT) with ADT. Guideline-concordant multimodal treatment was defined as RP with appropriate use of multimodal therapy (optimal RP), EBRT with at least 2 years of ADT (optimal EBRT), or EBRT with BT with at least 1 year ADT (optimal EBRT with BT).

MAIN OUTCOMES AND MEASURES

The primary outcome was prostate cancer-specific mortality; distant metastasis was a secondary outcome. Differences were evaluated using inverse probability of treatment weight-adjusted Fine-Gray competing risk regression models.

RESULTS

A total of 6004 men (median [interquartile range] age, 66.4 [60.9-71.8] years) with high-risk prostate cancer were analyzed, including 3175 patients (52.9%) who underwent RP, 1830 patients (30.5%) who underwent EBRT alone, and 999 patients (16.6%) who underwent EBRT with BT. Compared with RP, treatment with EBRT with BT (subdistribution hazard ratio [sHR] 0.78, [95% CI, 0.63-0.97]; P = .03) or with EBRT alone (sHR, 0.70 [95% CI, 0.53-0.92]; P = .01) was associated with significantly improved prostate cancer-specific mortality; there was no difference in prostate cancer-specific mortality between EBRT with BT and EBRT alone (sHR, 0.89 [95% CI, 0.67-1.18]; P = .43). No significant differences in prostate cancer-specific mortality were found across treatment cohorts among 2940 patients who received guideline-concordant multimodality treatment (eg, optimal EBRT alone vs optimal RP: sHR, 0.76 [95% CI, 0.52-1.09]; P = .14). However, treatment with EBRT alone or EBRT with BT was consistently associated with lower rates of distant metastasis compared with treatment with RP (eg, EBRT vs RP: sHR, 0.50 [95% CI, 0.44-0.58]; P < .001).

CONCLUSIONS AND RELEVANCE

These findings suggest that among patients with high-risk prostate cancer and additional unfavorable clinicopathologic features receiving guideline-concordant multimodal therapy, prostate cancer-specific mortality outcomes were equivalent among those treated with RP, EBRT, and EBRT with BT, although distant metastasis outcomes were more favorable among patients treated with EBRT and EBRT with BT. Optimal multimodality treatment is critical for improving outcomes in patients with high-risk prostate cancer.

Making apples from oranges: Comparing noncollapsible effect estimators and their standard errors after adjustment for different covariate sets

We revisit the well-known but often misunderstood issue of (non)collapsibility of effect measures in regression models for binary and time-to-event outcomes. We describe an existing simple but largely ignored procedure for marginalizing estimates of conditional odds ratios and propose a similar procedure for marginalizing estimates of conditional hazard ratios (allowing for right censoring), demonstrating its performance in simulation studies and in a reanalysis of data from a small randomized trial in primary biliary cirrhosis patients. In addition, we aim to provide an educational summary of issues surrounding (non)collapsibility from a causal inference perspective and to promote the idea that the words conditional and adjusted (likewise marginal and unadjusted) should not be used interchangeably.

Doubly robust estimator of risk in the presence of censoring dependent on time-varying covariates: application to a primary prevention trial for coronary events with pravastatin

Background

In the presence of dependent censoring even after stratification of baseline covariates, the Kaplan–Meier estimator provides an inconsistent estimate of risk. To account for dependent censoring, time-varying covariates can be used along with two statistical methods: the inverse probability of censoring weighted (IPCW) Kaplan–Meier estimator and the parametric g-formula estimator. The consistency of the IPCW Kaplan–Meier estimator depends on the correctness of the model specification of censoring hazard, whereas that of the parametric g-formula estimator depends on the correctness of the models for event hazard and time-varying covariates.

Methods

We combined the IPCW Kaplan–Meier estimator and the parametric g-formula estimator into a doubly robust estimator that can adjust for dependent censoring. The estimator is theoretically more robust to model misspecification than the IPCW Kaplan–Meier estimator and the parametric g-formula estimator. We conducted simulation studies with a time-varying covariate that affected both time-to-event and censoring under correct and incorrect models for censoring, event, and time-varying covariates. We applied our proposed estimator to a large clinical trial data with censoring before the end of follow-up.

