Causal inference on the difference of the restricted mean lifetime between two groups

Propensity score matching for estimating a marginal hazard ratio

Propensity score matching is commonly used to draw causal inference from observational survival data. However, its asymptotic properties have yet to be established, and variance estimation is still open to debate. We derive the statistical properties of the propensity score matching estimator of the marginal causal hazard ratio based on matching with replacement and a fixed number of matches. We also propose a double-resampling technique for variance estimation that takes into account the uncertainty due to propensity score estimation prior to matching.

Scaling and interpreting treatment effects in clinical trials using restricted mean survival time

BACKGROUND

Restricted mean survival time is the expected duration of survival up to a chosen time of restriction τ . For comparison studies, the difference in restricted mean survival times between two groups provides a summary measure of the treatment effect that is free of assumptions regarding the relative shape of the two survival curves, such as proportional hazards. However, it can be difficult to judge the magnitude of the effect from a comparison of restricted means due to the truncation of observation at time τ .

METHODS

In this article, we describe additional ways of expressing the treatment effect based on restricted means that can be helpful in this regard. These include the ratio of restricted means, the ratio of life-years (or time) lost, and the average integrated difference between the survival curves, equal to the difference in restricted means divided by τ . These alternative metrics are straightforward to calculate and provide a means for scaling the effect size as an aid to interpretation. Examples from two randomized, multicenter clinical trials in prostate cancer, NRG/RTOG 0521 and NRG/RTOG 0534, with primary endpoints of overall survival and biochemical/radiological progression-free survival, respectively, are presented to illustrate the ideas.

RESULTS

The four effect measures (restricted mean survival time difference, restricted mean survival time ratio, time lost ratio, and average survival rate difference) were 0.45 years, 1.05, 0.81, and 0.038 for RTOG 0521 and 1.36 years, 1.17, 0.56, and 0.12 for RTOG 0534 with τ  = 12 and 11 years, respectively. Thus, for example, the 0.45-year difference in the first trial translates into a 19% reduction in time lost and a 3.8% average absolute difference between the survival curves over the 12-year horizon, a modest effect size, whereas the 1.36-year difference in the second trial corresponds to a 44% reduction in time lost and a 12% absolute survival difference, a rather large effect.

CONCLUSIONS

In addition to the difference in restricted mean survival times, these alternative measures can be helpful in determining whether the magnitude of the treatment effect is clinically meaningful.

Covariate adjustment in randomized controlled trials: General concepts and practical considerations

There has been a growing interest in covariate adjustment in the analysis of randomized controlled trials in past years. For instance, the US Food and Drug Administration recently issued guidance that emphasizes the importance of distinguishing between conditional and marginal treatment effects. Although these effects may sometimes coincide in the context of linear models, this is not typically the case in other settings, and this distinction is often overlooked in clinical trial practice. Considering these developments, this article provides a review of when and how to use covariate adjustment to enhance precision in randomized controlled trials. We describe the differences between conditional and marginal estimands and stress the necessity of aligning statistical analysis methods with the chosen estimand. In addition, we highlight the potential misalignment of commonly used methods in estimating marginal treatment effects. We hereby advocate for the use of the standardization approach, as it can improve efficiency by leveraging the information contained in baseline covariates while remaining robust to model misspecification. Finally, we present practical considerations that have arisen in our respective consultations to further clarify the advantages and limitations of covariate adjustment.

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.

Heterogeneous Treatment Effects of Intensive Glycemic Control on Kidney Microvascular Outcomes and Mortality in ACCORD

SIGNIFICANCE STATEMENT

Identifying and quantifying treatment effect variation across patients is the fundamental challenge of precision medicine. Here we quantify heterogeneous treatment effects of intensive glycemic control in the Action to Control Cardiovascular Risk in Diabetes (ACCORD) trial, considering three outcomes of interest-a composite kidney outcome (driven by macroalbuminuria), all-cause mortality, and first assisted hypoglycemic event. We demonstrate that the effects of intensive glycemic control vary with risk of kidney failure, as predicted by the kidney failure risk equation (KFRE). Participants at highest risk of kidney failure gain the largest absolute kidney benefit of intensive glycemic control but also experience the largest absolute risk of death and hypoglycemic events. Our findings illustrate the value of identifying clinically meaningful treatment heterogeneity, particularly when treatments have different effects on multiple end points.

OBJECTIVE

Clear criteria to individualize glycemic targets in patients with type II diabetes are lacking. In this post hoc analysis of the ACCORD, we evaluate whether the KFRE can identify patients for whom intensive glycemic control confers more benefit in preventing kidney microvascular outcomes.

RESEARCH DESIGN AND METHODS

We divided the ACCORD trial population into quartiles on the basis of 5-year kidney failure risk using the KFRE. We estimated conditional treatment effects within each quartile and compared them with the average treatment effect in the trial. The treatment effects of interest were the 7-year restricted mean survival time (RMST) differences between intensive and standard glycemic control arms on ( 1 ) time-to-first development of severely elevated albuminuria or kidney failure and ( 2 ) all-cause mortality.

RESULTS

We found evidence that the effect of intensive glycemic control on kidney microvascular outcomes and all-cause mortality varies with baseline risk of kidney failure. Patients with elevated baseline risk of kidney failure derived the most from intensive glycemic control in reducing kidney microvascular outcomes (7-year RMST difference of 114.8 [95% confidence interval 58.1 to 176.4] versus 48.4 [25.3 to 69.6] days in the entire trial population) However, this same patient group also experienced a shorter time to death (7-year RMST difference of -56.7 [-100.2 to -17.5] v. -23.6 [-42.2 to -6.6] days).

