RKHS-based covariate balancing for survival causal effect estimation

Survival causal effect estimation based on right-censored data is of key interest in both survival analysis and causal inference. Propensity score weighting is one of the most popular methods in the literature. However, since it involves the inverse of propensity score estimates, its practical performance may be very unstable, especially when the covariate overlap is limited between treatment and control groups. To address this problem, a covariate balancing method is developed in this paper to estimate the counterfactual survival function. The proposed method is nonparametric and balances covariates in a reproducing kernel Hilbert space (RKHS) via weights that are counterparts of inverse propensity scores. The uniform rate of convergence for the proposed estimator is shown to be the same as that for the classical Kaplan-Meier estimator. The appealing practical performance of the proposed method is demonstrated by a simulation study as well as two real data applications to study the causal effect of smoking on survival time of stroke patients and that of endotoxin on survival time for female patients with lung cancer respectively.

Analysis of survival data with nonproportional hazards: A comparison of propensity-score-weighted methods

One of the most common ways researchers compare cancer survival outcomes across treatments from observational data is using Cox regression. This model depends on its underlying assumption of proportional hazards, but in some real-world cases, such as when comparing different classes of cancer therapies, substantial violations may occur. In this situation, researchers have several alternative methods to choose from, including Cox models with time-varying hazard ratios; parametric accelerated failure time models; Kaplan-Meier curves; and pseudo-observations. It is unclear which of these models are likely to perform best in practice. To fill this gap in the literature, we perform a neutral comparison study of candidate approaches. We examine clinically meaningful outcome measures that can be computed and directly compared across each method, namely, survival probability at time T, median survival, and restricted mean survival. To adjust for differences between treatment groups, we use inverse probability of treatment weighting based on the propensity score. We conduct simulation studies under a range of scenarios, and determine the biases, coverages, and standard errors of the average treatment effects for each method. We then demonstrate the use of these approaches using two published observational studies of survival after cancer treatment. The first examines chemotherapy in sarcoma, which has a late treatment effect (i.e., similar survival initially, but after 2 years the chemotherapy group shows a benefit). The other study is a comparison of surgical techniques for kidney cancer, where survival differences are attenuated over time.

Performance of modeling and balancing approach methods when using weights to estimate treatment effects in observational time-to-event settings

In observational studies weighting techniques are often used to overcome bias due to confounding. Modeling approaches, such as inverse propensity score weighting, are popular, but often rely on the correct specification of a parametric model wherein neither balance nor stability are targeted. More recently, balancing approach methods that directly target covariate imbalances have been proposed, and these allow the researcher to explicitly set the desired balance constraints. In this study, we evaluate the finite sample properties of different modeling and balancing approach methods, when estimating the marginal hazard ratio, through Monte Carlo simulations. The use of the different methods is also illustrated by analyzing data from the Swedish stroke register to estimate the effect of prescribing oral anticoagulants on time to recurrent stroke or death in stroke patients with atrial fibrillation. In simulated scenarios with good overlap and low or no model misspecification the balancing approach methods performed similarly to the modeling approach methods. In scenarios with bad overlap and model misspecification, the modeling approach method incorporating variable selection performed better than the other methods. The results indicate that it is valuable to use methods that target covariate balance when estimating marginal hazard ratios, but this does not in itself guarantee good performance in situations with, e.g., poor overlap, high censoring, or misspecified models/balance constraints.

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.

causalCmprsk: An R package for nonparametric and Cox-based estimation of average treatment effects in competing risks data

BACKGROUND AND OBJECTIVE

Competing risks data arise in both observational and experimental clinical studies with time-to-event outcomes, when each patient might follow one of the multiple mutually exclusive competing paths. Ignoring competing risks in the analysis can result in biased conclusions. In addition, possible confounding bias of the treatment-outcome relationship has to be addressed, when estimating treatment effects from observational data. In order to provide tools for estimation of average treatment effects on time-to-event outcomes in the presence of competing risks, we developed the R package causalCmprsk. We illustrate the package functionality in the estimation of effects of a right heart catheterization procedure on discharge and in-hospital death from observational data.

METHODS

The causalCmprsk package implements an inverse probability weighting estimation approach, aiming to emulate baseline randomization and alleviate possible treatment selection bias. The package allows for different types of weights, representing different target populations. causalCmprsk builds on existing methods from survival analysis and adapts them to the causal analysis in non-parametric and semi-parametric frameworks.

