Interval Censoring Research Articles

Epistaxis Versus Nonepistaxis Bleeding in Anticoagulated Patients With Atrial Fibrillation: Results From the ENGAGE AF-TIMI 48 Trial.

Epistaxis is common with antithrombotic therapy and is often troublesome to patients, yet its frequency, severity, and outcomes are poorly characterized. Effective Anticoagulation with Factor Xa Next Generation in Atrial Fibrillation-Thrombolysis in Myocardial Infarction 48 (ENGAGE AF-TIMI 48) randomized 21 105 patients with atrial fibrillation and CHADS2 risk score ≥2 to higher-dose edoxaban regimen (60 mg daily, dose-reduced to 30 mg), lower-dose edoxaban regimen (30 mg, dose reduced to 15 mg, daily), or warfarin. Bleeds were adjudicated using International Society on Thrombosis and Haemostasis criteria. Patients with intracranial hemorrhage during follow-up were excluded; those with >1 bleeding event were categorized according to their most severe event. The safety cohort with interval censoring during drug interruption was analyzed. Proportions were compared using Pearson's chi-square test and treatment arms were compared using a Cox proportional hazards model. Among 5247 patients with a bleeding event, 1008 (19.2%) had epistaxis and 4239 (80.8%) had nonepistaxis bleeding. Epistaxis events were less severe than nonepistaxis bleeds (International Society on Thrombosis and Haemostasis major: 3.2% versus 20.7%; clinically relevant nonmajor: 64.7% versus 60.1%; minor: 32.1% versus 19.2%; P<0.001). Permanent drug discontinuation was similar following epistaxis versus nonepistaxis bleeding in patients with major (59.4% versus 53.6%; P=0.52) or clinically relevant nonmajor (32.5% versus 33.3%; P=0.70) bleeding but was significantly higher in patients with minor epistaxis versus other minor bleeds (33.3% versus 23.9%; P=0.001). Compared with warfarin, higher-dose edoxaban regimen had similar risk of epistaxis (hazard ratio [HR], 1.09 [95% CI, 0.95-1.26]), whereas lower-dose edoxaban regimen conferred reduced risk (HR, 0.73 [95% CI, 0.62-0.86]). Epistaxis was frequent, and despite being overall less severe than nonepistaxis bleeding, was associated with similar rates of anticoagulant discontinuation. Compared with warfarin, lower-dose edoxaban regimen reduced the risk of epistaxis by 27% whereas higher-dose edoxaban regimen had no effect. URL: https://clinicaltrials.gov; Unique Identifier: NCT00781391.

Feature screening for case-cohort studies in the presence of interval censoring

A great literature has been established for both feature screening under various situations and the analysis of case-cohort studies. Also several methods have been proposed for feature screening when one faces case-cohort studies but all of the existing methods apply only to right-censored failure time data. In this paper, we discuss feature screening for case-cohort studies in the presence of interval censoring, a type of censoring that occurs more generally and includes right censoring as a special case. For the problem, two methods, a model-based procedure and a model-free procedure, are proposed. The former, an inverse probability weighted joint likelihood screening approach, is developed under the proportional hazards model, the most commonly used model for failure time data analysis. The latter is a weighted smooth partial rank screening method that allows for both ultrahigh-dimensional covariates and covariate-dependent censoring. For the proposed methods, the sure screening properties are established under mild regularity conditions. An extensive simulation study is conducted to assess the performance of the proposed methods and indicates that they work well in practical situations.

Caries Incidence in School-Based Prevention Programs in the Presence of Interval Censoring.

School-based caries prevention can increase access to critical dental services and reduce oral health inequities. However, little is known regarding the incidence of dental caries in children participating in school caries prevention, and caries diagnosis is often interval censored. In this paper, we used data from a longitudinal, school-based, randomized clinical trial of minimally invasive treatments for dental caries to estimate the per-visit incidence rate and compare the hazard of dental caries in children receiving either silver diamine fluoride or glass ionomer dental sealants. To account for interval censoring, we used semiparametric transformation models for univariate failure time data and imputed caries incidence using G-imputation. There were 3040 children that met inclusion criteria for analysis, 1516 (49.9%) of which were randomly assigned to receive silver diamine fluoride and 1524 (50.1%) were assigned to receive glass ionomer dental sealants and atraumatic restorations. There were no differences in the hazard of caries between treatments (HR = 0.99, 95% CI = 0.72, 1.24), while children with caries at baseline had a significant increase in the hazard of new caries (HR = 2.54, 95% CI = 2.26, 2.83) compared to those that were caries free. The per-visit caries incidence ranged from 4.8 to 11.1 at the individual level and increased with each successive study observation. School-based caries prevention can positively affect caries incidence, and the results can be used to inform future program design and implementation.