CONCLUSIONS

We found evidence of heterogenous treatment effects of intensive glycemic control on kidney microvascular outcomes in ACCORD as a function of predicted baseline risk of kidney failure. Patients with higher kidney failure risk experienced the most pronounced reduction in kidney microvascular outcomes but also experienced the highest risk of all-cause mortality.

A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection

We recently developed a new method random-intercept accelerated failure time model with Bayesian additive regression trees (riAFT-BART) to draw causal inferences about population treatment effect on patient survival from clustered and censored survival data while accounting for the multilevel data structure. The practical utility of this method goes beyond the estimation of population average treatment effect. In this work, we exposit how riAFT-BART can be used to solve two important statistical questions with clustered survival data: estimating the treatment effect heterogeneity and variable selection. Leveraging the likelihood-based machine learning, we describe a way in which we can draw posterior samples of the individual survival treatment effect from riAFT-BART model runs, and use the drawn posterior samples to perform an exploratory treatment effect heterogeneity analysis to identify subpopulations who may experience differential treatment effects than population average effects. There is sparse literature on methods for variable selection among clustered and censored survival data, particularly ones using flexible modeling techniques. We propose a permutation-based approach using the predictor's variable inclusion proportion supplied by the riAFT-BART model for variable selection. To address the missing data issue frequently encountered in health databases, we propose a strategy to combine bootstrap imputation and riAFT-BART for variable selection among incomplete clustered survival data. We conduct an expansive simulation study to examine the practical operating characteristics of our proposed methods, and provide empirical evidence that our proposed methods perform better than several existing methods across a wide range of data scenarios. Finally, we demonstrate the methods via a case study of predictors for in-hospital mortality among severe COVID-19 patients and estimating the heterogeneous treatment effects of three COVID-specific medications. The methods developed in this work are readily available in the R ${\textsf {R}}$ package riAFTBART $\textsf {riAFTBART}$ .

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.

Restricted mean survival time to estimate an intervention effect in a cluster randomized trial

For time-to-event outcomes, the difference in restricted mean survival time is a measure of the intervention effect, an alternative to the hazard ratio, corresponding to the expected survival duration gain due to the intervention up to a predefined time t*. We extended two existing approaches of restricted mean survival time estimation for independent data to clustered data in the framework of cluster randomized trials: one based on the direct integration of Kaplan-Meier curves and the other based on pseudo-values regression. Then, we conducted a simulation study to assess and compare the statistical performance of the proposed methods, varying the number and size of clusters, the degree of clustering, and the magnitude of the intervention effect under proportional and non-proportional hazards assumption. We found that the extended methods well estimated the variance and controlled the type I error if there was a sufficient number of clusters (≥ 50) under both proportional and non-proportional hazards assumption. For cluster randomized trials with a limited number of clusters (< 50), a permutation test for pseudo-values regression was implemented and corrected the type I error. We also provided a procedure to estimate permutation-based confidence intervals which produced adequate coverage. All the extended methods performed similarly, but the pseudo-values regression offered the possibility to adjust for covariates. Finally, we illustrated each considered method with a cluster randomized trial evaluating the effectiveness of an asthma-control education program.

Joint inference for competing risks data using multiple endpoints

Competing risks data are commonly encountered in randomized clinical trials and observational studies. This paper considers the situation where the ending statuses of competing events have different clinical interpretations and/or are of simultaneous interest. In clinical trials, often more than one competing event has meaningful clinical interpretations even though the trial effects of different events could be different or even opposite to each other. In this paper, we develop estimation procedures and inferential properties for the joint use of multiple cumulative incidence functions (CIFs). Additionally, by incorporating longitudinal marker information, we develop estimation and inference procedures for weighted CIFs and related metrics. The proposed methods are applied to a COVID-19 in-patient treatment clinical trial, where the outcomes of COVID-19 hospitalization are either death or discharge from the hospital, two competing events with completely different clinical implications.

Simultaneous hypothesis testing for multiple competing risks in comparative clinical trials

Competing risks data are commonly encountered in randomized clinical trials or observational studies. Ignoring competing risks in survival analysis leads to biased risk estimates and improper conclusions. Often, one of the competing events is of primary interest and the rest competing events are handled as nuisances. These approaches can be inadequate when multiple competing events have important clinical interpretations and thus of equal interest. For example, in COVID-19 in-patient treatment trials, the outcomes of COVID-19 related hospitalization are either death or discharge from hospital, which have completely different clinical implications and are of equal interest, especially during the pandemic. In this paper we develop nonparametric estimation and simultaneous inferential methods for multiple cumulative incidence functions (CIFs) and corresponding restricted mean times. Based on Monte Carlo simulations and a data analysis of COVID-19 in-patient treatment clinical trial, we demonstrate that the proposed method provides global insights of the treatment effects across multiple endpoints.

Heterogeneous treatment effects of intensive glycemic control on kidney microvascular outcomes in ACCORD

Objective

Clear criteria to individualize glycemic targets are lacking. In this post-hoc analysis of the Action to Control Cardiovascular Risk in Diabetes trial (ACCORD), we evaluate whether the kidney failure risk equation (KFRE) can identify patients who disproportionately benefit from intensive glycemic control on kidney microvascular outcomes.

