Two-Step Estimation Procedure for Parametric Copula-Based Regression Models for Semi-Competing Risks Data

Non-terminal and terminal events in semi-competing risks data are typically associated and may be influenced by covariates. We employed regression modeling for semi-competing risks data under a copula-based framework to evaluate the effects of covariates on the two events and the association between them. Due to the complexity of the copula structure, we propose a new method that integrates a novel two-step algorithm with the Bound Optimization by Quadratic Approximation (BOBYQA) method. This approach effectively mitigates the influence of initial values and demonstrates greater robustness. The simulations validate the performance of the proposed method. We further applied our proposed method to the Amsterdam Cohort Study (ACS) real data, where some improvements could be found.

Inference for Cumulative Incidences and Treatment Effects in Randomized Controlled Trials With Time-to-Event Outcomes Under ICH E9 (R1)

In randomized controlled trials (RCTs) that focus on time-to-event outcomes, intercurrent events can arise in two ways: as semi-competing events, which modify the hazard of the primary outcome events, or as competing events, which make the definition of the primary outcome events unclear. Although five strategies have been proposed in the ICH E9 (R1) addendum to address intercurrent events in RCTs, these strategies are not easily applicable to time-to-event outcomes when aiming for causal interpretations. In this study, we show how to define, estimate, and make inferences concerning objectives that have causal interpretations within these contexts. Specifically, we derive the mathematical formulations of the causal estimands corresponding to the five strategies and clarify the data structure needed to identify these causal estimands. Furthermore, we introduce nonparametric methods for estimating and making inferences about these causal estimands, including the asymptotic variance of estimators and the construction of hypothesis tests. Finally, we illustrate our methods using data from the LEADER Trial, which aims to investigate the effect of liraglutide on cardiovascular outcomes.

Estimating the Effects of Hypothetical Ambient PM2.5 Interventions on the Risk of Dementia Using the Parametric g-Formula in the UK Biobank Cohort

BACKGROUND

Emerging evidence identifies ambient particulate matter (PM) with an aerodynamic diameter ≤ 2.5 μ m (PM 2.5 ) as a modifiable risk factor for dementia, but the potential health benefits gained by enacting regulations that reduce PM 2.5 remain unclear.

OBJECTIVES

Our aim was to estimate the total effects of hypothetical ambient PM 2.5 interventions starting in late life on the risk of dementia in a cohort using the parametric g-formula.

METHODS

We used data from 291,495 participants in the UK Biobank cohort who were free of dementia and ≥ 55 y of age at baseline (2010). We estimated the total effects of hypothetical ambient PM 2.5 interventions (achieving annual average standards of 12   μ g / m 3 , 10   μ g / m 3 , and 9   μ g / m 3 ) from 2010 to 2019 on the risk of dementia by calculating the difference between the estimated 10-y risk of dementia under a specified hypothetical intervention and the risk under no intervention using the parametric g-formula.

RESULTS

In comparison with no intervention, the estimated 10-y risk difference of dementia was - 0.54 per 1,000 population [95% confidence interval (CI): - 1.00 , - 0.10 ], - 1.36 per 1,000 population (95% CI: - 2.44 , - 0.25 ), - 1.92 per 1,000 population (95% CI: - 3.39 , - 0.33 ), with PM 2.5 interventions achieving annual average standards of 12   μ g / m 3 , 10   μ g / m 3 , and 9   μ g / m 3 , respectively.

DISCUSSION

The estimated 10-y risk of dementia decreased if the individual ambient PM 2.5 exposure was reduced due to more stringent PM 2.5 standards in late life in comparison with the natural course without intervention on ambient PM 2.5 exposure. Our findings, obtained using the parametric g-formula-a causal inference method that can directly evaluate the impact of hypothetical interventions-suggest that policies reducing ambient PM 2.5 pollution may lower the risk of dementia among UK Biobank participants who would experience more stringent ambient PM 2.5 standards in late life. https://doi.org/10.1289/EHP14723.

Causal mediation analysis for time-to-event mediator and outcome in the presence of left truncation

We propose a causal mediation approach to semi-competing risks under left truncation sampling by considering an intermediate event as a mediator and a terminal event as an outcome. We focus on the causal relationship from exposure to the terminal outcome in relation to the intermediate event. In particular, we study the direct effect, the effect of exposure on the terminal event that is not through the intermediate event, and the indirect effect-the effect of exposure on the terminal event that is mediated through the intermediate event. We propose nonparametric and semiparametric methods, both accounting for left truncation. The nonparametric estimator can be viewed as a model-free time-varying Nelson-Aalen estimator that is robust to model misspecification. The semiparametric estimator calculated with the Cox proportional hazards model enjoys flexibility in adjusting for potential confounders as covariates. The asymptotic properties for both estimators, including uniform consistency and weak convergence, were established using the martingale theorem and functional delta method. The finite sample performance of the proposed estimators was evaluated through extensive numerical studies that investigated the influences of left truncation, confounding, and sample size. The utility of the proposed methods was illustrated using a hepatitis study.

Subjective Cognitive Impairment (SCI) and Future Dementia Risk in the National Health and Aging Trends Study (NHATS) During 2012-2019

BackgroundSubjective cognitive impairment (SCI), assessed in national surveys, offers potential for dementia monitoring and early detection. However, its causal link to dementia risk remains unclear.ObjectiveTo evaluate whether SCI causally affects dementia risk in U.S. older adults (≥65 years), considering mortality as a competing risk.MethodsUsing data from 1622 dementia-free older adults in the National Health and Aging Trends Study (NHATS) during 2011-2019, we estimated total, direct, and separable effects of SCI on dementia and mortality risks.ResultsSCI was reported by 7.6% at baseline and associated with a twofold increased dementia risk over 8 years (RR: 1.95, 95% CI: 1.07-3.07) and lower mortality risk (RR: 0.31, 95% CI: 0.10-0.67). Direct effect analysis indicated a potential direct causal link between SCI and dementia.ConclusionsSCI predicts dementia onset and inversely affects mortality, highlighting the importance of early detection and precise analytic approaches.

