Data-Driven Simulations to Assess the Impact of Study Imperfections in Time-to-Event Analyses.

Quantitative bias analysis (QBA) permits assessment of the expected impact of various imperfections of the available data on the results and conclusions of a particular real-world study. This article extends QBA methodology to multivariable time-to-event analyses with right-censored endpoints, possibly including time-varying exposures or covariates. The proposed approach employs data-driven simulations, which preserve important features of the data at hand while offering flexibility in controlling the parameters and assumptions that may affect the results. First, the steps required to perform data-driven simulations are described, and then two examples of real-world time-to-event analyses illustrate their implementation and the insights they may offer. The first example focuses on the omission of an important time-invariant predictor of the outcome in a prognostic study of cancer mortality, and permits separating the expected impact of confounding bias from non-collapsibility. The second example assesses how imprecise timing of an interval-censored event - ascertained only at sparse times of clinic visits - affects its estimated association with a time-varying drug exposure. The simulation results also provide a basis for comparing the performance of two alternative strategies for imputing the unknown event times in this setting. The R scripts that permit the reproduction of our examples are provided.

A competing risks model to estimate the risk of graft failure and patient death after kidney transplantation using continuous donor-recipient age combinations.

Graft failure and recipient death with functioning graft are important competing outcomes after kidney transplantation. Risk prediction models typically censor for the competing outcome thereby overestimating the cumulative incidence. The magnitude of this overestimation is not well described in real-world transplant data. This retrospective cohort study analyzed data from the European Collaborative Transplant Study (n = 125 250) and from the American Scientific Registry of Transplant Recipients (n = 190 258). Separate cause-specific hazard models using donor and recipient age as continuous predictors were developed for graft failure and recipient death. The hazard of graft failure increased quadratically with increasing donor age and decreased decaying with increasing recipient age. The hazard of recipient death increased linearly with increasing donor and recipient age. The cumulative incidence overestimation due to competing risk-censoring was largest in high-risk populations for both outcomes (old donors/recipients), sometimes amounting to 8.4 and 18.8 percentage points for graft failure and recipient death, respectively. In our illustrative model for posttransplant risk prediction, the absolute risk of graft failure and death is overestimated when censoring for the competing event, mainly in older donors and recipients. Prediction models for absolute risks should treat graft failure and death as competing events.

Doubly robust nonparametric instrumental variable estimators for survival outcomes.

Instrumental variable (IV) methods allow us the opportunity to address unmeasured confounding in causal inference. However, most IV methods are only applicable to discrete or continuous outcomes with very few IV methods for censored survival outcomes. In this article, we propose nonparametric estimators for the local average treatment effect on survival probabilities under both covariate-dependent and outcome-dependent censoring. We provide an efficient influence function-based estimator and a simple estimation procedure when the IV is either binary or continuous. The proposed estimators possess double-robustness properties and can easily incorporate nonparametric estimation using machine learning tools. In simulation studies, we demonstrate the flexibility and double robustness of our proposed estimators under various plausible scenarios. We apply our method to the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial for estimating the causal effect of screening on survival probabilities and investigate the causal contrasts between the two interventions under different censoring assumptions.

Extending prediction models for use in a new target population with failure time outcomes.

Prediction models are often built and evaluated using data from a population that differs from the target population where model-derived predictions are intended to be used in. In this article, we present methods for evaluating model performance in the target population when some observations are right censored. The methods assume that outcome and covariate data are available from a source population used for model development and covariates, but no outcome data, are available from the target population. We evaluate the finite sample performance of the proposed estimators using simulations and apply the methods to transport a prediction model built using data from a lung cancer screening trial to a nationally representative population of participants eligible for lung cancer screening.

Reproducibility and Sensitivity of Resting-State fMRI in Patients With Parkinson's Disease Using Cross Validation-Based Data Censoring.