Research design and methods

We divided the ACCORD trial population in quartiles based on 5-year kidney failure risk using the KFRE. We estimated conditional treatment effects within each quartile and compared them to the average treatment effect in the trial. The treatment effects of interest were the 7-year restricted-mean-survival-time (RMST) differences between intensive and standard glycemic control arms on (1) time-to-first development of severely elevated albuminuria or kidney failure and (2) all-cause mortality.

Results

We found evidence that the effect of intensive glycemic control on kidney microvascular outcomes and all-cause mortality varies with baseline risk of kidney failure. Patients with elevated baseline risk of kidney failure benefitted the most from intensive glycemic control on kidney microvascular outcomes (7-year RMST difference of 115 v. 48 days in the entire trial population) However, this same patient group also experienced shorter times to death (7-year RMST difference of -57 v. -24 days).

Conclusions

We found evidence of heterogenous treatment effects of intensive glycemic control on kidney microvascular outcomes in ACCORD as a function of predicted baseline risk of kidney failure. Patients with higher kidney failure risk experienced the most pronounced benefits of treatment on kidney microvascular outcomes but also experienced the highest risk of all-cause mortality.

Causal inference in survival analysis using longitudinal observational data: Sequential trials and marginal structural models

Longitudinal observational data on patients can be used to investigate causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for estimating such effects by controlling for the time-dependent confounding that typically occurs. The most commonly used is marginal structural models (MSM) estimated using inverse probability of treatment weights (IPTW) (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, and involves creating a sequence of "trials" from new time origins and comparing treatment initiators and non-initiators. Individuals are censored when they deviate from their treatment assignment at the start of each "trial" (initiator or noninitiator), which is accounted for using inverse probability of censoring weights. The analysis uses data combined across trials. We show that the sequential trials approach can estimate the parameters of a particular MSM. The causal estimand that we focus on is the marginal risk difference between the sustained treatment strategies of "always treat" vs "never treat." We compare how the sequential trials approach and MSM-IPTW estimate this estimand, and discuss their assumptions and how data are used differently. The performance of the two approaches is compared in a simulation study. The sequential trials approach, which tends to involve less extreme weights than MSM-IPTW, results in greater efficiency for estimating the marginal risk difference at most follow-up times, but this can, in certain scenarios, be reversed at later time points and relies on modelling assumptions. We apply the methods to longitudinal observational data from the UK Cystic Fibrosis Registry to estimate the effect of dornase alfa on survival.

On High-Dimensional Covariate Adjustment for Estimating Causal Effects in Randomized Trials with Survival Outcomes

The purpose of this work is to improve the efficiency in estimating the average causal effect (ACE) on the survival scale where right-censoring exists and high-dimensional covariate information is available. We propose new estimators using regularized survival regression and survival Random Forest (RF) to adjust for the high-dimensional covariate to improve efficiency. We study the behavior of the adjusted estimators under mild assumptions and show theoretical guarantees that the proposed estimators are more efficient than the unadjusted ones asymptotically when using RF for the adjustment. In addition, these adjusted estimators aren - consistent and asymptotically normally distributed. The finite sample behavior of our methods is studied by simulation. The simulation results are in agreement with the theoretical results. We also illustrate our methods by analyzing the real data from transplant research to identify the relative effectiveness of identical sibling donors compared to unrelated donors with the adjustment of cytogenetic abnormalities.

On restricted mean time in favor of treatment

The restricted mean time in favor (RMT-IF) of treatment is a nonparametric effect size for complex life history data. It is defined as the net average time the treated spend in a more favorable state than the untreated over a prespecified time window. It generalizes the familiar restricted mean survival time (RMST) from the two-state life-death model to account for intermediate stages in disease progression. The overall estimand can be additively decomposed into stage-wise effects, with the standard RMST as a component. Alternate expressions of the overall and stage-wise estimands as integrals of the marginal survival functions for a sequence of landmark transitioning events allow them to be easily estimated by plug-in Kaplan-Meier estimators. The dynamic profile of the estimated treatment effects as a function of follow-up time can be visualized using a multilayer, cone-shaped "bouquet plot." Simulation studies under realistic settings show that the RMT-IF meaningfully and accurately quantifies the treatment effect and outperforms traditional tests on time to the first event in statistical efficiency thanks to its fuller utilization of patient data. The new methods are illustrated on a colon cancer trial with relapse and death as outcomes and a cardiovascular trial with recurrent hospitalizations and death as outcomes. The R-package rmt implements the proposed methodology and is publicly available from the Comprehensive R Archive Network (CRAN).

SMIM: A unified framework of survival sensitivity analysis using multiple imputation and martingale

Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account missing data due to censoring. Multiple imputation facilitates the use of simple full-sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the nonparametric bootstrap counterpart. We evaluate the finite-sample performance of the proposed SMIM through simulation and an application on an HIV clinical trial.

Fast approximations of pseudo-observations in the context of right censoring and interval censoring

In the context of right-censored and interval-censored data, we develop asymptotic formulas to compute pseudo-observations for the survival function and the restricted mean survival time (RMST). These formulas are based on the original estimators and do not involve computation of the jackknife estimators. For right-censored data, Von Mises expansions of the Kaplan-Meier estimator are used to derive the pseudo-observations. For interval-censored data, a general class of parametric models for the survival function is studied. An asymptotic representation of the pseudo-observations is derived involving the Hessian matrix and the score vector. Theoretical results that justify the use of pseudo-observations in regression are also derived. The formula is illustrated on the piecewise-constant-hazard model for the RMST. The proposed approximations are extremely accurate, even for small sample sizes, as illustrated by Monte Carlo simulations and real data. We also study the gain in terms of computation time, as compared to the original jackknife method, which can be substantial for a large dataset.