Non-Parametric Estimation for Semi-Competing Risks Data With Event Misascertainment

The semi-competing risks data model is a special type of disease-state model that focuses on studying the association between an intermediate event and a terminal event and proves to be a useful tool in modeling disease progression. The study of the semi-competing risk data model not only allows us to evaluate whether a disease episode is related to death but also provides a toolkit to predict death, given that the episode occurred at a certain time. However, the computation of the semi-competing risk models is a numerically challenging task. The Gamma-Frailty conditional Markov model has been shown to be an efficient computation model for studying semi-competing risks data. Building on recent advances in studying semi-competing risks data, this work proposes a non-parametric pseudo-likelihood method equipped with an EM-like algorithm to study semi-competing risks data with event misascertainment under the restricted Gamma-Frailty conditional Markov model. A thorough simulation study is conducted to demonstrate the inference validity of the proposed method and its numerical stability. The proposed method is applied to a large HIV cohort study, EA-IeDEA, that has a severe death under-reporting issue to assess the degree of adverse impact of the interruption of ART care on HIV mortality.

Nonparametric Path-Specific Effects on a Survival Outcome Through Multiple Time-to-Event Mediators

A causal mediation model with multiple time-to-event mediators is exemplified by the natural course of human disease marked by sequential milestones with a time-to-event nature. For example, from hepatitis B infection to death, patients may experience intermediate events such as liver cirrhosis and liver cancer. The sequential events of hepatitis, cirrhosis, cancer, and death are susceptible to right censoring; moreover, the latter events may preclude the former events. Casting the natural course of human diseases in the framework of causal mediation modeling, we establish a model with intermediate and terminal events as the mediators and outcomes, respectively. We define the interventional analog of path-specific effects (iPSEs) as the effect of an exposure on a terminal event mediated (or not mediated) by any combination of intermediate events without parametric models. The expression of a counting process-based counterfactual hazard is derived under the sequential ignorability assumption. We employ composite nonparametric likelihood estimation to obtain maximum likelihood estimators for the counterfactual hazard and iPSEs. Our proposed estimators achieve asymptotic unbiasedness, uniform consistency, and weak convergence. Applying the proposed method, we show that hepatitis B induced mortality is mostly mediated through liver cancer and/or cirrhosis whereas hepatitis C induced mortality may be through extrahepatic diseases.

Evaluating time-to-event surrogates for time-to-event true endpoints: an information-theoretic approach based on causal inference

Putative surrogate endpoints must undergo a rigorous statistical evaluation before they can be used in clinical trials. Numerous frameworks have been introduced for this purpose. In this study, we extend the scope of the information-theoretic causal-inference approach to encompass scenarios where both outcomes are time-to-event endpoints, using the flexibility provided by D-vine copulas. We evaluate the quality of the putative surrogate using the individual causal association (ICA)-a measure based on the mutual information between the individual causal treatment effects. However, in spite of its appealing mathematical properties, the ICA may be ill defined for composite endpoints. Therefore, we also propose an alternative rank-based metric for assessing the ICA. Due to the fundamental problem of causal inference, the joint distribution of all potential outcomes is only partially identifiable and, consequently, the ICA cannot be estimated without strong unverifiable assumptions. This is addressed by a formal sensitivity analysis that is summarized by the so-called intervals of ignorance and uncertainty. The frequentist properties of these intervals are discussed in detail. Finally, the proposed methods are illustrated with an analysis of pooled data from two advanced colorectal cancer trials. The newly developed techniques have been implemented in the R package Surrogate.

Two-stage pseudo maximum likelihood estimation of semiparametric copula-based regression models for semi-competing risks data

We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. With a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated using only the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated together via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness than the one-stage procedure developed in Chen YH (Lifetime Data Anal 18:36-57, 2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu H et al., (Commu Statistics-Theory Methods 51(22):7830-7845, 2021) . An R package PMLE4SCR is developed to implement our proposed method.

Live-Donor Kidney Transplant Outcome Prediction (L-TOP) using artificial intelligence

BACKGROUND

Outcome prediction for live-donor kidney transplantation improves clinical and patient decisions and donor selection. However, the currently used models are of limited discriminative or calibration power and there is a critical need to improve the selection process. We aimed to assess the value of various artificial intelligence (AI) algorithms to improve the risk stratification index.

METHODS

We evaluated pre-transplant variables among 66 914 live-donor kidney transplants (performed between 1 December 2007 and 1 June 2021) from the United Network of Organ Sharing database, randomized into training (80%) and test (20%) sets. The primary outcome measure was death-censored graft survival. We tested four machine learning models for discrimination [time-dependent concordance index (CTD) and area under the receiver operating characteristic curve (AUC)] and calibration [integrated Brier score (IBS)]. We used decision-curve analysis to assess the potential clinical utility.

RESULTS

Among the models, the deep Cox mixture model showed the best discriminative performance (AUC = 0.70, 0.68 and 0.68 at 5, 10 and 13 years post-transplant, respectively). CTD reached 0.70, 0.67 and 0.66 at 5, 10 and 13 years post-transplant. The IBS score was 0.09, indicating good calibration. In comparison, applying the Living Kidney Donor Profile Index (LKDPI) on the same cohort produced a CTD of 0.56 and an AUC of 0.55-0.58 only. Decision-curve analysis showed an additional net benefit compared with the LKDPI 'treat all' and 'treat none' approaches.

CONCLUSION

Our AI-based deep Cox mixture model, termed Live-Donor Kidney Transplant Outcome Prediction, outperforms existing prediction models, including the LKDPI, with the potential to improve decisions for optimum live-donor selection by ranking potential transplant pairs based on graft survival. This model could be adopted to improve the outcomes of paired exchange programs.

Joint modelling of survival and backwards recurrence outcomes: an analysis of factors associated with fertility treatment in the U.S

The motivation for this paper is to determine factors associated with time-to-fertility treatment (TTFT) among women currently attempting pregnancy in a cross-sectional sample. Challenges arise due to dependence between time-to-pregnancy (TTP) and TTFT. We propose appending a marginal accelerated failure time model to identify risk factors of TTFT with a model for TTP where fertility treatment is included as a time-varying treatment to account for their dependence. The latter requires extending backwards recurrence survival methods to incorporate time-varying covariates with time-varying coefficients. Since backwards recurrence survival methods are a function of mean survival, computational difficulties arise in formulating mean survival when fertility treatment is unobserved, i.e. when TTFT is censored. We address these challenges by developing computationally friendly forms for the double expectation of TTP and TTFT. The performance is validated via comprehensive simulation studies. We apply our approach to the National Survey of Family Growth and explore factors related to prolonged TTFT in the U.S.