A non-homogeneous alternating renewal process model for interval censoring

Abstract Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant. In this work, we introduce a model which allows for non-homogeneous behaviour in both cases. In particular, we outline a censoring mechanism based on a non-homogeneous alternating renewal process in which interval generation is assumed to be time-dependent, and we propose a Markov point process model for the underlying occurrence time distribution. We prove the existence of this process and derive the conditional distribution of the occurrence times given the intervals. We provide a framework within which the process can be accurately modelled, and subsequently compare our model to the homogeneous approach through a number of illustrative examples.

The Optimal Experimental Design for Exponentiated Frech’et Lifetime Products

In many manufacturing industries, the lifetime performance index CL is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to achieve a specified level of significance and test power for products with lifetimes following the Exponentiated Frech’et distribution. Since lifetime distribution is an asymmetrical probability distribution, this investigation is related to the topic of asymmetrical probability distributions and applications in various fields. When the termination time is fixed but the number of intervals is variable, the optimal number of inspection intervals and sample sizes yielding the minimized total experimental costs are determined and tabulated. When the termination time is varying, the optimal number of inspection intervals, sample sizes, and equal interval lengths achieving the minimum total experimental costs are determined and tabulated. Optimal parameter values are displayed in tabular form for feasible applications for users. Additionally, a practical example is provided to illustrate how this sampling design can be used to collect data by using the optimal setup of parameters, followed by a testing procedure to assess the capability of the production process.

Evaluating the impact of a trial of labor after cesarean section on labor duration: a retrospective cohort study

BackgroundCesarean section (C-section) rates are increasing globally, and repeated C-sections are associated with increased maternal morbidity. Trial of labor after C-section (TOLAC) is an approach to reduce the recurrence of C-sections. However, limited research exists on the impact of cesarean scars on labor duration in TOLAC, considering the termination of labor through C-section and selection bias. This study aimed to investigate the impact of cesarean scars on labor duration in TOLAC participants, accounting for potential confounding factors and biases.MethodsThis retrospective cohort study included 2,964 women who attempted vaginal birth at a single center in Japan from 2012 to 2021. The study categorized participants into TOLAC (n = 187) and non-TOLAC (n = 2,777) groups. Propensity scores were calculated based on 14 factors that could influence labor duration, and inverse probability of treatment weighting (IPTW) was applied. Cox proportional hazards regression analysis estimated hazard ratios (HRs) for labor duration, with and without IPTW adjustment. Sensitivity analyses used propensity score matching, bootstrapping, and interval censoring to address potential biases, including recall bias in the reported onset of labor.ResultsThe unadjusted HR for labor duration in the TOLAC group compared to the non-TOLAC group was 0.83 (95% CI: 0.70–0.98, P = 0.027), indicating a longer labor duration in the TOLAC group. After adjusting for confounding factors using IPTW, the HR was 0.98 (95% CI: 0.74–1.30, P = 0.91), suggesting no significant difference in labor duration between the groups. Sensitivity analyses using propensity score matching, bootstrapping, and interval censoring yielded consistent results. These findings suggested that the apparent association between TOLAC and longer labor duration was because of confounding factors rather than TOLAC itself.ConclusionsAfter adjusting for confounding factors and addressing potential biases, cesarean scars had a limited impact on labor duration in TOLAC participants. Maternal and fetal characteristics may have a more substantial influence on labor duration.

A stochastic ordering of multiple hypergeometric laws: Peakedness of category counts about half the population category sizes is symmetric unimodal in the sample size

Suppose X is a frequency vector that follows a central multiple hypergeometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We call the event where X satisfies a prespecified set of symmetrical—but otherwise arbitrary—interval constraints in each component a symmetric core event. We show that the probability of any symmetric core event—in other words, the multivariate peakedness in the sense of Birnbaum (1948) and Tong (1988)—is symmetric unimodal as a function of the sample size. Two proofs are given. The shorter one relies on a convolution property of ultra-log-concave sequences, which implies that the sequence of peakedness values is log-concave (even for asymmetric rectangular events). The longer, though more elementary, proof does not rely on notions of log-concavity. To illustrate the use of symmetric core events, we analyze a simple yet interesting wager in a sequential card game. Finally, we indicate that the unimodality result for symmetric core events is pivotal in proving a certain variance reduction inequality involving multinomial frequencies subject to arbitrary interval censoring.

Comparison of Time and Rate of Achieving Minimal Clinically Important Difference: Robotic Versus Manual Unicompartmental Knee Arthroplasty.