Unfractionated heparin versus nafamostat mesylate for anticoagulation during continuous kidney replacement therapy: an observational study

BACKGROUND

Unfractionated heparin sodium and nafamostat mesylate have long been used as anticoagulants in continuous kidney replacement therapy (CKRT) where citrate is unavailable. This study aimed to determine whether heparin or nafamostat mesylate used during CKRT was associated with a longer filter life.

METHODS

In this single-centre observational study, we included adult patients who required CKRT and used heparin or nafamostat mesylate for their first CKRT in the intensive care unit from September 1, 2013, to December 31, 2020. The primary outcome was filter life (from the start to the end of using the first filter). We used propensity score matching to adjust for the imbalance in patients' characteristics and laboratory data at the start of CKRT and compared the outcomes between the two groups. We also performed restricted mean survival time analysis to compare the filter survival times.

RESULTS

We included 286 patients, 157 patients on heparin and 129 patients on nafamostat mesylate. After propensity score matching, the mean filter life with heparin was 1.58 days (N = 91, Standard deviation [SD], 1.52) and with nafamostat mesylate was 1.06 days (N = 91, SD, 0.94, p = 0.006). Multivariable regression analysis adjusted for confounding factors supported that heparin was associated with a longer filter life compared with nafamostat mesylate (regression coefficient, days, 0.52 [95% CI, 0.15, 0.89]). The between group difference of the restricted mean filter survival time in the matched cohort was 0.29 (95% CI, 0.07-0.50, p = 0.008).

CONCLUSION

Compared to nafamostat mesylate, heparin was associated with one-third to one-half a day longer filter life.

TRIAL REGISTRATION

Not applicable.

A unified mediation analysis framework for integrative cancer proteogenomics with clinical outcomes

MOTIVATION

Multilevel molecular profiling of tumors and the integrative analysis with clinical outcomes have enabled a deeper characterization of cancer treatment. Mediation analysis has emerged as a promising statistical tool to identify and quantify the intermediate mechanisms by which a gene affects an outcome. However, existing methods lack a unified approach to handle various types of outcome variables, making them unsuitable for high-throughput molecular profiling data with highly interconnected variables.

RESULTS

We develop a general mediation analysis framework for proteogenomic data that include multiple exposures, multivariate mediators on various scales of effects as appropriate for continuous, binary and survival outcomes. Our estimation method avoids imposing constraints on model parameters such as the rare disease assumption, while accommodating multiple exposures and high-dimensional mediators. We compare our approach to other methods in extensive simulation studies at a range of sample sizes, disease prevalence and number of false mediators. Using kidney renal clear cell carcinoma proteogenomic data, we identify genes that are mediated by proteins and the underlying mechanisms on various survival outcomes that capture short- and long-term disease-specific clinical characteristics.

AVAILABILITY AND IMPLEMENTATION

Software is made available in an R package (https://github.com/longjp/mediateR).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

A flexible approach for causal inference with multiple treatments and clustered survival outcomes

When drawing causal inferences about the effects of multiple treatments on clustered survival outcomes using observational data, we need to address implications of the multilevel data structure, multiple treatments, censoring, and unmeasured confounding for causal analyses. Few off-the-shelf causal inference tools are available to simultaneously tackle these issues. We develop a flexible random-intercept accelerated failure time model, in which we use Bayesian additive regression trees to capture arbitrarily complex relationships between censored survival times and pre-treatment covariates and use the random intercepts to capture cluster-specific main effects. We develop an efficient Markov chain Monte Carlo algorithm to draw posterior inferences about the population survival effects of multiple treatments and examine the variability in cluster-level effects. We further propose an interpretable sensitivity analysis approach to evaluate the sensitivity of drawn causal inferences about treatment effect to the potential magnitude of departure from the causal assumption of no unmeasured confounding. Expansive simulations empirically validate and demonstrate good practical operating characteristics of our proposed methods. Applying the proposed methods to a dataset on older high-risk localized prostate cancer patients drawn from the National Cancer Database, we evaluate the comparative effects of three treatment approaches on patient survival, and assess the ramifications of potential unmeasured confounding. The methods developed in this work are readily available in the R $$ \mathsf{R}\kern.15em $$ package riAFTBART $$ \mathsf{riAFTBART} $$ .

Estimating causal effects in the presence of competing events using regression standardisation with the Stata command standsurv

BACKGROUND

When interested in a time-to-event outcome, competing events that prevent the occurrence of the event of interest may be present. In the presence of competing events, various estimands have been suggested for defining the causal effect of treatment on the event of interest. Depending on the estimand, the competing events are either accommodated or eliminated, resulting in causal effects with different interpretations. The former approach captures the total effect of treatment on the event of interest while the latter approach captures the direct effect of treatment on the event of interest that is not mediated by the competing event. Separable effects have also been defined for settings where the treatment can be partitioned into two components that affect the event of interest and the competing event through different causal pathways.

METHODS

We outline various causal effects that may be of interest in the presence of competing events, including total, direct and separable effects, and describe how to obtain estimates using regression standardisation with the Stata command standsurv. Regression standardisation is applied by obtaining the average of individual estimates across all individuals in a study population after fitting a survival model.