Latest Developments in "Adaptive Enrichment" Clinical Trial Designs in Oncology

As cancer has become better understood on the molecular level with the evolution of gene sequencing techniques, considerations for individualized therapy using predictive biomarkers (those associated with a treatment's effect) have shifted to a new level. In the last decade or so, randomized "adaptive enrichment" clinical trials have become increasingly utilized to strike a balance between enrolling all patients with a given tumor type, versus enrolling only a subpopulation whose tumors are defined by a potential predictive biomarker related to the mechanism of action of the experimental therapy. In this review article, we review recent innovative design extensions and adaptations to adaptive enrichment designs proposed during the last few years in the clinical trial methodology literature, both from Bayesian and frequentist perspectives.

An augmented illness-death model for semi-competing risks with clinically immediate terminal events

Preeclampsia is a pregnancy-associated condition posing risks of both fetal and maternal mortality and morbidity that can only resolve following delivery and removal of the placenta. Because in its typical form preeclampsia can arise before delivery, but not after, these two events exemplify the time-to-event setting of "semi-competing risks" in which a non-terminal event of interest is subject to the occurrence of a terminal event of interest. The semi-competing risks framework presents a valuable opportunity to simultaneously address two clinically meaningful risk modeling tasks: (i) characterizing risk of developing preeclampsia, and (ii) characterizing time to delivery after onset of preeclampsia. However, some people with preeclampsia deliver immediately upon diagnosis, while others are admitted and monitored for an extended period before giving birth, resulting in two distinct trajectories following the non-terminal event, which we call "clinically immediate" and "non-immediate" terminal events. Though such phenomena arise in many clinical contexts, to-date there have not been methods developed to acknowledge the complex dependencies between such outcomes, nor leverage these phenomena to gain new insight into individualized risk. We address this gap by proposing a novel augmented frailty-based illness-death model with a binary submodel to distinguish risk of immediate terminal event following the non-terminal event. The model admits direct dependence of the terminal event on the non-terminal event through flexible regression specification, as well as indirect dependence via a shared frailty term linking each submodel. We develop an efficient Bayesian sampler for estimation and corresponding model fit metrics, and derive formulae for dynamic risk prediction. In an extended example using pregnancy outcome data from an electronic health record, we demonstrate the proposed model's direct applicability to address a broad range of clinical questions.

Deceased-Donor Kidney Transplant Outcome Prediction Using Artificial Intelligence to Aid Decision-Making in Kidney Allocation

In kidney transplantation, pairing recipients with the highest longevity with low-risk allografts to optimize graft-donor survival is a complex challenge. Current risk prediction models exhibit limited discriminative and calibration capabilities and have not been compared to modern decision-assisting tools. We aimed to develop a highly accurate risk-stratification index using artificial intelligence (AI) techniques. Using data from the UNOS database (156,749 deceased kidney transplants, 2007-2021), we randomly divided transplants into training (80%) and validation (20%) sets. The primary measure was death-censored graft survival. Four machine learning models were assessed for calibration (integrated Brier score [IBS]) and discrimination (time-dependent concordance [CTD] index), compared with existing models. We conducted decision curve analysis and external validation using UK Transplant data. The Deep Cox mixture model showed the best discriminative performance (area under the curve [AUC] = 0.66, 0.67, and 0.68 at 6, 9, and 12 years post-transplant), with CTD at 0.66. Calibration was adequate (IBS = 0.12), while the kidney donor profile index (KDPI) model had lower CTD (0.59) and AUC (0.60). AI-based D-TOP outperformed the KDPI in evaluating transplant pairs based on graft survival, potentially enhancing deceased donor selection. Advanced computing is poised to influence kidney allocation schemes.

Competing risks and multivariate outcomes in epidemiological and clinical trial research

Data analysis methods for the study of treatments or exposures in relation to a clinical outcome in the presence of competing risks have a long history, often with inference targets that are hypothetical, thereby requiring strong assumptions for identifiability with available data. Here data analysis methods are considered that are based on single and higher dimensional marginal hazard rates, quantities that are identifiable under standard independent censoring assumptions. These lead naturally to joint survival function estimators for outcomes of interest, including competing risk outcomes, and provide the basis for addressing a variety of data analysis questions. These methods will be illustrated using simulations and Women's Health Initiative cohort and clinical trial data sets, and additional research needs will be described.

Association between diet quality and ovarian cancer risk and survival

BACKGROUND

Research on diet quality and ovarian cancer is limited. We examined the association between diet quality and ovarian cancer risk and survival in a large prospective cohort.

METHODS

We used data from women in the prospective National Institutes of Health-AARP Diet and Health Study enrolled from 1995 to 1996 who were aged 50-71 years at baseline with follow-up through December 31, 2017. Participants completed a 124-item food frequency questionnaire at baseline, and diet quality was assessed via the Healthy Eating Index-2015, the alternate Mediterranean diet score, and the Dietary Approaches to Stop Hypertension score. Primary outcomes were first primary epithelial ovarian cancer diagnosis from cancer registry data and among those diagnosed with ovarian cancer all-cause mortality. We used a semi-Markov multistate model with Cox proportional hazards regression to account for semicompeting events.

RESULTS

Among 150 643 participants with a median follow-up time of 20.5 years, 1107 individuals were diagnosed with a first primary epithelial ovarian cancer. There was no evidence of an association between diet quality and ovarian cancer risk. Among those diagnosed with epithelial ovarian cancer, 893 deaths occurred with a median survival of 2.5 years. Better prediagnosis diet quality, according to the Healthy Eating Index-2015 (quintile 5 vs quintile 1: hazard ratio [HR] = 0.75, 95% confidence interval [CI] = 0.60 to 0.93) and alternate Mediterranean diet score (quintile 5 vs quintile 1: HR = 0.68, 95% CI = 0.53 to 0.87), was associated with lower all-cause mortality. There was no evidence of an association between Dietary Approaches to Stop Hypertension score and all-cause mortality.

CONCLUSIONS

Better prediagnosis diet quality was associated with lower all-cause mortality after ovarian cancer diagnosis but was not associated with ovarian cancer risk.