Results

Simulation studies demonstrated that our proposed estimator is doubly robust, namely it is consistent if either the model for the IPCW Kaplan–Meier estimator or the models for the parametric g-formula estimator, but not necessarily both, is correctly specified. Simulation studies and data application demonstrated that our estimator can be more efficient than the IPCW Kaplan–Meier estimator.

Conclusions

The proposed estimator is useful for estimation of risk if censoring is affected by time-varying risk factors.

Doubly robust estimation and causal inference for recurrent event data

Many longitudinal databases record the occurrence of recurrent events over time. In this article, we propose a new method to estimate the average causal effect of a binary treatment for recurrent event data in the presence of confounders. We propose a doubly robust semiparametric estimator based on a weighted version of the Nelson-Aalen estimator and a conditional regression estimator under an assumed semiparametric multiplicative rate model for recurrent event data. We show that the proposed doubly robust estimator is consistent and asymptotically normal. In addition, a model diagnostic plot of residuals is presented to assess the adequacy of our proposed semiparametric model. We then evaluate the finite sample behavior of the proposed estimators under a number of simulation scenarios. Finally, we illustrate the proposed methodology via a database of circus artist injuries.

Adjusted restricted mean survival times in observational studies

In observational studies with censored data, exposure-outcome associations are commonly measured with adjusted hazard ratios from multivariable Cox proportional hazards models. The difference in restricted mean survival times (RMSTs) up to a pre-specified time point is an alternative measure that offers a clinically meaningful interpretation. Several regression-based methods exist to estimate an adjusted difference in RMSTs, but they digress from the model-free method of taking the area under the survival function. We derive the adjusted RMST by integrating an adjusted Kaplan-Meier estimator with inverse probability weighting (IPW). The adjusted difference in RMSTs is the area between the two IPW-adjusted survival functions. In a Monte Carlo-type simulation study, we demonstrate that the proposed estimator performs as well as two regression-based approaches: the ANCOVA-type method of Tian et al and the pseudo-observation method of Andersen et al. We illustrate the methods by reexamining the association between total cholesterol and the 10-year risk of coronary heart disease in the Framingham Heart Study.

Testing causal effects in observational survival data using propensity score matching design

Time-to-event data are very common in observational studies. Unlike randomized experiments, observational studies suffer from both observed and unobserved confounding biases. To adjust for observed confounding in survival analysis, the commonly used methods are the Cox proportional hazards (PH) model, the weighted logrank test, and the inverse probability of treatment weighted Cox PH model. These methods do not rely on fully parametric models, but their practical performances are highly influenced by the validity of the PH assumption. Also, there are few methods addressing the hidden bias in causal survival analysis. We propose a strategy to test for survival function differences based on the matching design and explore sensitivity of the P-values to assumptions about unmeasured confounding. Specifically, we apply the paired Prentice-Wilcoxon (PPW) test or the modified PPW test to the propensity score matched data. Simulation studies show that the PPW-type test has higher power in situations when the PH assumption fails. For potential hidden bias, we develop a sensitivity analysis based on the matched pairs to assess the robustness of our finding, following Rosenbaum's idea for nonsurvival data. For a real data illustration, we apply our method to an observational cohort of chronic liver disease patients from a Mayo Clinic study. The PPW test based on observed data initially shows evidence of a significant treatment effect. But this finding is not robust, as the sensitivity analysis reveals that the P-value becomes nonsignificant if there exists an unmeasured confounder with a small impact.

ON ESTIMATION OF THE OPTIMAL TREATMENT REGIME WITH THE ADDITIVE HAZARDS MODEL

We propose a doubly robust estimation method for the optimal treatment regime based on an additive hazards model with censored survival data. Specifically, we introduce a new semiparametric additive hazard model which allows flexible baseline covariate effects in the control group and incorporates marginal treatment effect and its linear interaction with covariates. In addition, we propose a time-dependent propensity score to construct an A-learning type of estimating equations. The resulting estimator is shown to be consistent and asymptotically normal when either the baseline effect model for covariates or the propensity score is correctly specified. The asymptotic variance of the estimator is consistently estimated using a simple resampling method. Simulation studies are conducted to evaluate the finite-sample performance of the estimators and an application to AIDS clinical trial data is also given to illustrate the methodology.

