Double inverse-weighted estimation of cumulative treatment effects under nonproportional hazards and dependent censoring

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.

Associations of periconceptional oral contraceptive use with pregnancy complications and adverse birth outcomes

BACKGROUND

Periconceptional use of oral contraceptives (OCs) has been reported to increase risks of pregnancy complications and adverse birth outcomes, but risks are suggested to differ depending on the timing of discontinuation, amount of oestrogen and progestin content.

METHODS

Prospective cohort study among 6470 pregnancies included in the PRegnancy and Infant DEvelopment (PRIDE) Study in 2012-19. Exposure was defined as any reported use of OCs within 12 months pre-pregnancy or after conception. Outcomes of interest were gestational diabetes, gestational hypertension, pre-eclampsia, pre-term birth, low birthweight and small for gestational age (SGA). Multivariable Poisson regression using stabilized inverse probability weighting estimated relative risks (RRs) with 95% CIs.

RESULTS

Any periconceptional OC use was associated with increased risks of pre-eclampsia (RR 1.38, 95% CI 0.99-1.93), pre-term birth (RR 1.38, 95% CI 1.09-1.75) and low birthweight (RR 1.45, 95% CI 1.10-1.92), but not with gestational hypertension (RR 1.09, 95% CI 0.91-1.31), gestational diabetes (RR 1.02, 95% CI 0.77-1.36) and SGA (RR 0.96, 95% CI 0.75-1.21). Associations with pre-eclampsia were strongest for discontinuation 0-3 months pre-pregnancy, for OCs containing ≥30 µg oestrogen and for first- or second-generation OCs. Pre-term birth and low birthweight were more likely to occur when OCs were discontinued 0-3 months pre-pregnancy, when using OCs containing <30 µg oestrogen and when using third-generation OCs. Associations with SGA were observed for OCs containing <30 µg oestrogen and for third- or fourth-generation OCs.

CONCLUSIONS

Periconceptional OC use, particularly those containing oestrogen, was associated with increased risks of pre-eclampsia, pre-term birth, low birthweight and SGA.

A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies

The hazard ratio (HR) is often reported as the main causal effect when studying survival data. Despite its popularity, the HR suffers from an unclear causal interpretation. As already pointed out in the literature, there is a built-in selection bias in the HR, because similarly to the truncation by death problem, the HR conditions on post-treatment survival. A recently proposed alternative, inspired by the Survivor Average Causal Effect, is the causal HR, defined as the ratio between hazards across treatment groups among the study participants that would have survived regardless of their treatment assignment. We discuss the challenge in identifying the causal HR and present a sensitivity analysis identification approach in randomized controlled trials utilizing a working frailty model. We further extend our framework to adjust for potential confounders using inverse probability of treatment weighting. We present a Cox-based and a flexible non-parametric kernel-based estimation under right censoring. We study the finite-sample properties of the proposed estimation methods through simulations. We illustrate the utility of our framework using two real-data examples.

Long-Term Prognostic Impact of Pulmonary Hypertension After Venous Thromboembolism

Pulmonary embolism is a risk factor for chronic thromboembolic pulmonary hypertension (CTEPH), but the prognostic impact of CTEPH on venous thromboembolism (VTE) mortality remains unclear. We examined the impact of CTEPH and other pulmonary hypertension (PH) subtypes on long-term mortality after VTE. We conducted a nationwide, population-based cohort study of all adult Danish patients alive 2 years after incident VTE without previous PH from 1995 to 2020 (n = 129,040). We used inverse probability of treatment weights in a Cox model to calculate standardized mortality rate ratios (SMRs) of the association between receiving a first-time PH diagnosis ≤2 years after incident VTE and mortality (all-cause, cardiovascular, and cancer). We grouped PH as PH associated with left-sided cardiac disease (group II), PH associated with lung diseases and/or hypoxia (group III), CTEPH (group IV), and unclassified (remaining patients). Total follow-up was 858,954 years. The SMR associated with PH overall was 1.99 (95% confidence interval 1.75 to 2.27) for all-cause, 2.48 (1.90 to 3.23) for cardiovascular, and 0.84 (0.60 to 1.17) for cancer mortality. The SMR for all-cause mortality was 2.62 (1.77 to 3.88) for group II, 3.98 (2.85 to 5.56) for group III, 1.88 (1.11 to 3.20) for group IV, and 1.73 (1.47 to 2.04) for unclassified PH. The cardiovascular mortality rate was increased approximately threefold for groups II and III but was not increased for group IV. Only group III was associated with increased cancer mortality. In conclusion, PH diagnosed ≤2 years after incident VTE was associated with an overall twofold increased long-term mortality driven by cardiovascular causes.