BACKGROUND: Uncontrollable body movements are typical symptoms of Parkinson's disease (PD), which results in inconsistent findings regarding resting-state functional connectivity (rsFC) networks, especially for group difference clusters. Systematically identifying the motion-associated data was highly demanded. PURPOSE: To determine data censoring criteria using a quantitative cross validation-based data censoring (CVDC) method and to improve the detection of rsFC deficits in PD. STUDY TYPE: Prospective. SUBJECTS: Forty-one PD patients (68.63 ± 9.17 years, 44% female) and 20 healthy controls (66.83 ± 12.94 years, 55% female). FIELD STRENGTH/SEQUENCE: 3-T, T1-weighted gradient echo and EPI sequences. ASSESSMENT: Clusters with significant differences between groups were found in three visual networks, default network, and right sensorimotor network. Five-fold cross-validation tests were performed using multiple motion exclusion criteria, and the selected criteria were determined based on cluster sizes, significance values, and Dice coefficients among the cross-validation tests. As a reference method, whole brain rsFC comparisons between groups were analyzed using a FMRIB Software Library (FSL) pipeline with default settings. STATISTICAL TESTS: Group difference clusters were calculated using nonparametric permutation statistics of FSL-randomize. The family-wise error was corrected. Demographic information was evaluated using independent sample t-tests and Pearson's Chi-squared tests. The level of statistical significance was set at P < 0.05. RESULTS: With the FSL processing pipeline, the mean Dice coefficient of the network clusters was 0.411, indicating a low reproducibility. With the proposed CVDC method, motion exclusion criteria were determined as frame-wise displacement >0.55 mm. Group-difference clusters showed a mean P-value of 0.01 and a 72% higher mean Dice coefficient compared to the FSL pipeline. Furthermore, the CVDC method was capable of detecting subtle rsFC deficits in the medial sensorimotor network and auditory network that were unobservable using the conventional pipeline. DATA CONCLUSION: The CVDC method may provide superior sensitivity and improved reproducibility for detecting rsFC deficits in PD. LEVEL OF EVIDENCE: 1 TECHNICAL EFFICACY: Stage 2.

Regression models for average hazard.

Limitations of using the traditional Cox's hazard ratio for summarizing the magnitude of the treatment effect on time-to-event outcomes have been widely discussed, and alternative measures that do not have such limitations are gaining attention. One of the alternative methods recently proposed, in a simple 2-sample comparison setting, uses the average hazard with survival weight (AH), which can be interpreted as the general censoring-free person-time incidence rate on a given time window. In this paper, we propose a new regression analysis approach for the AH with a truncation time τ. We investigate 3 versions of AH regression analysis, assuming (1) independent censoring, (2) group-specific censoring, and (3) covariate-dependent censoring. The proposed AH regression methods are closely related to robust Poisson regression. While the new approach needs to require a truncation time τ explicitly, it can be more robust than Poisson regression in the presence of censoring. With the AH regression approach, one can summarize the between-group treatment difference in both absolute difference and relative terms, adjusting for covariates that are associated with the outcome. This property will increase the likelihood that the treatment effect magnitude is correctly interpreted. The AH regression approach can be a useful alternative to the traditional Cox's hazard ratio approach for estimating and reporting the magnitude of the treatment effect on time-to-event outcomes.

Proportional rates models for multivariate panel count data.

Multivariate panel count data arise when there are multiple types of recurrent events, and the observation for each study subject consists of the number of recurrent events of each type between two successive examinations. We formulate the effects of potentially time-dependent covariates on multiple types of recurrent events through proportional rates models, while leaving the dependence structures of the related recurrent events completely unspecified. We employ nonparametric maximum pseudo-likelihood estimation under the working assumptions that all types of events are independent and each type of event is a nonhomogeneous Poisson process, and we develop a simple and stable EM-type algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that can be estimated consistently by a sandwich estimator. In addition, we develop a class of graphical and numerical methods for checking the adequacy of the fitted model. Finally, we evaluate the performance of the proposed methods through simulation studies and analysis of a skin cancer clinical trial.

Fitting the Cox proportional hazards model to big data.