RESULTS

With standsurv several contrasts of interest can be calculated including differences, ratios and other user-defined functions. Confidence intervals can also be obtained using the delta method. Throughout we use an example analysing a publicly available dataset on prostate cancer to allow the reader to replicate the analysis and further explore the different effects of interest.

CONCLUSIONS

Several causal effects can be defined in the presence of competing events and, under assumptions, estimates of those can be obtained using regression standardisation with the Stata command standsurv. The choice of which causal effect to define should be given careful consideration based on the research question and the audience to which the findings will be communicated.

A Review of Causal Inference for External Comparator Arm Studies

Randomized controlled trials (RCTs) are the gold standard design to establish the efficacy of new drugs and to support regulatory decision making. However, a marked increase in the submission of single-arm trials (SATs) has been observed in recent years, especially in the field of oncology due to the trend towards precision medicine contributing to the rise of new therapeutic interventions for rare diseases. SATs lack results for control patients, and information from external sources can be compiled to provide context for better interpretability of study results. External comparator arm (ECA) studies are defined as a clinical trial (most commonly a SAT) and an ECA of a comparable cohort of patients-commonly derived from real-world settings including registries, natural history studies, or medical records of routine care. This publication aims to provide a methodological overview, to sketch emergent best practice recommendations and to identify future methodological research topics. Specifically, existing scientific and regulatory guidance for ECA studies is reviewed and appropriate causal inference methods are discussed. Further topics include sample size considerations, use of estimands, handling of different data sources regarding differential baseline covariate definitions, differential endpoint measurements and timings. In addition, unique features of ECA studies are highlighted, specifically the opportunity to address bias caused by unmeasured ECA covariates, which are available in the SAT.

Regression modeling of restricted mean survival time for left-truncated right-censored data

The restricted mean survival time (RMST) is a clinically meaningful summary measure in studies with survival outcomes. Statistical methods have been developed for regression analysis of RMST to investigate impacts of covariates on RMST, which is a useful alternative to the Cox regression analysis. However, existing methods for regression modeling of RMST are not applicable to left-truncated right-censored data that arise frequently in prevalent cohort studies, for which the sampling bias due to left truncation and informative censoring induced by the prevalent sampling scheme must be properly addressed. The pseudo-observation (PO) approach has been used in regression modeling of RMST for right-censored data and competing-risks data. For left-truncated right-censored data, we propose to directly model RMST as a function of baseline covariates based on POs under general censoring mechanisms. We adjust for the potential covariate-dependent censoring or dependent censoring by the inverse probability of censoring weighting method. We establish large sample properties of the proposed estimators and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a prevalent cohort of women diagnosed with stage IV breast cancer identified from surveillance, epidemiology, and end results-medicare linked database.

Trial emulation and survival analysis for disease incidence registers: A case study on the causal effect of pre-emptive kidney transplantation

When drawing causal inference from observed data, failure time outcomes present additional challenges of censoring often combined with other missing data patterns. In this article, we follow incident cases of end‐stage renal disease to examine the effect on all‐cause mortality of starting treatment with transplant, so‐called pre‐emptive kidney transplantation, vs starting with dialysis possibly followed by delayed transplantation. The question is relatively simple: which start‐off treatment is expected to bring the best survival for a target population? To address it, we emulate a target trial drawing on the long term Swedish Renal Registry, where a growing common set of baseline covariates was measured nationwide. Several lessons are learned which pertain to long term disease registers more generally. With characteristics of cases and versions of treatment evolving over time, informative censoring is already introduced in unadjusted Kaplan‐Meier curves. This leads to misrepresented survival chances in observed treatment groups. The resulting biased treatment association may be aggravated upon implementing IPW for treatment. Aware of additional challenges, we further recall how similar studies to date have selected patients into treatment groups based on events occurring post treatment initiation. Our study reveals the dramatic impact of resulting immortal time bias combined with other typical features of long‐term incident disease registers, including missing covariates during the early phases of the register. We discuss feasible ways of accommodating these features when targeting relevant estimands, and demonstrate how more than one causal question can be answered relying on the no unmeasured baseline confounders assumption.

Restricted mean survival time regression model with time-dependent covariates

In clinical or epidemiological follow‐up studies, methods based on time scale indicators such as the restricted mean survival time (RMST) have been developed to some extent. Compared with traditional hazard rate indicator system methods, the RMST is easier to interpret and does not require the proportional hazard assumption. To date, regression models based on the RMST are indirect or direct models of the RMST and baseline covariates. However, time‐dependent covariates are becoming increasingly common in follow‐up studies. Based on the inverse probability of censoring weighting (IPCW) method, we developed a regression model of the RMST and time‐dependent covariates. Through Monte Carlo simulation, we verified the estimation performance of the regression parameters of the proposed model. Compared with the time‐dependent Cox model and the fixed (baseline) covariate RMST model, the time‐dependent RMST model has a better prediction ability. Finally, an example of heart transplantation was used to verify the above conclusions.