Robotics in unicompartmental knee arthroplasty (UKA) continues to increase with the ever-growing demand to use technology in the surgical setting. However, no studies have used minimal clinically important difference (MCID) to compare patient-reported outcome measures (PROMs) between robotic UKA (rUKA) and manual UKA (mUKA). This study aimed to compare the rate of achieving MCID for improvement (MCID-I) and worsening (MCID-W) and the time to achieving MCID. We conducted a retrospective analysis of robotic and manual UKAs performed between 2016 and 2022. Preoperative and postoperative Patient-Reported Outcomes Measurement Information System (PROMIS) Global Physical, PROMIS Physical Function Short-Form 10a (PF-10a), and Knee Injury and Osteoarthritis Outcome Score-Physical Function Short-Form (KOOS-PS) scores were collected. Patients were stratified on reaching MCID-I, MCID-W, or "no notable change" (score between MCID-W and MCID-I). Survival curves with and without interval censoring were used to assess the time to achieving the MCID. Log-rank and weighted log-rank tests were used to compare groups. A total of 256 UKAs (64 robotic and 192 manual) were analyzed. No differences were observed in the proportion of patients achieving MCID-I or MCID-W across all three PROMs. Similarly, median time to achieving MCID showed no significant differences between rUKA and mUKA for PROMIS Global Physical (3.3 versus 4.9 months, P = 0.44), PROMIS PF-10a (7.7 versus 8.3 months, P = 0.93), and KOOS-PS (3.0 versus 6.0 months, P = 0.055) scores, both with and without interval censoring. This study indicates that rUKA and mUKA exhibit comparable rates of achieving MCID-I and MCID-W, along with similar median time to reach MCID. These findings offer valuable patient-centric insights into the effectiveness of rUKA. Additional studies evaluating the long-term outcomes of rUKA are needed to determine its long-term advantages. Level III, retrospective comparative study.

Cause-specific hazard Cox models with partly interval censoring - Penalized likelihood estimation using Gaussian quadrature.

The cause-specific hazard Cox model is widely used in analyzing competing risks survival data, and the partial likelihood method is a standard approach when survival times contain only right censoring. In practice, however, interval-censored survival times often arise, and this means the partial likelihood method is not directly applicable. Two common remedies in practice are (i) to replace each censoring interval with a single value, such as the middle point; or (ii) to redefine the event of interest, such as the time to diagnosis instead of the time to recurrence of a disease. However, the mid-point approach can cause biased parameter estimates. In this article, we develop a penalized likelihood approach to fit semi-parametric cause-specific hazard Cox models, and this method is general enough to allow left, right, and interval censoring times. Penalty functions are used to regularize the baseline hazard estimates and also to make these estimates less affected by the number and location of knots used for the estimates. We will provide asymptotic properties for the estimated parameters. A simulation study is designed to compare our method with the mid-point partial likelihood approach. We apply our method to the Aspirin in Reducing Events in the Elderly (ASPREE) study, illustrating an application of our proposed method.

Regression trees for interval‐censored failure time data based on censoring unbiased transformations and pseudo‐observations

AbstractInterval‐censored data arise when a failure process is under intermittent observation and failure status is only known at assessment times. We consider the development of predictive algorithms when training samples involve interval censoring. Using censoring unbiased transformations and pseudo‐observations, we define observed data loss functions, which are unbiased estimates of the corresponding complete data loss functions. We show that regression trees based on these loss functions can recover the tree structure and yield good predictive accuracy. An application is given to a study involving individuals with psoriatic arthritis where the aim is to identify genetic markers useful for the prediction of axial disease within 10 years of a baseline assessment.

Bayesian estimation of the mean time between failures of subsystems with different causes using interval‐censored system maintenance data

AbstractEnsuring an acceptable level of reliability stands as a primary imperative for any mission‐focused operation since it serves as a critical determinant of success. Inadequate reliability can lead to severe repercussions, including substantial expenses for repairs and replacements, missed opportunities, service disruptions, and in the worst cases, safety violations and human casualties. Within national defense organizations such as the USAF, the precise assessment and maintenance of system reliability play a pivotal role in ensuring the success of mission‐critical operations. In this research, our primary objective is to model the reliability of repairable subsystems within the framework of competing and complementary risks. Subsequently, we construct the overall reliability of the entire repairable system, utilizing day‐to‐day group‐censored maintenance data from two identical aircraft systems. Assuming that the lifetimes of subsystems follow non‐identical exponential distributions, it is theoretically justified that the system reliability can be modeled by homogeneous Poisson processes even though the number of subsystems of any particular type is unknown and the temporal order of multiple subsystem failures within a given time interval is uncertain due to interval censoring. Using the proposed model, we formulate the likelihood function for the mean time between failures of subsystems with different causes, and subsequently establish an inferential procedure for the model parameters. Given a considerable number of parameters to estimate, we explore the efficacy of a Bayesian approach, treating the contractor‐supplied estimates as the hyperparameters of prior distributions. This approach mitigates potential model uncertainty as well as the practical limitation of a frequentist‐based approach. It also facilitates continuous updates of the estimates as new maintenance data become available. Finally, the entire inferential procedures were implemented in Microsoft Excel so that it is easy for any reliability practitioner to use without the need to learn sophisticated programming languages. Thus, this research supports an ongoing, real‐time assessment of the overall mission reliability and helps early detection of any subsystem whose reliability is below the threshold level.