The semiparametric Cox proportional hazards model, together with the partial likelihood principle, has been widely used to study the effects of potentially time-dependent covariates on a possibly censored event time. We propose a computationally efficient method for fitting the Cox model to big data involving millions of study subjects. Specifically, we perform maximum partial likelihood estimation on a small subset of the whole data and improve the initial estimator by incorporating the remaining data through one-step estimation with estimated efficient score functions. We show that the final estimator has the same asymptotic distribution as the conventional maximum partial likelihood estimator using the whole dataset but requires only a small fraction of computation time. We demonstrate the usefulness of the proposed method through extensive simulation studies and an application to the UK Biobank data.

Factor-augmented transformation models for interval-censored failure time data.

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

Handling missing disease information due to death in diseases that need two visits to diagnose.

In studies that assess disease status periodically, time of disease onset is interval censored between visits. Participants who die between two visits may have unknown disease status after their last visit. In this work, we consider an additional scenario where diagnosis requires two consecutive positive tests, such that disease status can also be unknown at the last visit preceding death. We show that this impacts the choice of censoring time for those who die without an observed disease diagnosis. We investigate two classes of models that quantify the effect of risk factors on disease outcome: a Cox proportional hazards model with death as a competing risk and an illness death model that treats disease as a possible intermediate state. We also consider four censoring strategies: participants without observed disease are censored at death (Cox model only), the last visit, the last visit with a negative test, or the second last visit. We evaluate the performance of model and censoring strategy combinations on simulated data with a binary risk factor and illustrate with a real data application. We find that the illness death model with censoring at the second last visit shows the best performance in all simulation settings. Other combinations show bias that varies in magnitude and direction depending on the differential mortality between diseased and disease-free subjects, the gap between visits, and the choice of the censoring time.

Latent classification model for censored longitudinal binary outcome.

Latent classification model is a class of statistical methods for identifying unobserved class membership among the study samples using some observed data. In this study, we proposed a latent classification model that takes a censored longitudinal binary outcome variable and uses its changing pattern over time to predict individuals' latent class membership. Assuming the time-dependent outcome variables follow a continuous-time Markov chain, the proposed method has two primary goals: (1) estimate the distribution of the latent classes and predict individuals' class membership, and (2) estimate the class-specific transition rates and rate ratios. To assess the model's performance, we conducted a simulation study and verified that our algorithm produces accurate model estimates (ie, small bias) with reasonable confidence intervals (ie, achieving approximately 95% coverage probability). Furthermore, we compared our model to four other existing latent class models and demonstrated that our approach yields higher prediction accuracies for latent classes. We applied our proposed method to analyze the COVID-19 data in Houston, Texas, US collected between January first 2021 and December 31st 2021. Early reports on the COVID-19 pandemic showed that the severity of a SARS-CoV-2 infection tends to vary greatly by cases. We found that while demographic characteristics explain some of the differences in individuals' experience with COVID-19, some unaccounted-for latent variables were associated with the disease.

A discrete approximation method for modeling interval-censored multistate data.

Many longitudinal studies are designed to monitor participants for major events related to the progression of diseases. Data arising from such longitudinal studies are usually subject to interval censoring since the events are only known to occur between two monitoring visits. In this work, we propose a new method to handle interval-censored multistate data within a proportional hazards model framework where the hazard rate of events is modeled by a nonparametric function of time and the covariates affect the hazard rate proportionally. The main idea of this method is to simplify the likelihood functions of a discrete-time multistate model through an approximation and the application of data augmentation techniques, where the assumed presence of censored information facilitates a simpler parameterization. Then the expectation-maximization algorithm is used to estimate the parameters in the model. The performance of the proposed method is evaluated by numerical studies. Finally, the method is employed to analyze a dataset on tracking the advancement of coronary allograft vasculopathy following heart transplantation.

A flexible model based on piecewise linear approximation for the analysis of left truncated right censored data with covariates, and applications to Worcester Heart Attack Study data and Channing House data.