Doubly-robust estimator of the difference in restricted mean times lost with competing risks data

In the context of competing risks data, the subdistribution hazard ratio has limited clinical interpretability to measure treatment effects. An alternative is the difference in restricted mean times lost (RMTL), which gives the mean time lost to a specific cause of failure between treatment groups. In non-randomized studies, the average causal effect is conventionally used for decision-making about treatment and public health policies. We show how the difference in RMTL can be estimated by contrasting the integrated cumulative incidence functions from a Fine-Gray model. We also show how the difference in RMTL can be estimated by using inverse probability of treatment weighting and contrasts between weighted non-parametric estimators of the area below the cumulative incidence. We use pseudo-observation approaches to estimate both component models and we integrate them into a doubly-robust estimator. We demonstrate that this estimator is consistent when either component is correctly specified. We conduct simulation studies to assess its finite-sample performance and demonstrate its inherited consistency property from its component models. We also examine the performance of this estimator under varying degrees of covariate overlap and under a model misspecification of nonlinearity. We apply the proposed method to assess biomarker-treatment interaction in subpopulations of the POPLAR and OAK randomized controlled trials of second-line therapy for advanced 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.

Stratified Restricted Mean Survival Time Model for Marginal Causal Effect in Observational Survival Data

Time to event outcomes is commonly encountered in epidemiologic research. Multiple papers have discussed the inadequacy of using the hazard ratio as a causal effect measure due to its noncollapsibility and the time-varying nature. In this paper, we further clarified that the hazard ratio might be used as a conditional causal effect measure, but it is generally not a valid marginal effect measure, even under randomized design. We proposed to use the restricted mean survival time (RMST) difference as a causal effect measure, since it essentially measures the mean difference over a specified time horizon and has a simple interpretation as the area under survival curves. For observational studies, propensity score adjustment can be implemented with RMST estimation to remove observed confounding bias. We proposed a propensity score stratified RMST estimation strategy, which performs well in our simulation evaluation and is relatively easy to implement for epidemiologists in practice. Our stratified RMST estimation includes two different versions of implementation, depending on whether researchers want to involve regression modeling adjustment, which provides a powerful tool to examine the marginal causal effect with observational survival data.

Improving precision and power in randomized trials for COVID-19 treatments using covariate adjustment, for binary, ordinal, and time-to-event outcomes

Time is of the essence in evaluating potential drugs and biologics for the treatment and prevention of COVID-19. There are currently 876 randomized clinical trials (phase 2 and 3) of treatments for COVID-19 registered on clinicaltrials.gov. Covariate adjustment is a statistical analysis method with potential to improve precision and reduce the required sample size for a substantial number of these trials. Though covariate adjustment is recommended by the U.S. Food and Drug Administration and the European Medicines Agency, it is underutilized, especially for the types of outcomes (binary, ordinal, and time-to-event) that are common in COVID-19 trials. To demonstrate the potential value added by covariate adjustment in this context, we simulated two-arm, randomized trials comparing a hypothetical COVID-19 treatment versus standard of care, where the primary outcome is binary, ordinal, or time-to-event. Our simulated distributions are derived from two sources: longitudinal data on over 500 patients hospitalized at Weill Cornell Medicine New York Presbyterian Hospital and a Centers for Disease Control and Prevention preliminary description of 2449 cases. In simulated trials with sample sizes ranging from 100 to 1000 participants, we found substantial precision gains from using covariate adjustment-equivalent to 4-18% reductions in the required sample size to achieve a desired power. This was the case for a variety of estimands (targets of inference). From these simulations, we conclude that covariate adjustment is a low-risk, high-reward approach to streamlining COVID-19 treatment trials. We provide an R package and practical recommendations for implementation.

Life-years lost due to cancer among solid organ transplant recipients in the United States, 1987 to 2014

BACKGROUND

Solid organ transplant recipients have an elevated risk of cancer. Quantifying the life-years lost (LYL) due to cancer provides a complementary view of the burden of cancer distinct from other metrics and may identify subgroups of transplant recipients who are most affected.

METHODS

Linked transplant and cancer registry data were used to identify incident cancers and deaths among solid organ transplant recipients in the United States (1987-2014). Data on LYL due to cancer within 10 years posttransplant were derived using mean survival estimates from Cox models.

RESULTS

Among 221,962 transplant recipients, 13,074 (5.9%) developed cancer within 10 years of transplantation. During this period, the mean LYL due to cancer were 0.16 years per transplant recipient and 2.7 years per cancer case. Cancer was responsible for a loss of 1.9% of the total life-years expected in the absence of cancer in this population. Lung recipients had the highest proportion of total LYL due to cancer (0.45%) followed by heart recipients (0.29%). LYL due to cancer increased with age, from 0.5% among those aged birth to 34 years at transplant to 3.2% among those aged 50 years and older. Among recipients overall, lung cancer was the largest contributor, accounting for 24% of all LYL due to cancer, and non-Hodgkin lymphoma had the next highest contribution (15%).

CONCLUSIONS

Transplant recipients have a shortened lifespan after developing cancer. Lung cancer and non-Hodgkin lymphoma contribute strongly to LYL due to cancer within the first 10 years after transplant, highlighting opportunities to reduce cancer mortality through prevention and screening.

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.

SACRED: Effect of simvastatin on hepatic decompensation and death in subjects with high-risk compensated cirrhosis: Statins and Cirrhosis: Reducing Events of Decompensation

BACKGROUND/AIMS

The development of decompensation in cirrhosis demarcates a marked change in the natural history of chronic liver disease. HMG-CoA reductase inhibitors (statins) exert pleiotropic effects that reduce inflammation and fibrosis as well as improve vascular reactivity. Retrospective studies uniformly have associated statin utilization with improved outcomes for patients with cirrhosis. Prospective human studies have shown that statins reduce portal hypertension and reduce death in patients with decompensated cirrhosis after variceal hemorrhage when added to standard therapy with an acceptable safety profile. This proposal aims to extend these findings to demonstrate that simvastatin reduces incident hepatic decompensation events among cirrhotic patients at high risk for hepatic decompensation.