On the Use of Covariate Supersets for Identification Conditions

The union of distinct covariate sets, or the superset, is often used in proofs for the identification or the statistical consistency of an estimator when multiple sources of bias are present. However, the use of a superset can obscure important nuances. Here, we provide two illustrative examples: one in the context of missing data on outcomes, and one in which the average causal effect is transported to another target population. As these examples demonstrate, the use of supersets may indicate a parameter is not identifiable when the parameter is indeed identified. Furthermore, a series of exchangeability conditions may lead to successively weaker conditions. Future work on approaches to address multiple biases can avoid these pitfalls by considering the more general case of nonoverlapping covariate sets.

Estimating the optimal individualized treatment rule from a cost-effectiveness perspective

Optimal individualized treatment rules (ITRs) provide customized treatment recommendations based on subject characteristics to maximize clinical benefit in accordance with the objectives in precision medicine. As a result, there is growing interest in developing statistical tools for estimating optimal ITRs in evidence-based research. In health economic perspectives, policy makers consider the tradeoff between health gains and incremental costs of interventions to set priorities and allocate resources. However, most work on ITRs has focused on maximizing the effectiveness of treatment without considering costs. In this paper, we jointly consider the impact of effectiveness and cost on treatment decisions and define ITRs under a composite-outcome setting, so that we identify the most cost-effective ITR that accounts for individual-level heterogeneity through direct optimization. In particular, we propose a decision-tree-based statistical learning algorithm that uses a net-monetary-benefit-based reward to provide nonparametric estimations of the optimal ITR. We provide several approaches to estimating the reward underlying the ITR as a function of subject characteristics. We present the strengths and weaknesses of each approach and provide practical guidelines by comparing their performance in simulation studies. We illustrate the top-performing approach from our simulations by evaluating the projected 15-year personalized cost-effectiveness of the intensive blood pressure control of the Systolic Blood Pressure Intervention Trial (SPRINT) study.

Fully nonparametric survival analysis in the presence of time-dependent covariates and dependent censoring

In the presence of informative right censoring and time-dependent covariates, we estimate the survival function in a fully nonparametric fashion. We introduce a novel method for incorporating multiple observations per subject when estimating the survival function at different covariate values and compare several competing methods via simulation. The proposed method is applied to survival data from people awaiting liver transplant.

CauchyCP: A powerful test under non-proportional hazards using Cauchy combination of change-point Cox regressions

Non-proportional hazards data are routinely encountered in randomized clinical trials. In such cases, classic Cox proportional hazards model can suffer from severe power loss, with difficulty in interpretation of the estimated hazard ratio since the treatment effect varies over time. We propose CauchyCP, an omnibus test of change-point Cox regression models, to overcome both challenges while detecting signals of non-proportional hazards patterns. Extensive simulation studies demonstrate that, compared to existing treatment comparison tests under non-proportional hazards, the proposed CauchyCP test (a) controls the type I error better at small α levels (<0.01); (b) increases the power of detecting time-varying effects; and (c) is more computationally efficient than popular methods like MaxCombo for large-scale data analysis. The superior performance of CauchyCP is further illustrated using retrospective analyses of two randomized clinical trial datasets and a pharmacogenetic biomarker study dataset. The R package CauchyCP is publicly available on CRAN.

Weighted estimators of the complier average causal effect on restricted mean survival time with observed instrument-outcome confounders

A major concern in any observational study is unmeasured confounding of the relationship between a treatment and outcome of interest. Instrumental variable (IV) analysis methods are able to control for unmeasured confounding. However, IV analysis methods developed for censored time-to-event data tend to rely on assumptions that may not be reasonable in many practical applications, making them unsuitable for use in observational studies. In this report, we develop weighted estimators of the complier average causal effect (CACE) on the restricted mean survival time in the overall population as well as in an evenly matchable population (CACE-m). Our method is able to accommodate instrument-outcome confounding and adjust for covariate-dependent censoring, making it particularly suited for causal inference from observational studies. We establish the asymptotic properties and derive easily implementable asymptotic variance estimators for the proposed estimators. Through simulation studies, we show that the proposed estimators tend to be more efficient than instrument propensity score matching-based estimators or IPIW estimators. We apply our method to compare dialytic modality-specific survival for end stage renal disease patients using data from the U.S. Renal Data System.