RESULTS

The causalCmprsk package has two main functions: fit.cox assumes a semiparametric structural Cox proportional hazards model for the counterfactual cause-specific hazards, while fit.nonpar does not impose any structural assumptions. In both frameworks, causalCmprsk implements estimators of (i) absolute risks for each treatment arm, e.g., cumulative hazards or cumulative incidence functions, and (ii) relative treatment effects, e.g., hazard ratios, or restricted mean time differences. The latter treatment effect measure translates the treatment effect from probability into more intuitive time domain and allows the user to quantify, for example, by how many days or months the treatment accelerates the recovery or postpones illness or death.

CONCLUSIONS

The causalCmprsk package provides a convenient and useful tool for causal analysis of competing risks data. It allows the user to distinguish between different causes of the end of follow-up and provides several time-varying measures of treatment effects. The package is accompanied by a vignette that contains more details, examples and code, making the package accessible even for non-expert users.

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

BACKGROUND

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

METHOD

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

RESULTS

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

CONCLUSIONS

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

Propensity score weighting methods for causal subgroup analysis with time-to-event outcomes

Evaluating causal effects of an intervention in pre-specified subgroups is a standard goal in comparative effectiveness research. Despite recent advancements in causal subgroup analysis, research on time-to-event outcomes has been lacking. This article investigates the propensity score weighting method for causal subgroup survival analysis. We introduce two causal estimands, the subgroup marginal hazard ratio and subgroup restricted average causal effect, and provide corresponding propensity score weighting estimators. We analytically established that the bias of subgroup-restricted average causal effect is determined by subgroup covariate balance. Using extensive simulations, we compare the performance of various combinations of propensity score models (logistic regression, random forests, least absolute shrinkage and selection operator, and generalized boosted models) and weighting schemes (inverse probability weighting, and overlap weighting) for estimating the causal estimands. We find that the logistic model with subgroup-covariate interactions selected by least absolute shrinkage and selection operator consistently outperforms other propensity score models. Also, overlap weighting generally outperforms inverse probability weighting in terms of balance, bias and variance, and the advantage is particularly pronounced in small subgroups and/or in the presence of poor overlap. We applied the methods to the observational Comparing Options for Management: PAtient-centered REsults for Uterine Fibroids study to evaluate the causal effects of myomectomy versus hysterectomy on the time to disease recurrence in a number of pre-specified subgroups of patients with uterine fibroids.

Confounding adjustment in the analysis of augmented randomized controlled trial with hybrid control arm

The augmented randomized controlled trial (RCT) with hybrid control arm includes a randomized treatment group (RT), a smaller randomized control group (RC), and a large synthetic control (SC) group from real-world data. This kind of trial is useful when there is logistics and ethics hurdle to conduct a fully powered RCT with equal allocation, or when it is necessary to increase the power of the RCT by incorporating real-world data. A difficulty in the analysis of augmented RCT is that the SC and RC may be systematically different in the distribution of observed and unmeasured confounding factors, causing bias when the two control groups are analyzed together as hybrid controls. We propose to use propensity score (PS) analysis to balance the observed confounders between SC and RC. The possible bias caused by unmeasured confounders can be estimated and tested by analyzing propensity score adjusted outcomes from SC and RC. We also propose a partial bias correction (PBC) procedure to reduce bias from unmeasured confounding. Extensive simulation studies show that the proposed PS + PBC procedures can improve the efficiency and statistical power by effectively incorporating the SC into the RCT data analysis, while still control the estimation bias and Type I error inflation that might arise from unmeasured confounding. We illustrate the proposed statistical procedures with data from an augmented RCT in oncology.

Robust weights that optimally balance confounders for estimating marginal hazard ratios

Covariate balance is crucial in obtaining unbiased estimates of treatment effects in observational studies. Methods that target covariate balance have been successfully proposed and largely applied to estimate treatment effects on continuous outcomes. However, in many medical and epidemiological applications, the interest lies in estimating treatment effects on time-to-event outcomes. With this type of data, one of the most common estimands of interest is the marginal hazard ratio of the Cox proportional hazards model. In this article, we start by presenting robust orthogonality weights, a set of weights obtained by solving a quadratic constrained optimization problem that maximizes precision while constraining covariate balance defined as the correlation between confounders and treatment. By doing so, robust orthogonality weights optimally deal with both binary and continuous treatments. We then evaluate the performance of the proposed weights in estimating marginal hazard ratios of binary and continuous treatments with time-to-event outcomes in a simulation study. We finally apply robust orthogonality weights in the evaluation of the effect of hormone therapy on time to coronary heart disease and on the effect of red meat consumption on time to colon cancer among 24,069 postmenopausal women enrolled in the Women's Health Initiative observational study.