METHODS

We will perform the SACRED Trial (NCT03654053), a phase III, prospective, multi-center, double-blind, randomized clinical trial at 11 VA Medical Centers. Patients with compensated cirrhosis with clinically significant portal hypertension will be stratified based upon the concomitant use of nonselective beta-blockers and randomized to simvastatin 40 mg/day versus placebo for up to 24 months. Patients will be observed for the development of hepatic decompensation (variceal hemorrhage, ascites, encephalopathy), hepatocellular carcinoma, liver-related death, death from any cause, and/or complications of statin therapy. Ancillary studies will evaluate patient-reported outcomes and pharmacogenetic corollaries of safety and/or efficacy.

CONCLUSION

Statins have a long track-record of safety and tolerability. This class of medications is generic and inexpensive, and thus, if the hypothesis is proven, there will be few barriers to widespread acceptance of the role of statins to prevent decompensation in patients with compensated cirrhosis. ClinicalTrials.gov Identifier: NCT03654053.

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.

Analysis of time-to-event for observational studies: Guidance to the use of intensity models

This paper provides guidance for researchers with some mathematical background on the conduct of time-to-event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model. We provide check lists that may be useful both when fitting the model and assessing its goodness of fit and when interpreting the results. Special attention is paid to how to avoid problems with immortal time bias by introducing time-dependent covariates. We discuss prediction based on hazard models and difficulties when attempting to draw proper causal conclusions from such models. Finally, we present a series of examples where the methods and check lists are exemplified. Computational details and implementation using the freely available R software are documented in Supplementary Material. The paper was prepared as part of the STRATOS initiative.

Estimation of Heterogeneous Restricted Mean Survival Time Using Random Forest

Estimation and prediction of heterogeneous restricted mean survival time (hRMST) is of great clinical importance, which can provide an easily interpretable and clinically meaningful summary of the survival function in the presence of censoring and individual covariates. The existing methods for the modeling of hRMST rely on proportional hazards or other parametric assumptions on the survival distribution. In this paper, we propose a random forest based estimation of hRMST for right-censored survival data with covariates and prove a central limit theorem for the resulting estimator. In addition, we present a computationally efficient construction for the confidence interval of hRMST. Our simulations show that the resulting confidence intervals have the correct coverage probability of the hRMST, and the random forest based estimate of hRMST has smaller prediction errors than the parametric models when the models are mis-specified. We apply the method to the ovarian cancer data set from The Cancer Genome Atlas (TCGA) project to predict hRMST and show an improved prediction performance over the existing methods. A software implementation, srf using R and C++, is available at https://github.com/lmy1019/SRF.

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.

Improving Precision and Power in Randomized Trials for COVID-19 Treatments Using Covariate Adjustment, for Binary, Ordinal, and Time-to-Event Outcomes

Time is of the essence in evaluating potential drugs and biologics for the treatment and prevention of COVID-19. There are currently over 400 clinical trials (phase 2 and 3) of treatments for COVID-19 registered on clinicaltrials.gov. Covariate adjustment is a statistical analysis method with potential to improve precision and reduce the required sample size for a substantial number of these trials. Though covariate adjustment is recommended by the U.S. Food and Drug Administration and the European Medicines Agency, it is underutilized, especially for the types of outcomes (binary, ordinal and time-to-event) that are common in COVID-19 trials. To demonstrate the potential value added by covariate adjustment in this context, we simulated two-arm, randomized trials comparing a hypothetical COVID-19 treatment versus standard of care, where the primary outcome is binary, ordinal, or time-to-event. Our simulated distributions are derived from two sources: longitudinal data on over 500 patients hospitalized at Weill Cornell Medicine New York Presbyterian Hospital, and a Centers for Disease Control and Prevention (CDC) preliminary description of 2449 cases. We found substantial precision gains from using covariate adjustment--equivalent to 9-21% reductions in the required sample size to achieve a desired power--for a variety of estimands (targets of inference) when the trial sample size was at least 200. We provide an R package and practical recommendations for implementing covariate adjustment. The estimators that we consider are robust to model misspecification.

Evaluating biomarkers for treatment selection from reproducibility studies

We consider evaluating new or more accurately measured predictive biomarkers for treatment selection based on a previous clinical trial involving standard biomarkers. Instead of rerunning the clinical trial with the new biomarkers, we propose a more efficient approach which requires only either conducting a reproducibility study in which the new biomarkers and standard biomarkers are both measured on a set of patient samples, or adopting replicated measures of the error-contaminated standard biomarkers in the original study. This approach is easier to conduct and much less expensive than studies that require new samples from patients randomized to the intervention. In addition, it makes it possible to perform the estimation of the clinical performance quickly, since there will be no requirement to wait for events to occur as would be the case with prospective validation. The treatment selection is assessed via a working model, but the proposed estimator of the mean restricted lifetime is valid even if the working model is misspecified. The proposed approach is assessed through simulation studies and applied to a cancer study.