Estimating restricted mean survival time and expected life-years lost in the presence of competing risks within flexible parametric survival models

Background

Royston-Parmar flexible parametric survival models (FPMs) can be fitted on either the cause-specific hazards or cumulative incidence scale in the presence of competing risks. An advantage of modelling within this framework for competing risks data is the ease at which alternative predictions to the (cause-specific or subdistribution) hazard ratio can be obtained. Restricted mean survival time (RMST), or restricted mean failure time (RMFT) on the mortality scale, is one such measure. This has an attractive interpretation, especially when the proportionality assumption is violated. Compared to similar measures, fewer assumptions are required and it does not require extrapolation. Furthermore, one can easily obtain the expected number of life-years lost, or gained, due to a particular cause of death, which is a further useful prognostic measure as introduced by Andersen.

Methods

In the presence of competing risks, prediction of RMFT and the expected life-years lost due to a cause of death are presented using Royston-Parmar FPMs. These can be predicted for a specific covariate pattern to facilitate interpretation in observational studies at the individual level, or at the population-level using standardisation to obtain marginal measures. Predictions are illustrated using English colorectal data and are obtained using the Stata post-estimation command, standsurv.

Results

Reporting such measures facilitate interpretation of a competing risks analysis, particularly when the proportional hazards assumption is not appropriate. Standardisation provides a useful way to obtain marginal estimates to make absolute comparisons between two covariate groups. Predictions can be made at various time-points and presented visually for each cause of death to better understand the overall impact of different covariate groups.

Conclusions

We describe estimation of RMFT, and expected life-years lost partitioned by each competing cause of death after fitting a single FPM on either the log-cumulative subdistribution, or cause-specific hazards scale. These can be used to facilitate interpretation of a competing risks analysis when the proportionality assumption is in doubt.

Hepatitis C Virus (HCV) Treatment With Directly Acting Agents Reduces the Risk of Incident Diabetes: Results From Electronically Retrieved Cohort of HCV Infected Veterans (ERCHIVES)

BACKGROUND

The effects of interferon-based therapies for hepatitis C virus (HCV) upon the risk of diabetes are controversial. The effects of newer, directly acting antiviral agents (DAA) upon this risk are unknown. We sought to determine the effects of HCV treatment upon the risk and incidence of diabetes.

METHODS

Using the Electronically Retrieved Cohort of HCV Infected Veterans (ERCHIVES) database for persons with chronic HCV infection (n = 242 680), we identified those treated with a pegylated interferon and ribavirin regimen (PEG/RBV, n = 4764) or a DAA-containing regimen (n = 21 279), after excluding those with diabetes at baseline, those with a human immunodeficiency virus or hepatitis B virus coinfection, and those treated with both PEG/RBV and DAA regimens. Age-, race-, sex-, and propensity score-matched controls (1:1) were also identified.

RESULTS

Diabetes incidence rates per 1000 person-years were 20.6 (95% confidence interval [CI] 19.6-21.6) among untreated persons, 19.8 (95% CI 18.3-21.4) among those treated with PEG/RBV, and 9.89 (95% CI 8.7-11.1) among DAA-treated persons (P < .001). Among the treated, rates were 13.3 (95% CI 12.2-14.5) for those with a sustained virologic response (SVR) and 19.2 (95% CI 17.4-21.1) for those without an SVR (P < .0001). A larger reduction was observed in persons with more advanced fibrosis/cirrhosis (absolute difference 2.9 for fibrosis severity score [FIB-4] < 1.25; 5.7 for FIB-4 1.26-3.25; 9.8 for FIB-4 >3.25). DAA treatment (hazard ratio [HR] 0.53, 95% CI .46-.63) and SVR (HR 0.81, 95% CI .70-.93) were associated with a significantly reduced risk of diabetes. DAA-treated persons had longer diabetes-free survival rates, compared to untreated and PEG/RBV-treated persons. There was no significant difference in diabetes-free survival rates between untreated and PEG/RBV-treated persons. The results were similar in inverse probability of treatment and censoring weight models.

CONCLUSIONS

DAA therapy significantly reduces the incidence and risk of subsequent diabetes. Treatment benefits are more pronounced in persons with more advanced liver fibrosis.

Deep Neural Networks For Predicting Restricted Mean Survival Times

 

Restricted mean survival time (RMST) is a useful summary measurement of the time-to-event data, and it has attracted great attention for its straightforward clinical interpretation. In this article, I propose a deep neural network model that directly relates the RMST to its baseline covariates for simultaneous prediction of RSMT at multiple times. Each subject's survival time is transformed into a series of jackknife pseudo observations and then used as quantitative response variables in a deep neural network model. By using the pseudo values, a complex survival analysis is reduced to a standard regression problem, which greatly simplifies the neural network construction. By jointly modelling RMST at multiple times, the neural network model gains prediction accuracy by information sharing across times. The proposed network model was evaluated by extensive simulation studies and was further illustrated on three real datasets. In real data analyses, I also used methods to open the blackbox by identifying subject-specific predictors and their importance in contributing to the risk prediction.