Enhancing long-term survival prediction with two short-term events: Landmarking with a flexible varying coefficient model

Patients with cardiovascular diseases who experience disease-related short-term events, such as hospitalizations, often exhibit diverse long-term survival outcomes compared to others. In this study, we aim to improve the prediction of long-term survival probability by incorporating two short-term events using a flexible varying coefficient landmark model. Our objective is to predict the long-term survival among patients who survived up to a pre-specified landmark time since the initial admission. Inverse probability weighting estimation equations are formed based on the information of the short-term outcomes before the landmark time. The kernel smoothing method with the use of cross-validation for bandwidth selection is employed to estimate the time-varying coefficients. The predictive performance of the proposed model is evaluated and compared using predictive measures: area under the receiver operating characteristic curve and Brier score. Simulation studies confirm that parameters under the landmark models can be estimated accurately and the predictive performance of the proposed method consistently outperforms existing methods that either do not incorporate or only partially incorporate information from two short-term events. We demonstrate the practical application of our model using a community-based cohort from the Atherosclerosis Risk in Communities (ARIC) study.

Bayesian semi-parametric inference for clustered recurrent events with zero inflation and a terminal event

Recurrent events are common in clinical studies and are often subject to terminal events. In pragmatic trials, participants are often nested in clinics and can be susceptible or structurally unsusceptible to the recurrent events. We develop a Bayesian shared random effects model to accommodate this complex data structure. To achieve robustness, we consider the Dirichlet processes to model the residual of the accelerated failure time model for the survival process as well as the cluster-specific shared frailty distribution, along with an efficient sampling algorithm for posterior inference. Our method is applied to a recent cluster randomized trial on fall injury prevention.

Bias reduction for semi-competing risks frailty model with rare events: application to a chronic kidney disease cohort study in South Korea

In a semi-competing risks model in which a terminal event censors a non-terminal event but not vice versa, the conventional method can predict clinical outcomes by maximizing likelihood estimation. However, this method can produce unreliable or biased estimators when the number of events in the datasets is small. Specifically, parameter estimates may converge to infinity, or their standard errors can be very large. Moreover, terminal and non-terminal event times may be correlated, which can account for the frailty term. Here, we adapt the penalized likelihood with Firth's correction method for gamma frailty models with semi-competing risks data to reduce the bias caused by rare events. The proposed method is evaluated in terms of relative bias, mean squared error, standard error, and standard deviation compared to the conventional methods through simulation studies. The results of the proposed method are stable and robust even when data contain only a few events with the misspecification of the baseline hazard function. We also illustrate a real example with a multi-centre, patient-based cohort study to identify risk factors for chronic kidney disease progression or adverse clinical outcomes. This study will provide a better understanding of semi-competing risk data in which the number of specific diseases or events of interest is rare.

Direct and indirect treatment effects in the presence of semicompeting risks

Semicompeting risks refer to the phenomenon that the terminal event (such as death) can censor the nonterminal event (such as disease progression) but not vice versa. The treatment effect on the terminal event can be delivered either directly following the treatment or indirectly through the nonterminal event. We consider 2 strategies to decompose the total effect into a direct effect and an indirect effect under the framework of mediation analysis in completely randomized experiments by adjusting the prevalence and hazard of nonterminal events, respectively. They require slightly different assumptions on cross-world quantities to achieve identifiability. We establish asymptotic properties for the estimated counterfactual cumulative incidences and decomposed treatment effects. We illustrate the subtle difference between these 2 decompositions through simulation studies and two real-data applications in the Supplementary Materials.

A review on statistical and machine learning competing risks methods

When modeling competing risks (CR) survival data, several techniques have been proposed in both the statistical and machine learning literature. State-of-the-art methods have extended classical approaches with more flexible assumptions that can improve predictive performance, allow high-dimensional data and missing values, among others. Despite this, modern approaches have not been widely employed in applied settings. This article aims to aid the uptake of such methods by providing a condensed compendium of CR survival methods with a unified notation and interpretation across approaches. We highlight available software and, when possible, demonstrate their usage via reproducible R vignettes. Moreover, we discuss two major concerns that can affect benchmark studies in this context: the choice of performance metrics and reproducibility.

Model-based hypothesis tests for the causal mediation of semi-competing risks

Analyzing the causal mediation of semi-competing risks has become important in medical research. Semi-competing risks refers to a scenario wherein an intermediate event may be censored by a primary event but not vice versa. Causal mediation analyses decompose the effect of an exposure on the primary outcome into an indirect (mediation) effect: an effect mediated through a mediator, and a direct effect: an effect not through the mediator. Here we proposed a model-based testing procedure to examine the indirect effect of the exposure on the primary event through the intermediate event. Under the counterfactual outcome framework, we defined a causal mediation effect using counting process. To assess statistical evidence for the mediation effect, we proposed two tests: an intersection-union test (IUT) and a weighted log-rank test (WLR). The test statistic was developed from a semi-parametric estimator of the mediation effect using a Cox proportional hazards model for the primary event and a series of logistic regression models for the intermediate event. We built a connection between the IUT and WLR. Asymptotic properties of the two tests were derived, and the IUT was determined to be a size [Formula: see text] test and statistically more powerful than the WLR. In numerical simulations, both the model-based IUT and WLR can properly adjust for confounding covariates, and the Type I error rates of the proposed methods are well protected, with the IUT being more powerful than the WLR. Our methods demonstrate the strongly significant effects of hepatitis B or C on the risk of liver cancer mediated through liver cirrhosis incidence in a prospective cohort study. The proposed method is also applicable to surrogate endpoint analyses in clinical trials.

Estimation of separable direct and indirect effects in a continuous-time illness-death model

In this article we study the effect of a baseline exposure on a terminal time-to-event outcome either directly or mediated by the illness state of a continuous-time illness-death process with baseline covariates. We propose a definition of the corresponding direct and indirect effects using the concept of separable (interventionist) effects (Robins and Richardson in Causality and psychopathology: finding the determinants of disorders and their cures, Oxford University Press, 2011; Robins et al. in arXiv:2008.06019 , 2021; Stensrud et al. in J Am Stat Assoc 117:175-183, 2022). Our proposal generalizes Martinussen and Stensrud (Biometrics 79:127-139, 2023) who consider similar causal estimands for disentangling the causal treatment effects on the event of interest and competing events in the standard continuous-time competing risk model. Unlike natural direct and indirect effects (Robins and Greenland in Epidemiology 3:143-155, 1992; Pearl in Proceedings of the seventeenth conference on uncertainty in artificial intelligence, Morgan Kaufmann, 2001) which are usually defined through manipulations of the mediator independently of the exposure (so-called cross-world interventions), separable direct and indirect effects are defined through interventions on different components of the exposure that exert their effects through distinct causal mechanisms. This approach allows us to define meaningful mediation targets even though the mediating event is truncated by the terminal event. We present the conditions for identifiability, which include some arguably restrictive structural assumptions on the treatment mechanism, and discuss when such assumptions are valid. The identifying functionals are used to construct plug-in estimators for the separable direct and indirect effects. We also present multiply robust and asymptotically efficient estimators based on the efficient influence functions. We verify the theoretical properties of the estimators in a simulation study, and we demonstrate the use of the estimators using data from a Danish registry study.