Left truncated right censored (LTRC) data arise quite commonly from survival studies. In this article, a model based on piecewise linear approximation is proposed for the analysis of LTRC data with covariates. Specifically, the model involves a piecewise linear approximation for the cumulative baseline hazard function of the proportional hazards model. The principal advantage of the proposed model is that it does not depend on restrictive parametric assumptions while being flexible and data-driven. Likelihood inference for the model is developed. Through detailed simulation studies, the robustness property of the model is studied by fitting it to LTRC data generated from different processes covering a wide range of lifetime distributions. A sensitivity analysis is also carried out by fitting the model to LTRC data generated from a process with a piecewise constant baseline hazard. It is observed that the performance of the model is quite satisfactory in all those cases. Analyses of two real LTRC datasets by using the model are provided as illustrative examples. Applications of the model in some practical prediction issues are discussed. In summary, the proposed model provides a comprehensive and flexible approach to model a general structure for LTRC lifetime data.

Dealing with time-dependent exposures and confounding when defining and estimating attributable fractions-Revisiting estimands and estimators.

The population-attributable fraction (PAF) is commonly interpreted as the proportion of events that can be ascribed to a certain exposure in a certain population. Its estimation is sensitive to common forms of time-dependent bias in the face of a time-dependent exposure. Predominant estimation approaches based on multistate modeling fail to fully eliminate such bias and, as a result, do not permit a causal interpretation, even in the absence of confounding. While recently proposed multistate modeling approaches can successfully eliminate residual time-dependent bias, and moreover succeed to adjust for time-dependent confounding by means of inverse probability of censoring weighting, inadequate application, and misinterpretation prevails in the medical literature. In this paper, we therefore revisit recent work on previously proposed PAF estimands and estimators in settings with time-dependent exposures and competing events and extend this work in several ways. First, we critically revisit the interpretation and applied terminology of these estimands. Second, we further formalize the assumptions under which a causally interpretable PAF estimand can be identified and provide analogous weighting-based representations of the identifying functionals of other proposed estimands. This representation aims to enhance the applied statistician's understanding of different sources of bias that may arise when the aim is to obtain a valid estimate of a causally interpretable PAF. To illustrate and compare these representations, we present a real-life application to observational data from the Ghent University Hospital ICUs to estimate the fraction of ICU deaths attributable to hospital-acquired infections.

Revising model for end-stage liver disease from calendar-time cross-sections with correction for selection bias.

BACKGROUND: Eurotransplant liver transplant candidates are prioritized by Model for End-stage Liver Disease (MELD), a 90-day waitlist survival risk score based on the INR, creatinine and bilirubin. Several studies revised the original MELD score, UNOS-MELD, with transplant candidate data by modelling 90-day waitlist mortality from waitlist registration, censoring patients at delisting or transplantation. This approach ignores biomarkers reported after registration, and ignores informative censoring by transplantation and delisting. METHODS: We study how MELD revision is affected by revision from calendar-time cross-sections and correction for informative censoring with inverse probability censoring weighting (IPCW). For this, we revised UNOS-MELD on patients with chronic liver cirrhosis on the Eurotransplant waitlist between 2007 and 2019 (n = 13,274) with Cox models with as endpoints 90-day survival (a) from registration and (b) from weekly drawn calendar-time cross-sections. We refer to the revised score from cross-section with IPCW as DynReMELD, and compare DynReMELD to UNOS-MELD and ReMELD, a prior revision of UNOS-MELD for Eurotransplant, in geographical validation. RESULTS: Revising MELD from calendar-time cross-sections leads to significantly different MELD coefficients. IPCW increases estimates of absolute 90-day waitlist mortality risks by approximately 10 percentage points. DynReMELD has improved discrimination over UNOS-MELD (delta c-index: 0.0040, p < 0.001) and ReMELD (delta c-index: 0.0015, p < 0.01), with differences comparable in magnitude to the addition of an extra biomarker to MELD (delta c-index: ± 0.0030). CONCLUSION: Correcting for selection bias by transplantation/delisting does not improve discrimination of revised MELD scores, but substantially increases estimated absolute 90-day mortality risks. Revision from cross-section uses waitlist data more efficiently, and improves discrimination compared to revision of MELD exclusively based on information available at listing.