AVAILABILITY AND IMPLEMENTATION

The source code is freely available at http://github.com/lilizhaoUM/DnnRMST.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

Treatment of HCV reduces viral hepatitis-associated liver-related mortality in patients: An ERCHIVES study

BACKGROUND & AIMS

Treating HCV infection reduces overall mortality and reduces the risk of multiple extrahepatic complications. Whether the reduction in mortality is primarily due to a reduction in liver-related causes or extrahepatic complications is unknown.

METHODS

We identified HCV-positive individuals treated for HCV, and propensity score-matched them to HCV-positive/untreated and HCV-uninfected individuals in ERCHIVES between 2002-2016. We extracted cause of death data from the National Center for Health Statistics' National Death Index. Viral hepatitis-associated liver-related mortality rates among treated and untreated HCV-infected persons were calculated by treatment and attainment of sustained virologic response (SVR).

RESULTS

Among 50,674 HCV-positive/treated (Group A), 31,749 HCV-positive/untreated (Group B) and 73,526 HCV-uninfected persons (Group C), 8.6% in Group A, 35.0% in Group B, and 14.3% in Group C died. Among those who died, viral hepatitis-associated liver-related mortality rates per 100 patient-years (95% CI) were: 0.28 (0.27-0.30) for Group A; 1.44 (1.38-1.49) for Group B; and 0.06 (0.05-0.06) for Group C; (p <0.0001 for both comparisons). Among HCV-positive/treated persons, rates were 0.06 (0.05-0.06) for those with SVR vs. 0.78 (0.74-0.83) for those without SVR. In competing risks Cox proportional hazards analysis, treatment with all-oral DAA regimens (adjusted hazard ratio 0.11; 95% CI 0.09-0.14) and SVR (adjusted hazard ratio 0.10; 95% CI 0.08-0.11) were associated with reduced hazards of liver-related mortality.

CONCLUSIONS

Treatment for HCV is associated with a significant reduction in viral hepatitis-associated liver-related mortality, which is particularly pronounced in those treated with DAA regimens and those who attain SVR. This may account for a significant proportion of the reduction in all-cause mortality reported in previous studies.

LAY SUMMARY

Treating hepatitis C virus (HCV) infection is known to reduce overall mortality. However, whether the reduction in mortality is primarily due to a reduction in liver-related causes or extrahepatic complications was previously unknown. Herein, we show that while treating HCV with direct-acting antiviral regimens has numerous extrahepatic benefits, a significant benefit can be attributed specifically to the reduction in liver-related mortality.

Checkpoint inhibitor immunotherapy in kidney cancer

Kidney cancer has unique features that make this malignancy attractive for therapeutic approaches that target components of the immune system. Immune checkpoint inhibition is a well-established part of kidney cancer treatment, and rapid advances continue to be made in this field. Initial preclinical studies that elucidated the biology of the programmed cell death 1 (PD-1), programmed cell death 1 ligand 1 (PD-L1) and cytotoxic T lymphocyte antigen 4 (CTLA-4) immune checkpoints led to a series of clinical trials that resulted in regulatory approval of nivolumab and the combination of ipilimumab plus nivolumab for the treatment of advanced renal cell carcinoma. Subsequent data led to approvals of combination strategies of immune checkpoint inhibition plus agents that target the vascular endothelial growth factor receptor and a shift in the current standard of renal cell carcinoma care. However, controversies remain regarding the optimal therapy selection and treatment strategy for individual patients, which might be eventually overcome by current intensive efforts in biomarker research. That work includes evaluation of tumour cell PD-L1 expression, gene expression signatures, CD8⁺ T cell density and others. In the future, further advances in the understanding of immune checkpoint biology might reveal new therapeutic targets beyond PD-1, PD-L1 and CTLA-4, as well as new combination approaches.

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.

Direct-Acting Antiviral Therapy for HCV Infection Is Associated With a Reduced Risk of Cardiovascular Disease Events

BACKGROUND & AIMS

Infection with hepatitis virus C (HCV) is associated with an increased risk of cardiovascular disease (CVD) events. It is not clear whether treatment with direct-acting antiviral (DAA) agents affects risk of CVD.

METHODS

We searched the Electronically Retrieved Cohort of HCV-Infected Veterans database for patients with chronic HCV infection (n = 242,680) and identified patients who had been treated with a pegylated interferon and ribavirin regimen (n = 4436) or a DAA-containing regimen (n = 12,667). Treated patients were matched for age, race, sex, and baseline values with patients who had never received treatment for HCV infection (controls). All subjects were free of any CVD event diagnosis of HCV infection at baseline. The primary outcome was incident CVD events, identified by International Classification of Diseases, Ninth Edition, Clinical Modification or International Classification of Diseases, Tenth Edition code, in the different groups and in patients with vs without a sustained virologic response to therapy.