Causal inference in medical records and complementary systems pharmacology for metformin drug repurposing towards dementia

Metformin, a diabetes drug with anti-aging cellular responses, has complex actions that may alter dementia onset. Mixed results are emerging from prior observational studies. To address this complexity, we deploy a causal inference approach accounting for the competing risk of death in emulated clinical trials using two distinct electronic health record systems. In intention-to-treat analyses, metformin use associates with lower hazard of all-cause mortality and lower cause-specific hazard of dementia onset, after accounting for prolonged survival, relative to sulfonylureas. In parallel systems pharmacology studies, the expression of two AD-related proteins, APOE and SPP1, was suppressed by pharmacologic concentrations of metformin in differentiated human neural cells, relative to a sulfonylurea. Together, our findings suggest that metformin might reduce the risk of dementia in diabetes patients through mechanisms beyond glycemic control, and that SPP1 is a candidate biomarker for metformin's action in the brain.

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.

Bootstrap vs asymptotic variance estimation when using propensity score weighting with continuous and binary outcomes

We used Monte Carlo simulations to compare the performance of asymptotic variance estimators to that of the bootstrap when estimating standard errors of differences in means, risk differences, and relative risks using propensity score weighting. We considered four different sets of weights: conventional inverse probability of treatment weights with the average treatment effect (ATE) as the target estimand, weights for estimating the average treatment effect in the treated (ATT), matching weights, and overlap weights. We considered sample sizes ranging from 250 to 10 000 and allowed the prevalence of treatment to range from 0.1 to 0.9. We found that, when using ATE weights and sample sizes were ≤ 1000, then the use of the bootstrap resulted in estimates of SE that were more accurate than the asymptotic estimates. A similar finding was observed when using ATT weights and sample sizes were ≤ 1000 and the prevalence of treatment was moderate to high. When using matching weights and overlap weights, both the asymptotic estimator and the bootstrap resulted in accurate estimates of SE across all sample sizes and prevalences of treatment. Even when using the bootstrap with ATE weights, empirical coverage rates of confidence intervals were suboptimal when sample sizes were low to moderate and the prevalence of treatment was either very low or very high. A similar finding was observed when using the bootstrap with ATT weights when sample sizes were low to moderate and the prevalence of treatment was very high.

Statistical methods of indirect comparison with real-world data for survival endpoint under non-proportional hazards

In clinical studies that utilize real-world data, time-to-event outcomes are often germane to scientific questions of interest. Two main obstacles are the presence of non-proportional hazards and confounding bias. Existing methods that could adjust for NPH or confounding bias, but no previous work delineated the complexity of simultaneous adjustments for both. In this paper, a propensity score stratified MaxCombo and weighted Cox model is proposed. This model can adjust for confounding bias and NPH and can be pre-specified when NPH pattern is unknown in advance. The method has robust performance as demonstrated in simulation studies and in a case study.

Addressing Extreme Propensity Scores in Estimating Counterfactual Survival Functions via the Overlap Weights

The inverse probability of treatment weighting (IPTW) approach is popular for evaluating causal effects in observational studies, but extreme propensity scores could bias the estimator and induce excessive variance. Recently, the overlap weighting approach has been proposed to alleviate this problem, which smoothly down-weights the subjects with extreme propensity scores. Although advantages of overlap weighting have been extensively demonstrated in literature with continuous and binary outcomes, research on its performance with time-to-event or survival outcomes is limited. In this article, we propose estimators that combine propensity score weighting and inverse probability of censoring weighting to estimate the counterfactual survival functions. These estimators are applicable to the general class of balancing weights, which includes IPTW, trimming, and overlap weighting as special cases. We conduct simulations to examine the empirical performance of these estimators with different propensity score weighting schemes in terms of bias, variance, and 95% confidence interval coverage, under various degrees of covariate overlap between treatment groups and censoring rates. We demonstrate that overlap weighting consistently outperforms IPTW and associated trimming methods in bias, variance, and coverage for time-to-event outcomes, and the advantages increase as the degree of covariate overlap between the treatment groups decreases.