Unified semicompeting risks analysis of hepatitis natural history through mediation modeling

Natural history of hepatitis B or C is comprised of multiple milestones such as liver cirrhosis and liver cancer. To fully characterize its natural course, semicompeting risks represent a common problem where liver cirrhosis and liver cancer are both of interest, but only the former may be censored by the latter. Copula, frailty and multistate models serve as well-established analytics for semicompeting risks. Here, we cast the semicompeting risks in a mediation framework, with liver cirrhosis as a mediator and liver cancer as an outcome. We define the indirect and direct effects as the effects of an exposure on the liver cancer incidence mediated and not mediated through liver cirrhosis, respectively. With the estimands derived as conditional probabilities, we derive respective expressions under the copula, frailty, and multistate models. Next, we propose estimators based on nonparametric maximum likelihood or U-statistics and establish their asymptotic results. Numerical studies demonstrate that the efficiency of copula models leads to potential bias due to model misspecification. Moreover, the robustness of frailty models is accompanied by a loss in efficiency, and multistate models balance the efficiency and robustness. We demonstrate the utility of the proposed methods by a hepatitis study, showing that hepatitis B and C lead to a higher incidence of liver cancer by increasing liver cirrhosis incidence. Thus, mediation modeling provides a unified framework that accommodates various semicompeting risks models.

Bivariate copula regression models for semi-competing risks

Time-to-event semi-competing risk endpoints may be correlated when both events occur on the same individual. These events and the association between them may also be influenced by individual characteristics. In this article, we propose copula survival models to estimate hazard ratios of covariates on the non-terminal and terminal events, along with the effects of covariates on the association between the two events. We use the Normal, Clayton, Frank and Gumbel copulas to provide a variety of association structures between the non-terminal and terminal events. We apply the proposed methods to model semi-competing risks of graft failure and death for kidney transplant patients. We find that copula survival models perform better than the Cox proportional hazards model when estimating the non-terminal event hazard ratio of covariates. We also find that the inclusion of covariates in the association parameter of the copula models improves the estimation of the hazard ratios.

Survival prediction and prognostic factors in colorectal cancer after curative surgery: insights from cox regression and neural networks

Medical research frequently relies on Cox regression to analyze the survival distribution of cancer patients. Nonetheless, in specific scenarios, neural networks hold the potential to serve as a robust alternative. In this study, we aim to scrutinize the effectiveness of Cox regression and neural network models in assessing the survival outcomes of patients who have undergone treatment for colorectal cancer. We conducted a retrospective study on 284 colorectal cancer patients who underwent surgery at Imam Khomeini clinic in Hamadan between 2001 and 2017. The data was used to train both Cox regression and neural network models, and their predictive accuracy was compared using diagnostic measures such as sensitivity, specificity, positive predictive value, accuracy, negative predictive value, and area under the receiver operating characteristic curve. The analyses were performed using STATA 17 and R4.0.4 software. The study revealed that the best neural network model had a sensitivity of 74.5% (95% CI 61.0-85.0), specificity of 83.3% (65.3-94.4), positive predictive value of 89.1% (76.4-96.4), negative predictive value of 64.1% (47.2-78.8), AUC of 0.79 (0.70-0.88), and accuracy of 0.776 for death prediction. For recurrence, the best neural network model had a sensitivity of 88.1% (74.4-96.0%), specificity of 83.7% (69.3-93.2%), positive predictive value of 84.1% (69.9-93.4%), negative predictive value of 87.8% (73.8-95.9%), AUC of 0.86 (0.78-0.93), and accuracy of 0.859. The Cox model had comparable results, with a sensitivity of 73.6% (64.8-81.2) and 85.5% (78.3-91.0), specificity of 89.6% (83.8-93.8) and 98.0% (94.4-99.6), positive predictive value of 84.0% (75.6-90.4) and 97.4% (92.6-99.5), negative predictive value of 82.0% (75.6-90.4) and 88.8% (0.83-93.1), AUC of 0.82 (0.77-0.86) and 0.92 (0.89-0.95), and accuracy of 0.88 and 0.92 for death and recurrence prediction, respectively. In conclusion, the study found that both Cox regression and neural network models are effective in predicting early recurrence and death in patients with colorectal cancer after curative surgery. The neural network model showed slightly better sensitivity and negative predictive value for death, while the Cox model had better specificity and positive predictive value for recurrence. Overall, both models demonstrated high accuracy and AUC, indicating their usefulness in predicting these outcomes.

Penalized estimation of frailty-based illness-death models for semi-competing risks

Semi-competing risks refer to the time-to-event analysis setting, where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event. Models that acknowledge semi-competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi-competing risks in high dimensions are lacking. Moreover, in such settings researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility-in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap, we propose a novel penalized estimation framework for frailty-based illness-death multi-state modeling of semi-competing risks. Our approach combines non-convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels. We perform estimation and model selection via a pathwise routine for non-convex optimization, and prove statistical error rate results in this setting. We present a simulation study investigating estimation error and model selection performance, and a comprehensive application of the method to joint risk modeling of preeclampsia and timing of delivery using pregnancy data from an electronic health record.

Considering Questions Before Methods in Dementia Research With Competing Events and Causal Goals

Studying causal exposure effects on dementia is challenging when death is a competing event. Researchers often interpret death as a potential source of bias, although bias cannot be defined or assessed if the causal question is not explicitly specified. Here we discuss 2 possible notions of a causal effect on dementia risk: the "controlled direct effect" and the "total effect." We provide definitions and discuss the "censoring" assumptions needed for identification in either case and their link to familiar statistical methods. We illustrate concepts in a hypothetical randomized trial on smoking cessation in late midlife, and emulate such a trial using observational data from the Rotterdam Study, the Netherlands, 1990-2015. We estimated a total effect of smoking cessation (compared with continued smoking) on 20-year dementia risk of 2.1 (95% confidence interval: -0.1, 4.2) percentage points and a controlled direct effect of smoking cessation on 20-year dementia risk had death been prevented of -2.7 (95% confidence interval: -6.1, 0.8) percentage points. Our study highlights how analyses corresponding to different causal questions can have different results, here with point estimates on opposite sides of the null. Having a clear causal question in view of the competing event and transparent and explicit assumptions are essential to interpreting results and potential bias.