RESULTS

There were 1239 (7.2%) incident CVD events in the treated groups and 2361 (13.8%) events in the control group. Incidence rates were 30.9 per 1000 patient-years (95% CI 29.6-32.1) in the control group and 20.3 per 1000 patient-years (95% CI 19.2-21.5) in the treated groups (P < .0001). Treatment with pegylated interferon and ribavirin (hazard ratio 0.78; 95% CI 0.71-0.85) or a DAA regimen (hazard ratio 0.57; 95% CI 0.51-0.65) was associated with a significantly lower risk of a CVD event compared with no treatment (controls). Incidence rates for CVD events were 23.5 per 1000 patient-years (95% CI 21.8-25.3) in the group treated with the pegylated interferon and ribavirin regimen, 16.3 per 1000 patient-years (95% CI 14.7-18.0) in the group treated with a DAA regimen, and 30.4 (95% CI 29.2-31.7) in the control group. A sustained virologic response was associated with a lower risk of incident CVD events (hazard ratio 0.87; 95% CI 0.77-0.98).

CONCLUSIONS

In an analysis of a cohort of HCV-infected veterans, treatment of HCV infection was associated with a significant decrease in risk of CVD events. Patients treated with a DAA regimen and patients who achieved sustained virologic responses had the lowest risk for CVD events.

Interfacility Transfer is Associated With Lower Mortality in Undertriaged Gunshot Wound Patients

BACKGROUND

Treatment at a Level I trauma center yields better outcomes for patients with moderate-to-severe injury as compared with treatment in nontrauma centers. We examined the association between interfacility transfer to a level I or II trauma center and mortality for gunshot wound patients, among patients initially transported to a lower level or undesignated facility.

MATERIALS AND METHODS

This retrospective cohort study included all patients from the National Trauma Data Bank (2010-2015) with firearm as the external cause of injury, who met CDC criteria for emergency medical services triage to a higher level (American College of Surgeons [ACS] Level II or above) trauma center. We compared outcomes between patients (a) treated in an ACS level III or below facility and not transferred versus (b) transferred to an ACS level II or above facility, adjusting for confounders using inverse probability of treatment weights.

RESULTS

Of the total 62,277 patients, 10,968 (17.6%) were transferred to a level II center or above, and 51,309 (82.4%) were treated at a level III or below or undesignated center. In adjusted analysis comparing transferred versus not transferred patients, risk was lower for mortality (risk ratio [RR] 0.81, 95% confidence interval [CI] 0.70 to 0.95 P = 0.011) but similar for any complication (RR 1.02, 95% CI 0.83 to 1.25 P = 0.87) and the five most common complications. Results were consistent when accounting for data missing at random, and when including state trauma center designations in the definition of Level II or greater versus III and below.

CONCLUSIONS

Our study found lower mortality but similar complication risk associated with interfacility transfer for undertriaged gunshot wound patients. This suggests that transfer to a higher level center is warranted among these patients, with improved care potentially outweighing potential harms because of transfer.

Doubly robust weighted log-rank tests and Renyi-type tests under non-random treatment assignment and dependent censoring

The log-rank test is widely used to test difference in event time distribution between treatment groups. However, if subjects are not randomly assigned to treatment groups, which is often the case in observation studies, the log-rank test is not asymptotically correct for detecting group survival difference due to the imbalance of confounding variables between groups. We develop a class of modified weighted log-rank tests and Renyi-type tests for two-sample survival comparison under non-random treatment assignment. The new tests can also account for non-random censoring that depends on baseline covariates. The proposed methods involve building working models for treatment assignment, cause-specific hazard of dependent censoring, and the time to event. We prove that, when either the models for treatment assignment and dependent censoring or the model for the event time is true, the new tests are asymptotically correct, i.e. being doubly robust. Numerical experiments demonstrate the tests' double-robustness property in finite samples of realistic sizes, and also show that the doubly robust log-rank test is at least as powerful as the regular log-rank test when the treatment assignment is random and there is no dependent censoring. An application to a kidney transplant data set illustrates the utility of the proposed methods.