Landmark estimation of survival and treatment effects in observational studies

Clinical studies aimed at identifying effective treatments to reduce the risk of disease or death often require long term follow-up of participants in order to observe a sufficient number of events to precisely estimate the treatment effect. In such studies, observing the outcome of interest during follow-up may be difficult and high rates of censoring may be observed which often leads to reduced power when applying straightforward statistical methods developed for time-to-event data. Alternative methods have been proposed to take advantage of auxiliary information that may potentially improve efficiency when estimating marginal survival and improve power when testing for a treatment effect. Recently, Parast et al. (J Am Stat Assoc 109(505):384-394, 2014) proposed a landmark estimation procedure for the estimation of survival and treatment effects in a randomized clinical trial setting and demonstrated that significant gains in efficiency and power could be obtained by incorporating intermediate event information as well as baseline covariates. However, the procedure requires the assumption that the potential outcomes for each individual under treatment and control are independent of treatment group assignment which is unlikely to hold in an observational study setting. In this paper we develop the landmark estimation procedure for use in an observational setting. In particular, we incorporate inverse probability of treatment weights (IPTW) in the landmark estimation procedure to account for selection bias on observed baseline (pretreatment) covariates. We demonstrate that consistent estimates of survival and treatment effects can be obtained by using IPTW and that there is improved efficiency by using auxiliary intermediate event and baseline information. We compare our proposed estimates to those obtained using the Kaplan-Meier estimator, the original landmark estimation procedure, and the IPTW Kaplan-Meier estimator. We illustrate our resulting reduction in bias and gains in efficiency through a simulation study and apply our procedure to an AIDS dataset to examine the effect of previous antiretroviral therapy on survival.

Observational Studies of Drug Safety in Multi-Database Studies: Methodological Challenges and Opportunities

INTRODUCTION/OBJECTIVE

The Canadian Network for Observational Drug Effect Studies (CNODES), a network of researchers and databases, is a collaborating center of the Drug Safety and Effectiveness Network. CNODES' main mandate is to conduct observational studies of drug safety based on queries developed and submitted by Health Canada and other federal, provincial, and territorial stakeholders. Through a case study we explore several methodological opportunities and challenges that arise in distributed pharmacoepidemiology networks.

CASE STUDY

We use as a case study a study of proton pump inhibitors and hospitalization for community-acquired pneumonia. Challenges arise in the design and conduct of studies at individual sites, and then with processes and methods for combining data. On the other hand, distributed networks provide opportunities, such as the ability to detect and understand heterogeneity, in sample sizes that would typically be impossible for a single study.

CONCLUSIONS

Networks such as CNODES provide the opportunity to detect and quantify important safety signals from administrative data, and provide many challenges for methods research in pharmacoepidemiology using distributed data. As networks increase in size and scope of research questions, the need for methodological developments should continue to grow.

A log rank type test in observational survival studies with stratified sampling

In randomized clinical trials, the log rank test is often used to test the null hypothesis of the equality of treatment-specific survival distributions. In observational studies, however, the ordinary log rank test is no longer guaranteed to be valid. In such studies we must be cautious about potential confounders; that is, the covariates that affect both the treatment assignment and the survival distribution. In this paper, two cases were considered: the first is when it is believed that all the potential confounders are captured in the primary database, and the second case where a substudy is conducted to capture additional confounding covariates. We generalize the augmented inverse probability weighted complete case estimators for treatment-specific survival distribution proposed in Bai et al. (Biometrics 69:830-839, 2013) and develop the log rank type test in both cases. The consistency and double robustness of the proposed test statistics are shown in simulation studies. These statistics are then applied to the data from the observational study that motivated this research.