A multistate approach for the study of interventions on an intermediate time-to-event in health disparities research

We propose a novel methodology to quantify the effect of stochastic interventions for a non-terminal intermediate time-to-event on a terminal time-to-event outcome. Investigating these effects is particularly important in health disparities research when we seek to quantify inequities in the timely delivery of treatment and its impact on patients' survival time. Current approaches fail to account for time-to-event intermediates and semi-competing risks arising in this setting. Under the potential outcome framework, we define causal contrasts relevant in health disparities research and provide identifiability conditions when stochastic interventions on an intermediate non-terminal time-to-event are of interest. Causal contrasts are estimated in continuous time within a multistate modeling framework and analytic formulae for the estimators of the causal contrasts are developed. We show via simulations that ignoring censoring in intermediate and/or terminal time-to-event processes or ignoring semi-competing risks may give misleading results. This work demonstrates that a rigorous definition of the causal effects and joint estimation of the terminal outcome and intermediate non-terminal time-to-event distributions are crucial for valid investigation of interventions and mechanisms in continuous time. We employ this novel methodology to investigate the role of delaying treatment uptake in explaining racial disparities in cancer survival in a cohort study of colon cancer patients.

Predicting the Risk of Alzheimer's Disease and Related Dementia in Patients with Mild Cognitive Impairment Using a Semi-Competing Risk Approach

Alzheimer's disease (AD) and AD-related dementias (AD/ADRD) are a group of progressive neurodegenerative diseases. The progression of AD can be conceptualized as a continuum in which patients progress from normal cognition to preclinical AD (i.e., no symptoms but biological changes in the brain) to mild cognitive impairment (MCI) due to AD (i.e., mild symptoms but not interfere with daily activities), followed by increasing severity of dementia due to AD. Early detection and prediction models for the transition of MCI to AD/ADRD are needed, and efforts have been made to build predictions of MCI conversion to AD/ADRD. However, most existing studies developing such prediction models did not consider the competing risks of death, which may result in biased risk estimates. In this study, we aim to develop a prediction model for AD/ADRD among patients with MCI considering the competing risks of death using a semi-competing risk approach.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

A novel approach to joint prediction of preeclampsia and delivery timing using semicompeting risks

BACKGROUND

Preeclampsia is a pregnancy complication that contributes substantially to perinatal morbidity and mortality worldwide. Existing approaches to modeling and prediction of preeclampsia typically focus either on predicting preeclampsia risk alone, or on the timing of delivery following a diagnosis of preeclampsia. As such, they are misaligned with typical healthcare interactions during which the 2 events are generally considered simultaneously.

OBJECTIVE

This study aimed to describe the "semicompeting risks" framework as an innovative approach for jointly modeling the risk and timing of preeclampsia and the timing of delivery simultaneously. Through this approach, one can obtain, at any point during the pregnancy, clinically relevant summaries of an individual's predicted outcome trajectories in 4 risk categories: not developing preeclampsia and not having delivered, not developing preeclampsia but having delivered because of other causes, developing preeclampsia but not having delivered, and developing preeclampsia and having delivered.

STUDY DESIGN

To illustrate the semicompeting risks methodology, we presented an example analysis of a pregnancy cohort from the electronic health record of an urban, academic medical center in Boston, Massachusetts (n=9161 pregnancies). We fit an illness-death model with proportional-hazards regression specifications describing 3 hazards for timings of preeclampsia, delivery in the absence of preeclampsia, and delivery following preeclampsia diagnosis.

RESULTS

The results indicated nuanced relationships between a variety of risk factors and the timings of preeclampsia diagnosis and delivery, including maternal age, race/ethnicity, parity, body mass index, diabetes mellitus, chronic hypertension, cigarette use, and proteinuria at 20 weeks' gestation. Sample predictions for a diverse set of individuals highlighted differences in projected outcome trajectories with regard to preeclampsia risk and timing, and timing of delivery either before or after preeclampsia diagnosis.

CONCLUSION

The semicompeting risks framework enables characterization of the joint risk and timing of preeclampsia and delivery, providing enhanced, meaningful information regarding clinical decision-making throughout the pregnancy.

Simulating time-to-event data subject to competing risks and clustering: A review and synthesis

Simulation studies play an important role in evaluating the performance of statistical models developed for analyzing complex survival data such as those with competing risks and clustering. This article aims to provide researchers with a basic understanding of competing risks data generation, techniques for inducing cluster-level correlation, and ways to combine them together in simulation studies, in the context of randomized clinical trials with a binary exposure or treatment. We review data generation with competing and semi-competing risks and three approaches of inducing cluster-level correlation for time-to-event data: the frailty model framework, the probability transform, and Moran's algorithm. Using exponentially distributed event times as an example, we discuss how to introduce cluster-level correlation into generating complex survival outcomes, and illustrate multiple ways of combining these methods to simulate clustered, competing and semi-competing risks data with pre-specified correlation values or degree of clustering.

Time to second treatment can be used to predict overall survival in chronic lymphocytic leukemia: identifying risk factors to help guide treatment selection

Targeted therapies have largely replaced chemoimmunotherapy (CIT) in first-line treatment of chronic lymphocytic leukemia (CLL). We aimed to develop a prognostic model to determine who would benefit from first-line CIT vs target therapy. In follicular lymphoma, time from diagnosis to second treatment (TT2T) correlates better with overall survival (OS) than time from diagnosis to first treatment (TT1T). We hypothesized that TT2T is a potential surrogate for OS in CLL. In a model-building cohort (n = 298), we evaluated potential predictors for TT2T and derived a risk score, which we validated in an external cohort (n = 1141). Our data demonstrated that TT2T and OS were more strongly correlated than TT1T and OS. Our risk score model consisted of three predictors (unmutated IGHV, β2-microglobulin >297 nmol/L, and Rai stage I-IV), and was prognostic for TT2T and OS. TT2T is a promising surrogate for OS in CLL, but further validation is needed to establish this association.