Two-sample tests for survival data from observational studies

When observational data are used to compare treatment-specific survivals, regular two-sample tests, such as the log-rank test, need to be adjusted for the imbalance between treatments with respect to baseline covariate distributions. Besides, the standard assumption that survival time and censoring time are conditionally independent given the treatment, required for the regular two-sample tests, may not be realistic in observational studies. Moreover, treatment-specific hazards are often non-proportional, resulting in small power for the log-rank test. In this paper, we propose a set of adjusted weighted log-rank tests and their supremum versions by inverse probability of treatment and censoring weighting to compare treatment-specific survivals based on data from observational studies. These tests are proven to be asymptotically correct. Simulation studies show that with realistic sample sizes and censoring rates, the proposed tests have the desired Type I error probabilities and are more powerful than the adjusted log-rank test when the treatment-specific hazards differ in non-proportional ways. A real data example illustrates the practical utility of the new methods.

Assessing the effect of a partly unobserved, exogenous, binary time-dependent covariate on survival probabilities using generalised pseudo-values

Background

Investigating the impact of a time-dependent intervention on the probability of long-term survival is statistically challenging. A typical example is stem-cell transplantation performed after successful donor identification from registered donors. Here, a suggested simple analysis based on the exogenous donor availability status according to registered donors would allow the estimation and comparison of survival probabilities. As donor search is usually ceased after a patient’s event, donor availability status is incompletely observed, so that this simple comparison is not possible and the waiting time to donor identification needs to be addressed in the analysis to avoid bias. It is methodologically unclear, how to directly address cumulative long-term treatment effects without relying on proportional hazards while avoiding waiting time bias.

Methods

The pseudo-value regression technique is able to handle the first two issues; a novel generalisation of this technique also avoids waiting time bias. Inverse-probability-of-censoring weighting is used to account for the partly unobserved exogenous covariate donor availability.

Results

Simulation studies demonstrate unbiasedness and satisfying coverage probabilities of the new method. A real data example demonstrates that study results based on generalised pseudo-values have a clear medical interpretation which supports the clinical decision making process.

Conclusions

The proposed generalisation of the pseudo-value regression technique enables to compare survival probabilities between two independent groups where group membership becomes known over time and remains partly unknown. Hence, cumulative long-term treatment effects are directly addressed without relying on proportional hazards while avoiding waiting time bias.

Electronic supplementary material

The online version of this article (10.1186/s12874-017-0430-5) contains supplementary material, which is available to authorized users.

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.

Estimating restricted mean treatment effects with stacked survival models

The difference in restricted mean survival times between two groups is a clinically relevant summary measure. With observational data, there may be imbalances in confounding variables between the two groups. One approach to account for such imbalances is estimating a covariate-adjusted restricted mean difference by modeling the covariate-adjusted survival distribution and then marginalizing over the covariate distribution. Because the estimator for the restricted mean difference is defined by the estimator for the covariate-adjusted survival distribution, it is natural to expect that a better estimator of the covariate-adjusted survival distribution is associated with a better estimator of the restricted mean difference. We therefore propose estimating restricted mean differences with stacked survival models. Stacked survival models estimate a weighted average of several survival models by minimizing predicted error. By including a range of parametric, semi-parametric, and non-parametric models, stacked survival models can robustly estimate a covariate-adjusted survival distribution and, therefore, the restricted mean treatment effect in a wide range of scenarios. We demonstrate through a simulation study that better performance of the covariate-adjusted survival distribution often leads to better mean squared error of the restricted mean difference although there are notable exceptions. In addition, we demonstrate that the proposed estimator can perform nearly as well as Cox regression when the proportional hazards assumption is satisfied and significantly better when proportional hazards is violated. Finally, the proposed estimator is illustrated with data from the United Network for Organ Sharing to evaluate post-lung transplant survival between large-volume and small-volume centers. Copyright © 2016 John Wiley & Sons, Ltd.

Estimating the number of quit attempts it takes to quit smoking successfully in a longitudinal cohort of smokers

OBJECTIVES

The number of quit attempts it takes a smoker to quit successfully is a commonly reported figure among smoking cessation programmes, but previous estimates have been based on lifetime recall in cross-sectional samples of successful quitters only. The purpose of this study is to improve the estimate of number of quit attempts prior to quitting successfully.

DESIGN

We used data from 1277 participants who had made an attempt to quit smoking in the Ontario Tobacco Survey, a longitudinal survey of smokers followed every 6 months for up to 3 years beginning in 2005. We calculated the number of quit attempts prior to quitting successfully under four different sets of assumptions. Our expected best set of assumptions incorporated a life table approach accounting for the declining success rates for subsequent observed quit attempts in the cohort.

RESULTS

The estimated average number of quit attempts expected before quitting successfully ranged from 6.1 under the assumptions consistent with prior research, 19.6 using a constant rate approach, 29.6 using the method with the expected lowest bias, to 142 using an approach including previous recall history.