Uncovering interpretable potential confounders in electronic medical records

Randomized clinical trials (RCT) are the gold standard for informing treatment decisions. Observational studies are often plagued by selection bias, and expert-selected covariates may insufficiently adjust for confounding. We explore how unstructured clinical text can be used to reduce selection bias and improve medical practice. We develop a framework based on natural language processing to uncover interpretable potential confounders from text. We validate our method by comparing the estimated hazard ratio (HR) with and without the confounders against established RCTs. We apply our method to four cohorts built from localized prostate and lung cancer datasets from the Stanford Cancer Institute and show that our method shifts the HR estimate towards the RCT results. The uncovered terms can also be interpreted by oncologists for clinical insights. We present this proof-of-concept study to enable more credible causal inference using observational data, uncover meaningful insights from clinical text, and inform high-stakes medical decisions.

Randomized clinical trials are often plagued by selection bias, and expert-selected covariates may insufficiently adjust for confounding factors. Here, the authors develop a framework based on natural language processing to uncover interpretable potential confounders from text.

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.

Estimating the marginal hazard ratio by simultaneously using a set of propensity score models: A multiply robust approach

The inverse probability weighted Cox model is frequently used to estimate the marginal hazard ratio. Its validity requires a crucial condition that the propensity score model be correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in the empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux-en-Y gastric bypass using data from a large medical claims and billing database. We further extend the development to multisite studies to enable each site to postulate multiple site-specific propensity score models.

Flexible regression approach to propensity score analysis and its relationship with matching and weighting

In propensity score analysis, the frequently used regression adjustment involves regressing the outcome on the estimated propensity score and treatment indicator. This approach can be highly efficient when model assumptions are valid, but can lead to biased results when the assumptions are violated. We extend the simple regression adjustment to a varying coefficient regression model that allows for nonlinear association between outcome and propensity score. We discuss its connection with some propensity score matching and weighting methods, and show that the proposed analytical framework can shed light on the intrinsic connection among some mainstream propensity score approaches (stratification, regression, kernel matching, and inverse probability weighting) and handle commonly used causal estimands. We derive analytic point and variance estimators that properly take into account the sampling variability in the estimated propensity score. Extensive simulations show that the proposed approach possesses desired finite sample properties and demonstrates competitive performance in comparison with other methods estimating the same causal estimand. The proposed methodology is illustrated with a study on right heart catheterization.

Statistical Issues and Recommendations for Clinical Trials Conducted During the COVID-19 Pandemic

Abstract-The COVID-19 pandemic has had and continues to have major impacts on planned and ongoing clinical trials. Its effects on trial data create multiple potential statistical issues. The scale of impact is unprecedented, but when viewed individually, many of the issues are well defined and feasible to address. A number of strategies and recommendations are put forward to assess and address issues related to estimands, missing data, validity and modifications of statistical analysis methods, need for additional analyses, ability to meet objectives and overall trial interpretability.

On the use of flexible excess hazard regression models for describing long-term breast cancer survival: a case-study using population-based cancer registry data

BACKGROUND

Breast cancer prognosis has dramatically improved over 40 years. There is, however, no proof of population 'cure'. This research aimed to examine the pattern of long-term excess mortality due to breast cancer and evaluate its determinants in the context of cancer registry data.

METHODS

We used data from the Geneva Cancer Registry to identify women younger than 75 years diagnosed with invasive, localised and operated breast cancer between 1995 and 2002. Flexible modelling of excess mortality hazard, including time-dependent (TD) regression parameters, was used to estimate mortality related to breast cancer. We derived a single "final" model using a backward selection procedure and evaluated its stability through sensitivity analyses using a bootstrap technique.

RESULTS

We analysed data from 1574 breast cancer women including 351 deaths (22.3%). The model building strategy retained age at diagnosis (TD), tumour size and grade (TD), chemotherapy and hormonal treatment (TD) as prognostic factors, while the sensitivity analysis on bootstrap samples identified nodes involvement and hormone receptors (TD) as additional long-term prognostic factors but did not identify chemotherapy and hormonal treatment as important prognostic factors.

CONCLUSIONS

Two main issues were observed when describing the determinants of long-term survival. First, the modelling strategy presented a lack of robustness, probably due to the limited number of events observed in our study. The second was the misspecification of the model, probably due to confounding by indication. Our results highlight the need for more detailed data and the use of causal inference methods.