Doubly robust estimation of the hazard difference for competing risks data

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

A parametric approach to relaxing the independence assumption in relative survival analysis

With known cause of death (CoD), competing risk survival methods are applicable in estimating disease-specific survival. Relative survival analysis may be used to estimate disease-specific survival when cause of death is either unknown or subject to misspecification and not reliable for practical usage. This method is popular for population-based cancer survival studies using registry data and does not require CoD information. The standard estimator is the ratio of all-cause survival in the cancer cohort group to the known expected survival from a general reference population. Disease-specific death competes with other causes of mortality, potentially creating dependence among the CoD. The standard ratio estimate is only valid when death from disease and death from other causes are independent. To relax the independence assumption, we formulate dependence using a copula-based model. Likelihood-based parametric method is used to fit the distribution of disease-specific death without CoD information, where the copula is assumed known and the distribution of other cause of mortality is derived from the reference population. We propose a sensitivity analysis, where the analysis is conducted across a range of assumed dependence structures. We demonstrate the utility of our method through simulation studies and an application to French breast cancer data.

Modeling semi-competing risks data as a longitudinal bivariate process

As individuals age, death is a competing risk for Alzheimer's disease (AD) but the reverse is not the case. As such, studies of AD can be placed within the semi-competing risks framework. Central to semi-competing risks, and in contrast to standard competing risks , is that one can learn about the dependence structure between the two events. To-date, however, most methods for semi-competing risks treat dependence as a nuisance and not a potential source of new clinical knowledge. We propose a novel regression-based framework that views the two time-to-event outcomes through the lens of a longitudinal bivariate process on a partition of the time scales of the two events. A key innovation of the framework is that dependence is represented in two distinct forms, local and global dependence, both of which have intuitive clinical interpretations. Estimation and inference are performed via penalized maximum likelihood, and can accommodate right censoring, left truncation, and time-varying covariates. An important consequence of the partitioning of the time scale is that an ambiguity regarding the specific form of the likelihood contribution may arise; a strategy for sensitivity analyses regarding this issue is described. The framework is then used to investigate the role of gender and having ≥1 apolipoprotein E (APOE) ε4 allele on the joint risk of AD and death using data from the Adult Changes in Thought study.

Nonparametric Sieve Maximum Likelihood Estimation of Semi-Competing Risks Data

In biomedical studies involving time-to-event data, a subject may experience distinct types of events. We consider the problem of estimating the transition functions for a semi-competing risks model under illness-death model framework. We propose to estimate the intensity functions by maximizing a B-spline based sieve likelihood. The method yields smooth estimates without parametric assumptions. Our proposed approach facilitates easy computation of the covariance of the model parameters and yields direct interpretation. Compared with existing approaches, our proposed method requires neither the subjective specification of the frailty distribution nor the Markov or semi-Markov assumption which may be unmet in real applications. We establish the consistency, the convergence rate, and the asymptotic normality of the proposed estimators under some regularity conditions. We also provide simulation studies to assess the finite-sample performance of the proposed modeling and estimation strategy. A real data application is further used to illustrate the proposed methodology.

Using Information Available at the Time of Donor Offer to Predict Kidney Transplant Survival Outcomes: A Systematic Review of Prediction Models

Statistical models that can predict graft and patient survival outcomes following kidney transplantation could be of great clinical utility. We sought to appraise existing clinical prediction models for kidney transplant survival outcomes that could guide kidney donor acceptance decision-making. We searched for clinical prediction models for survival outcomes in adult recipients with single kidney-only transplants. Models that require information anticipated to become available only after the time of transplantation were excluded as, by that time, the kidney donor acceptance decision would have already been made. The outcomes of interest were all-cause and death-censored graft failure, and death. We summarised the methodological characteristics of the prediction models, predictive performance and risk of bias. We retrieved 4,026 citations from which 23 articles describing 74 models met the inclusion criteria. Discrimination was moderate for all-cause graft failure (C-statistic: 0.570–0.652; Harrell’s C: 0.580–0.660; AUC: 0.530–0.742), death-censored graft failure (C-statistic: 0.540–0.660; Harrell’s C: 0.590–0.700; AUC: 0.450–0.810) and death (C-statistic: 0.637–0.770; Harrell’s C: 0.570–0.735). Calibration was seldom reported. Risk of bias was high in 49 of the 74 models, primarily due to methods for handling missing data. The currently available prediction models using pre-transplantation information show moderate discrimination and varied calibration. Further model development is needed to improve predictions for the purpose of clinical decision-making.

Systematic Review Registration:https://osf.io/c3ehp/l.

On recurrent-event win ratio

The win ratio approach proposed by Pocock et al. (2012) has become a popular tool for analyzing composite endpoints of death and non-fatal events like hospitalization. Its standard version, however, draws on the non-fatal event only through the first occurrence. For statistical efficiency and clinical interpretability, we construct and compare different win ratio variants that make fuller use of recurrent events. We pay special attention to a variant called last-event-assisted win ratio, which compares two patients on the cumulative frequency of the non-fatal event, with ties broken by the time of its latest episode. It is shown that last-event-assisted win ratio uses more data than the standard win ratio does but reduces to the latter when the non-fatal event occurs at most once. We further prove that last-event-assisted win ratio rejects the null hypothesis with large probability if the treatment stochastically delays all events. Simulations under realistic settings show that the last-event-assisted win ratio test consistently enjoys higher power than the standard win ratio and other competitors. Analysis of a real cardiovascular trial provides further evidence for the practical advantages of the last-event-assisted win ratio. Finally, we discuss future work to develop meaningful effect size estimands based on the extended rules of comparison. The R-code for the proposed methods is included in the package WR openly available on the Comprehensive R Archive Network.

SCI: A Bayesian adaptive phase I/II dose-finding design accounting for semi-competing risks outcomes for immunotherapy trials

An immunotherapy trial often uses the phase I/II design to identify the optimal biological dose, which monitors the efficacy and toxicity outcomes simultaneously in a single trial. The progression‐free survival rate is often used as the efficacy outcome in phase I/II immunotherapy trials. As a result, patients developing disease progression in phase I/II immunotherapy trials are generally seriously ill and are often treated off the trial for ethical consideration. Consequently, the happening of disease progression will terminate the toxicity event but not vice versa, so the issue of the semi‐competing risks arises. Moreover, this issue can become more intractable with the late‐onset outcomes, which happens when a relatively long follow‐up time is required to ascertain progression‐free survival. This paper proposes a novel Bayesian adaptive phase I/II design accounting for semi‐competing risks outcomes for immunotherapy trials, referred to as the dose‐finding design accounting for semi‐competing risks outcomes for immunotherapy trials (SCI) design. To tackle the issue of the semi‐competing risks in the presence of late‐onset outcomes, we re‐construct the likelihood function based on each patient's actual follow‐up time and develop a data augmentation method to efficiently draw posterior samples from a series of Beta‐binomial distributions. We propose a concise curve‐free dose‐finding algorithm to adaptively identify the optimal biological dose using accumulated data without making any parametric dose–response assumptions. Numerical studies show that the proposed SCI design yields good operating characteristics in dose selection, patient allocation, and trial duration.