CONCLUSIONS

Previous estimates of number of quit attempts required to quit may be underestimating the average number of attempts as these estimates excluded smokers who have greater difficulty quitting and relied on lifetime recall of number of attempts. Understanding that for many smokers it may take 30 or more quit attempts before being successful may assist with clinical expectations.

Propensity score-based survival benefit of simultaneous liver-kidney transplant over liver transplant alone for recipients with pretransplant renal dysfunction

The survival benefit of simultaneous liver-kidney transplantation (SLKT) over liver transplantation alone (LTA) is unclear from the current literature. Additionally, the role of donor kidney quality, measured by the kidney donor risk index (KDRI), in survival benefit of SLKT is not studied. We compared survival benefit after SLKT and LTA among recipients with similar pretransplant renal dysfunction using novel methodology, specifically with respect to survival probability and area under the survival curve by dialysis status and KDRI. Data were obtained from the Scientific Registry of Transplant Recipients. The study cohort included patients with pre-liver transplantation (LT) renal dysfunction who were wait-listed and received either a SLKT (n = 1326) or a LTA (n = 4283) between March 1, 2002 and December 31, 2009. Inverse Probability of Treatment Weighting-SLKT and LTA survival curves, along with the 5-year area under the survival curve, were computed by dialysis status at transplant. The difference in the area under the curve represents the average additional survival time gained via SLKT over LTA. For patients not on dialysis, SLKT resulted in a significant 3.7-month gain in 5-year mean posttransplant survival time. The decrease in mortality rate differs significantly by KDRI, and an estimated 76% of SLKT recipients received a kidney with KDRI sufficiently low for mortality. The mortality decrease for SLKT was concentrated in the first year after transplant. The difference between SLKT and LTA 5-year mean posttransplant survival time was 1.4 months and was nonsignificant for patients on dialysis. In conclusion, the propensity score-adjusted survival among SLKT and LTA recipients was similar for those who were on dialysis at LT. Although statistically significant, the survival advantage of SLKT over LTA was of marginal clinical significance among patients not on dialysis and occurred only if the donor kidney was of sufficient quality. These results should be considered in the ongoing debate regarding the allocation of kidneys to extra-renal transplant candidates.

The Peritoneal Dialysis Outcomes and Practice Patterns Study (PDOPPS): Unifying Efforts to Inform Practice and Improve Global Outcomes in Peritoneal Dialysis

♦

BACKGROUND

Extending technique survival on peritoneal dialysis (PD) remains a major challenge in optimizing outcomes for PD patients while increasing PD utilization. The primary objective of the Peritoneal Dialysis Outcomes and Practice Patterns Study (PDOPPS) is to identify modifiable practices associated with improvements in PD technique and patient survival. In collaboration with the International Society for Peritoneal Dialysis (ISPD), PDOPPS seeks to standardize PD-related data definitions and provide a forum for effective international collaborative clinical research in PD. ♦

METHODS

The PDOPPS is an international prospective cohort study in Australia, Canada, Japan, the United Kingdom (UK), and the United States (US). Each country is enrolling a random sample of incident and prevalent patients from national samples of 20 to 80 sites with at least 20 patients on PD. Enrolled patients will be followed over an initial 3-year study period. Demographic, comorbidity, and treatment-related variables, and patient-reported data, will be collected over the study course. The primary outcome will be all-cause PD technique failure or death; other outcomes will include cause-specific technique failure, hospitalizations, and patient-reported outcomes. ♦

RESULTS

A high proportion of the targeted number of study sites has been recruited to date in each country. Several ancillary studies have been funded with high momentum toward expansion to new countries and additional participation. ♦

CONCLUSION

The PDOPPS is the first large, international study to follow PD patients longitudinally to capture clinical practice. With data collected, the study will serve as an invaluable resource and research platform for the international PD community, and provide a means to understand variation in PD practices and outcomes, to identify optimal practices, and to ultimately improve outcomes for PD patients.

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.

On the restricted mean survival time curve in survival analysis

For a study with an event time as the endpoint, its survival function contains all the information regarding the temporal, stochastic profile of this outcome variable. The survival probability at a specific time point, say t, however, does not transparently capture the temporal profile of this endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to summarize the profile. The RMST is the mean survival time of all subjects in the study population followed up to t, and is simply the area under the survival curve up to t. The advantages of using such a quantification over the survival rate have been discussed in the setting of a fixed-time analysis. In this article, we generalize this approach by considering a curve based on the RMST over time as an alternative summary to the survival function. Inference, for instance, based on simultaneous confidence bands for a single RMST curve and also the difference between two RMST curves are proposed. The latter is informative for evaluating two groups under an equivalence or noninferiority setting, and quantifies the difference of two groups in a time scale. The proposal is illustrated with the data from two clinical trials, one from oncology and the other from cardiology.