Direct adjusted survival and cumulative incidence curves for observational studies

SERIES EDITORS' NOTE

Large randomized clinical trials testing the impact of subject-, disease- and transplant-related co-variates on outcomes amongst recipients of haematopoietic cell transplants are uncommon. For example, who is the best donor, which is the best pretransplant conditioning regimen or the best regimen to prevent or treat acute and/or chronic graft-versus-host disease. To answer these questions we often rely on analyses of data from large observational datasets such as those of the Center for International Blood and Marrow Transplant Research (CIBMTR) and the European Society for Blood and Marrow Transplantation (EBMT). Such analyses have proved extremely important in advancing the field. However, in contrast to randomized trials, we cannot be certain potentially important prognostic or predictive co-variates are balanced between cohorts selected for comparison from an observational dataset, a limitation which can lead to incorrect conclusions. In the typescript which follows the authours describe a method to adjust for known imbalances in co-variates and get a closer approximation of the truth. They give two examples, the impact of a new pretransplant conditioning regimen on disease-free survival (DFS) in subjects with Ewing sarcoma and the impact of donor-type on treatment-related mortality (TRM) and leukaemia relapse in subjects with acute leukaemia. Direct adjusted survival and cumulative incidence function (CIF) analyses are an important step forward. These analyses can be done using available statistical packages and we encourage readers to use them rather than reporting unadjusted analyses. Finally, we must emphasize direct adjustment can only be done for know prognostic or predictive co-variates, not unknown co-variates. Unknown co-variates will be balanced in randomized trials which is why we do them. So direct adjustment is an important step forward but not a perfect substitute for randomized trials. But any step forward is important. To quote Laozi: (A journey of a thousand miles begins with a single step).

Propensity score matching for treatment delay effects with observational survival data

In observational studies with a survival outcome, treatment initiation may be time dependent, which is likely to be affected by both time-invariant and time-varying covariates. In situations where the treatment is necessary for the study population, all or most subjects may be exposed to the treatment sooner or later. In this scenario, the causal effect of interest is the delay in treatment reception. A simple comparison of those receiving treatment early vs. those receiving treatment late might not be appropriate, as the timing of the treatment reception is not randomized. Extending Lu's matching design with time-varying covariates, we propose a propensity score matching strategy to estimate the treatment delay effect. The goal is to balance the covariate distribution between on-time treatment and delayed treatment groups at each time point using risk set matching. Our simulation study shows that, in the presence of treatment delay effects, the matching-based analyses clearly outperform the conventional regression analysis using the naive Cox proportional hazards model. We apply this method to study the treatment delay effect of 17 alpha-hydroxyprogesterone caproate (17P) for patients with recurrent preterm birth.

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.

Computationally efficient inference for center effects based on restricted mean survival time

Restricted mean survival time (RMST) has gained increased attention in biostatistical and clinical studies. Directly modeling RMST (as opposed to modeling then transforming the hazard function) is appealing computationally and in terms of interpreting covariate effects. We propose computationally convenient methods for evaluating center effects based on RMST. A multiplicative model for the RMST is assumed. Estimation proceeds through an algorithm analogous to stratification, which permits the evaluation of thousands of centers. We derive the asymptotic properties of the proposed estimators and evaluate finite sample performance through simulation. We demonstrate that considerable decreases in computational burden are achievable through the proposed methods, in terms of both storage requirements and run time. The methods are applied to evaluate more than 5000 US dialysis facilities using data from a national end-stage renal disease registry.

Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards

We present a new estimator of the restricted mean survival time in randomized trials where there is right censoring that may depend on treatment and baseline variables. The proposed estimator leverages prognostic baseline variables to obtain equal or better asymptotic precision compared to traditional estimators. Under regularity conditions and random censoring within strata of treatment and baseline variables, the proposed estimator has the following features: (i) it is interpretable under violations of the proportional hazards assumption; (ii) it is consistent and at least as precise as the Kaplan-Meier and inverse probability weighted estimators, under identifiability conditions; (iii) it remains consistent under violations of independent censoring (unlike the Kaplan-Meier estimator) when either the censoring or survival distributions, conditional on covariates, are estimated consistently; and (iv) it achieves the nonparametric efficiency bound when both of these distributions are consistently estimated. We illustrate the performance of our method using simulations based on resampling data from a completed, phase 3 randomized clinical trial of a new surgical treatment for stroke; the proposed estimator achieves a 12% gain in relative efficiency compared to the Kaplan-Meier estimator. The proposed estimator has potential advantages over existing approaches for randomized trials with time-to-event outcomes, since existing methods either rely on model assumptions that are untenable in many applications, or lack some of the efficiency and consistency properties (i)-(iv). We focus on estimation of the restricted mean survival time, but our methods may be adapted to estimate any treatment effect measure defined as a smooth contrast between the survival curves for each study arm. We provide R code to implement the estimator.

Evaluating center-specific long-term outcomes through differences in mean survival time: Analysis of national kidney transplant data

Center-specific survival outcomes of kidney transplant recipients are an important quality measure, with several challenges. Existing methods based on restricted mean lifetime tend to focus on short- and medium-term clinical outcomes and may fail to capture long-term effects associated with quality of follow-up care. In this report, we propose methods that combine a lognormal frailty model and piecewise exponential baseline rates to compare the mean survival time across centers. The proposed methods allow for the consistent estimation of mean survival time as opposed to restricted mean lifetime and, within this context, permits more accurate profiling of long-term center-specific outcomes. Asymptotic properties of the proposed estimators are derived, and finite-sample properties are examined through simulation. The proposed methods are then applied to national kidney transplant data. The novelty of the proposed techniques arises from several angles. We utilize mean survival, in contrast to the most previous works that considered the restricted mean. Few previous studies have used the integrated survival function as a basis for center effects. Few provider profiling methods use a random effects model to estimate fixed center effects.