Impact of neutropenia on clinical manifestations and outcome of Staphylococcus aureus bloodstream infection - A propensity score-based overlap weight analysis in two large, prospectively evaluated cohorts

OBJECTIVE

To investigate whether neutropenia influenced mortality and long-term outcome of Staphylococcus aureus bloodstream infection (SAB).

METHODS

Data from two prospective, multicentre cohort studies (INSTINCT and ISAC) conducted in 20 tertiary care hospitals in 6 countries between 2006 and 2015 were analysed. Neutropenic and severely neutropenic patients (defined by the proxy of total white blood cell count <1000/μl and <500/μl, respectively, at onset of SAB) were compared to a control group using a propensity score model and overlap weights to adjust for baseline characteristics. Overall survival and time to SAB-related late complications (SAB recurrence, infective endocarditis, osteomyelitis, or other deep-seated manifestations) were analysed by Cox regression and competing risk analyses, respectively.

RESULTS

Of 3,187 patients, 102 were neutropenic and 70 were severely neutropenic at onset of SAB. Applying overlap weights yielded two groups of 83 neutropenic and 220 non-neutropenic patients, respectively. Baseline characteristics of these groups were exactly balanced. In the Cox regression analysis, we observed no significant difference in survival between the two groups (death during follow-up: 36.1 % in neutropenic vs. 30.6 % in non-neutropenic patients, hazard ratio 1.21 (95 % CI 0.79-1.83)). This finding remained unchanged when we considered severely neutropenic patients (hazard ratio 1.08 [0.60; 1.94]). Competing risk analysis showed a cause-specific hazard ratio (CSHR) of 0.39 (95 % CI 0.11-1.39) for SAB-related late-complications in neutropenic patients.

CONCLUSIONS

Neutropenia was not associated with a higher survival during follow-up. The lower rate of SAB-related late complications in neutropenic patients should be validated in other cohorts.

Hypothesis test for causal mediation of time-to-event mediator and outcome

Hepatitis B has been a well-documented risk factor of liver cancer and mortality. To what extent hepatitis B affects mortality through increasing liver cancer incidence is of research interest and remains to be studied. We formulate the research question as a hypothesis testing problem of causal mediation where both the mediator and the outcome are time-to-event variables. The problem is closely related to semicompeting risks because time to the intermediate event may be censored by an occurrence of the outcome. We propose two hypothesis testing methods: a weighted log-rank test (WLR) and an intersection-union test (IUT). A test statistic of the WLR is constructed by adapting a nonparametric estimator of the mediation effect; however, the test may be conservative regarding its Type I Error rate. To address this, we further propose the IUT, the test statistic of which is constructed under the composite null hypothesis. Asymptotic properties of the two tests are studied, showing that the IUT is a size α test with better statistical power than the WLR. The theoretical properties are supported by extensive simulation studies under finite samples. Applying the proposed methods to the motivating hepatitis study, both WLR and IUT provided strong evidence that hepatitis B had a significant mediation effect on mortality via liver cancer incidence.

A Bayesian nonparametric approach for evaluating the causal effect of treatment in randomized trials with semi-competing risks

We develop a Bayesian nonparametric (BNP) approach to evaluate the causal effect of treatment in a randomized trial where a nonterminal event may be censored by a terminal event, but not vice versa (i.e., semi-competing risks). Based on the idea of principal stratification, we define a novel estimand for the causal effect of treatment on the nonterminal event. We introduce identification assumptions, indexed by a sensitivity parameter, and show how to draw inference using our BNP approach. We conduct simulation studies and illustrate our methodology using data from a brain cancer trial. The R code implementing our model and algorithm is available for download at https://github.com/YanxunXu/BaySemiCompeting.

Accounting for Preinvasive Conditions in Analysis of Invasive Cancer Risk: Application to Breast Cancer

BACKGROUND

Preinvasive cancer conditions are often actively treated to minimize progression to life-threatening invasive cancers, but this creates challenges for analysis of invasive cancer risk. Conventional methods of treating preinvasive conditions as censoring events or targeting at the composite outcome could both lead to bias.

METHODS

We propose two solutions: one that provides exact estimates of risk based on distributional assumptions about progression, and one that provides risk bounds corresponding to extreme cases of no or complete progression. We compare these approaches through simulations and an analysis of the Sister Study data in the context of ductal carcinoma in situ (DCIS) and invasive breast cancer.

RESULTS

Simulations suggested important biases with conventional approaches, whereas the proposed estimate is consistent when progression parameters are correctly specified, and the risk bounds are robust in all scenarios. With Sister Study, the estimated lifetime risks for invasive breast cancer are 0.220 and 0.269 with DCIS censored or combined. Without detailed progression information, a sensitivity analysis suggested lifetime risk falls between the bounds of 0.214 and 0.269 across assumptions of 10%-95% of DCIS patients progressing to invasive cancer in an average of 1-10 years.

CONCLUSIONS

When estimating invasive cancer risk while preinvasive conditions are actively treated, it is important to consider the implied assumptions and potential biases of conventional approaches. Although still not perfect, we proposed two practical solutions that provide improved understanding of the underlying mechanism of invasive cancer.

Semiparametric copula-based regression modeling of semi-competing risks data

Semi-competing risks data often arise in medical studies where the terminal event (e.g., death) censors the non-terminal event (e.g., cancer recurrence), but the non-terminal event does not prevent the subsequent occurrence of the terminal event. This article considers regression modeling of semi-competing risks data to assess the covariate effects on the respective non-terminal and terminal event times. We propose a copula-based framework for semi-competing risks regression with time-varying coefficients, where the dependence between the non-terminal and terminal event times is characterized by a copula and the time-varying covariate effects are imposed on two marginal regression models. We develop a two-stage inferential procedure for estimating the association parameter in the copula model and time-varying regression parameters. We evaluate the finite sample performance of the proposed method through simulation studies and illustrate the method through an application to Surveillance, Epidemiology, and End Results-Medicare data for elderly women diagnosed with early-stage breast cancer and initially treated with breast-conserving surgery.