Modeling potential time to event data with competing risks

Patients receiving radical prostatectomy are at risk of metastasis or prostate cancer related death, and often need repeated clinical evaluations to determine whether additional adjuvant or salvage therapies are needed. Since the prostate cancer is a slowly progressing disease, and these additional therapies come with significant side effects, it is important for clinical decision making purposes to estimate a patient's risk of cancer metastasis, in the presence of a competing risk by death, under the hypothetical condition that the patient does not receive any additional therapy. In observational studies, patients may receive additional therapy by choice; the time to metastasis without any therapy is often a potential outcome and not always observed. We study the competing risks model of Fine and Gray (J Am Stat Assoc, 94:496-509, 1999) with adjustment for treatment choice by inverse probability censoring weighting (IPCW). The model can be fit using standard software for partial likelihood with double IPCW weights. The proposed methodology is used in a prostate cancer study to predict the post-prostatectomy cumulative incidence probability of cancer metastasis without additional adjuvant or salvage therapies.

Semiparametric inference on the absolute risk reduction and the restricted mean survival difference

For time-to-event data, when the hazards are non-proportional, in addition to the hazard ratio, the absolute risk reduction and the restricted mean survival difference can be used to describe the time-dependent treatment effect. The absolute risk reduction measures the direct impact of the treatment on event rate or survival, and the restricted mean survival difference provides a way to evaluate the cumulative treatment effect. However, in the literature, available methods are limited for flexibly estimating these measures and making inference on them. In this article, point estimates, pointwise confidence intervals and simultaneous confidence bands of the absolute risk reduction and the restricted mean survival difference are established under a semiparametric model that can be used in a sufficiently wide range of applications. These methods are motivated by and illustrated for data from the Women's Health Initiative estrogen plus progestin clinical trial.

Contrasting treatment-specific survival using double-robust estimators

In settings where a randomized trial is infeasible, observational data are frequently used to compare treatment-specific survival. The average causal effect (ACE) can be used to make inference regarding treatment policies on patient populations, and a valid ACE estimator must account for imbalances with respect to treatment-specific covariate distributions. One method through which the ACE on survival can be estimated involves appropriately averaging over Cox-regression-based fitted survival functions. A second available method balances the treatment-specific covariate distributions through inverse probability of treatment weighting and then contrasts weighted nonparametric survival function estimators. Because both methods have their advantages and disadvantages, we propose methods that essentially combine both estimators. The proposed methods are double robust, in the sense that they are consistent if at least one of the two working regression models (i.e., logistic model for treatment and Cox model for death hazard) is correct. The proposed methods involve estimating the ACE with respect to restricted mean survival time, defined as the area under the survival curve up to some prespecified time point. We derive and evaluate asymptotic results through simulation. We apply the proposed methods to estimate the ACE of donation-after-cardiac-death kidney transplantation with the use of data obtained from multiple centers in the Netherlands.

Overestimation of the probability of death on peritoneal dialysis by the Kaplan-Meier method: advantages of a competing risks approach

Background

In survival analysis, patients on peritoneal dialysis are confronted with three different outcomes: transfer to hemodialysis, renal transplantation, or death. The Kaplan-Meier method takes into account one event only, so whether it adequately considers these different risks is questionable. The more recent competing risks method has been shown to be more appropriate in analyzing such situations.

Methods

We compared the estimations obtained by the Kaplan-Meier method and the competing risks method (namely the Kalbfleisch and Prentice approach), in 383 consecutive incident peritoneal dialysis patients. By means of simulations, we then compared the Kaplan-Meier estimations obtained in two virtual centers where patients had exactly the same probability of death. The only difference between these two virtual centers was whether renal transplantation was available or not.

Results

At five years, 107 (27.9%) patients had died, 109 (28.4%) had been transferred to hemodialysis, 91 (23.8%) had been transplanted, and 37 (9.7%) were still alive on peritoneal dialysis; before five years, 39 (10.2%) patients were censored alive on peritoneal dialysis. The five-year probabilities estimated by the Kaplan-Meier and the competing risks methods were respectively: death: 50% versus 30%; transfer to hemodialysis: 59% versus 32%; renal transplantation: 39% versus 26%; event-free survival: 12% versus 12%. The sum of the Kaplan-Meier estimations exceeded 100%, implying that patients could experience more than one event, death and transplantation for example, which is impossible. In the simulations, the probability of death estimated by the Kaplan-Meier method increased as the probability of renal transplantation increased, although the probability of death actually remained constant.

Conclusion

The competing risks method appears more appropriate than the Kaplan-Meier method for estimating the probability of events in peritoneal dialysis in the context of univariable survival analysis.