Adverse events in single-arm clinical trials with non-fatal time-to-event efficacy endpoint: from clinical questions to methods for statistical analysis.

BACKGROUND: In any single-arm trial on novel treatments, assessment of toxicity plays an important role as occurrence of adverse events (AEs) is relevant for application in clinical practice. In the presence of a non-fatal time-to-event(s) efficacy endpoint, the analysis should be broadened to consider AEs occurrence in time. The AEs analysis could be tackled with two approaches, depending on the clinical question of interest. Approach 1 focuses on the occurrence of AE as first event. Treatment ability to protect from the efficacy endpoint event(s) has an impact on the chance of observing AEs due to competing risks action. Approach 2 considers how treatment affects the occurrence of AEs in the potential framework where the efficacy endpoint event(s) could not occur. METHODS: In the first part of the work we review the strategy of analysis for these two approaches. We identify theoretical quantities and estimators consistent with the following features: (a) estimators should address for the presence of right censoring; (b) theoretical quantities and estimators should be functions of time. In the second part of the work we propose the use of alternative methods (regression models, stratified Kaplan-Meier curves, inverse probability of censoring weighting) to relax the assumption of independence between the potential times to AE and to event(s) in the efficacy endpoint for addressing Approach 2. RESULTS: We show through simulations that the proposed methods overcome the bias due to the dependence between the two potential times and related to the use of standard estimators. CONCLUSIONS: We demonstrated through simulations that one can handle patients selection in the risk sets due to the competing event, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates that induce dependence.

Survival analysis under imperfect record linkage using historic census data.

BACKGROUND: Advancements in linking publicly available census records with vital and administrative records have enabled novel investigations in epidemiology and social history. However, in the absence of unique identifiers, the linkage of the records may be uncertain or only be successful for a subset of the census cohort, resulting in missing data. For survival analysis, differential ascertainment of event times can impact inference on risk associations and median survival. METHODS: We modify some existing approaches that are commonly used to handle missing survival times to accommodate this imperfect linkage situation including complete case analysis, censoring, weighting, and several multiple imputation methods. We then conduct simulation studies to compare the performance of the proposed approaches in estimating the associations of a risk factor or exposure in terms of hazard ratio (HR) and median survival times in the presence of missing survival times. The effects of different missing data mechanisms and exposure-survival associations on their performance are also explored. The approaches are applied to a historic cohort of residents in Ambler, PA, established using the 1930 US census, from which only 2,440 out of 4,514 individuals (54%) had death records retrievable from publicly available data sources and death certificates. Using this cohort, we examine the effects of occupational and paraoccupational asbestos exposure on survival and disparities in mortality by race and gender. RESULTS: We show that imputation based on conditional survival results in less bias and greater efficiency relative to a complete case analysis when estimating log-hazard ratios and median survival times. When the approaches are applied to the Ambler cohort, we find a significant association between occupational exposure and mortality, particularly among black individuals and males, but not between paraoccupational exposure and mortality. DISCUSSION: This investigation illustrates the strengths and weaknesses of different imputation methods for missing survival times due to imperfect linkage of the administrative or registry data. The performance of the methods may depend on the missingness process as well as the parameter being estimated and models of interest, and such factors should be considered when choosing the methods to address the missing event times.

The impact of different censoring methods for analyzing survival using real-world data with linked mortality information: a simulation study.