A Reassessment of the Survival Advantage of Simultaneous Kidney-Pancreas Versus Kidney-Alone Transplantation

Background

Simultaneous kidney and pancreas (SPK) transplantation is an attractive option for end-stage renal disease patients with type 1 diabetes. Although SPK transplantation is superior to remaining on dialysis, the survival advantage for SPK recipients compared to kidney transplantation alone (KTA) is controversial.

Methods

Using data obtained from the Scientific Registry of Transplant Recipients, we compared patient and graft survivals for 7308 SPK and 4653 KTA adult patients with type I diabetes transplanted in 1998 to 2009. Because SPK and KTA recipients are differently selected, comparison groups were chosen to maximize overlap in the case mixes. Most previous studies contrasted (unadjusted) Kaplan-Meier survival curves or, if covariate-adjusted, reported hazard ratios (HRs). Using newer statistical methods, we avoid relying on hazard ratios (which are seldom of inherent interest) and directly compare covariate-adjusted survival curves. Specifically, we compare average covariate-adjusted SPK- and KTA-specific survival curves (and 10-year area under the curve; ie, restricted mean survival time) to emulate a randomized clinical trial.

Results

Mean restricted mean kidney graft survival time was significantly greater by 0.18 years (P = 0.045) for SPK compared to KTA. Similarly, patient survival was 0.17 years greater (P = 0.033) for SPK than KTA. Increased graft survival was primarily observed in younger SPK recipients. Supplementary analysis revealed that the SPK hazards were nonproportional, meaning that it would be difficult to quantify the cumulative effect of SPK through a standard Cox regression analysis.

Conclusions

Using this novel methodology, we demonstrate that SPK is associated with statistically but not clinically significant increases in graft and patient survival.

Using a novel statistical approach with covariate-adjusted survival curves, Sung and colleagues show a statistically but not clinically significant graft and patient survival advantage to SPK compared to PTA.

Antifungal de-escalation was not associated with adverse outcome in critically ill patients treated for invasive candidiasis: post hoc analyses of the AmarCAND2 study data

PURPOSE

Systemic antifungal therapy (SAT) of invasive candidiasis needs to be initiated immediately upon clinical suspicion. Controversies exist about adequate time and potential harm of antifungal de-escalation (DE) in documented and suspected candidiasis in ICU patients. Our objective was to investigate whether de-escalation within 5 days of antifungal initiation is associated with an increase of the 28-day mortality in SAT-treated non-neutropenic adult ICU patients.

METHODS

From the 835 non-neutropenic adults recruited in the multicenter prospective observational AmarCAND2 study, we selected the patients receiving systemic antifungal therapy for a documented or suspected invasive candidiasis in the ICU and who were still alive 5 days after SAT initiation. They were included into two groups according to the occurrence of observed SAT de-escalation before day 6. The average causal SAT de-escalation effect on 28-day mortality was evaluated by using a double robust estimation.

RESULTS

Among the 647 included patients, early de-escalation at day 5 after antifungal initiation occurred in 142 patients (22%), including 48 (34%) patients whose SAT was stopped before day 6. After adjustment for the baseline confounders, early SAT de-escalation was the solely factor not associated with increased 28-day mortality (RR 1.12, 95% CI 0.76-1.66).

CONCLUSION

In non-neutropenic critically ill adult patients with documented or suspected invasive candidiasis, SAT de-escalation within 5 days was not related to increased day-28 mortality but it was associated with decreased SAT consumption. These results suggest for the first time that SAT de-escalation may be safe in these patients.

Doubly robust estimation of attributable fractions in survival analysis

The attributable fraction is a commonly used measure that quantifies the public health impact of an exposure on an outcome. It was originally defined for binary outcomes, but an extension has recently been proposed for right-censored survival time outcomes; the so-called attributable fraction function. A maximum likelihood estimator of the attributable fraction function has been developed, which requires a model for the outcome. In this paper, we derive a doubly robust estimator of the attributable fraction function. This estimator requires one model for the outcome, and one joint model for the exposure and censoring. The estimator is consistent if either model is correct, not necessarily both.