BACKGROUND: Evaluating outcome reliability is critical in real-world evidence studies. Overall survival is a common outcome in these studies; however, its capture in real-world data (RWD) sources is often incomplete and supplemented with linked mortality information from external sources. Conflicting recommendations exist for censoring overall survival in real-world evidence studies. This simulation study aimed to understand the impact of different censoring methods on estimating median survival and log hazard ratios when external mortality information is partially captured. METHODS: We used Monte Carlo simulation to emulate a non-randomized comparative effectiveness study of two treatments with RWD from electronic health records and linked external mortality data. We simulated the time to death, the time to last database activity, and the time to data cutoff. Death events after the last database activity were attributed to linked external mortality data and randomly set to missing to reflect the sensitivity of contemporary real-world data sources. Two censoring schemes were evaluated: (1) censoring at the last activity date and (2) censoring at the end of data availability (data cutoff) without an observed death. We assessed the performance of each method in estimating median survival and log hazard ratios using bias, coverage, variance, and rejection rate under varying amounts of incomplete mortality information and varying treatment effects, length of follow-up, and sample size. RESULTS: When mortality information was fully captured, median survival estimates were unbiased when censoring at data cutoff and underestimated when censoring at the last activity. When linked mortality information was missing, censoring at the last activity date underestimated the median survival, while censoring at the data cutoff overestimated it. As missing linked mortality information increased, bias decreased when censoring at the last activity date and increased when censoring at data cutoff. CONCLUSIONS: Researchers should consider the completeness of linked external mortality information when choosing how to censor the analysis of overall survival using RWD. Substantial bias in median survival estimates can occur if an inappropriate censoring scheme is selected. We advocate for RWD providers to perform validation studies of their mortality data and publish their findings to inform methodological decisions better.

Two biases in incubation time estimation related to exposure.

BACKGROUND: Estimation of the SARS-CoV-2 incubation time distribution is hampered by incomplete data about infection. We discuss two biases that may result from incorrect handling of such data. Notified cases may recall recent exposures more precisely (differential recall). This creates bias if the analysis is restricted to observations with well-defined exposures, as longer incubation times are more likely to be excluded. Another bias occurred in the initial estimates based on data concerning travellers from Wuhan. Only individuals who developed symptoms after their departure were included, leading to under-representation of cases with shorter incubation times (left truncation). This issue was not addressed in the analyses performed in the literature. METHODS: We performed simulations and provide a literature review to investigate the amount of bias in estimated percentiles of the SARS-CoV-2 incubation time distribution. RESULTS: Depending on the rate of differential recall, restricting the analysis to a subset of narrow exposure windows resulted in underestimation in the median and even more in the 95th percentile. Failing to account for left truncation led to an overestimation of multiple days in both the median and the 95th percentile. CONCLUSION: We examined two overlooked sources of bias concerning exposure information that the researcher engaged in incubation time estimation needs to be aware of.

An Emulated Target Trial Case Study of Real-World Overall Survival With Second-Line Maintenance Niraparib Versus Active Surveillance in Patients With Recurrent Ovarian Cancer.

PURPOSE: This retrospective real-world study compared overall survival (OS) between patients with BRCA wild-type (BRCAwt) recurrent epithelial ovarian cancer (OC) who received niraparib second-line maintenance (2LM) versus active surveillance (AS) using target trial emulation, cloning, inverse probability of censoring weighting (IPCW) methodology to minimize immortal time bias. METHODS: Eligible patients from a United States-based, deidentified, electronic health record-derived database were diagnosed with epithelial OC (January 1, 2011-May 31, 2021), were BRCAwt, and completed second-line (2L) therapy (January 1, 2017-March 2, 2022). Patient data were cloned at index (2L last treatment date), assigned to niraparib 2LM and AS cohorts, and censored when treatment deviated from clone assignment. Follow-up was measured from index to earliest of study end (May 31, 2022), last activity, or death. Median OS (mOS) and hazard ratios were estimated from stabilized IPCW Kaplan-Meier curves and Cox regression models. RESULTS: Overall, 199 patients received niraparib 2LM, and 707 had their care managed with AS. Key characteristics were balanced across cohorts after cloning and stabilized IPCW. Median follow-up was 15.6- and 9.3-months pre-cloning. IPCW mOS was 24.1 months (95% CI: 20.9-29.5) and 18.4 months (95% CI: 15.1-22.8) in niraparib 2LM and AS cohorts, respectively (hazard ratio, 0.77; 95% CI: 0.66-0.89). CONCLUSIONS: This real-world study provides supportive evidence of an OS benefit for patients with BRCAwt recurrent OC who received 2LM niraparib monotherapy compared with those whose care was managed with AS. The analytic strategies implemented were useful in minimizing immortal time bias and measured confounding.