Bayesian reliability acceptance sampling plans under interval censoring

. This work considers Bayesian reliability acceptance sampling plan (RASP) under interval censoring. It is considered that the consumer and manufacturer agree on a common lifetime distribution of the product. However, they differ in their assessment of the prior distributions and utility functions because of the adversarial nature of the consumer and manufacturer, but the manufacturer knows the consumer’s utility and prior. The consumer accepts or rejects a lot of products based on his/her own priors about the quality of the product and a utility function. If the consumer rejects the lot, the manufacturer gives additional information on lifetime based on a life test to update the consumer’s belief. The consumer decides on accepting or rejecting the lot based on updated information. The life test is conducted under an interval censoring scheme, where the decision on acceptance or rejection of the lot can be taken sequentially at pre-specified inspection times. The manufacturer’s task is to determine the optimal interval-censoring life testing plan which maximizes his/her utility. Last, we discuss a methodology where the manufacturer does not require knowledge of the consumer’s utility function and prior distribution for planning the life test.

Estimating disease transmission in a closed population under repeated testing

Abstract The article presents a novel statistical framework for COVID-19 transmission monitoring and control, which was developed and deployed at The Ohio State University main campus in Columbus during the Autumn term of 2020. Our approach effectively handles prevalence data with interval censoring and explicitly incorporates changes in transmission dynamics and human behaviour. To illustrate the methodology’s usefulness, we apply it to both synthetic and actual student SARS-CoV-2 testing data collected at the OSU Columbus campus in late 2020.

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.

Sex differences in post-acute neurological sequelae of SARS-CoV-2 and symptom resolution in adults after coronavirus disease 2019 hospitalization: an international multi-centre prospective observational study.

Although it is known that coronavirus disease 2019 can present with a range of neurological manifestations and in-hospital complications, sparse data exist on whether these initial neurological symptoms of coronavirus disease 2019 are closely associated with post-acute neurological sequelae of SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2; PANSC) and whether female versus male sex impacts symptom resolution. In this international, multi-centre, prospective, observational study across 407 sites from 15 countries (30 January 2020 to 30 April 2022), we report the prevalence and risk factors of PANSC among hospitalized adults and investigate the differences between males and females on neurological symptom resolution over time. PANSC symptoms included altered consciousness/confusion, fatigue/malaise, anosmia, dysgeusia and muscle ache/joint pain, on which information was collected at index hospitalization and during follow-up assessments. The analysis considered a time to the resolution of individual and all neurological symptoms. The resulting times were modelled by Weibull regression, assuming mixed-case interval censoring, with sex and age included as covariates. The model results were summarized as cumulative probability functions and age-adjusted and sex-adjusted median times to resolution. We included 6862 hospitalized adults with coronavirus disease 2019, who had follow-up assessments. The median age of the participants was 57 years (39.2% females). Males and females had similar baseline characteristics, except that more males (versus females) were admitted to the intensive care unit (30.5 versus 20.3%) and received mechanical ventilation (17.2 versus 11.8%). Approximately 70% of patients had multiple neurological symptoms at the first follow-up (median = 102 days). Fatigue (49.9%) and myalgia/arthralgia (45.2%) were the most prevalent symptoms of PANSC at the initial follow-up. The reported prevalence in females was generally higher (versus males) for all symptoms. At 12 months, anosmia and dysgeusia were resolved in most patients, although fatigue, altered consciousness and myalgia remained unresolved in >10% of the cohort. Females had a longer time to the resolution (5.2 versus 3.4 months) of neurological symptoms at follow-up for those with more than one neurological symptom. In the multivariable analysis, males were associated with a shorter time to the resolution of symptoms (hazard ratio = 1.53; 95% confidence interval = 1.39-1.69). Intensive care unit admission was associated with a longer time to the resolution of symptoms (hazard ratio = 0.68; 95% confidence interval = 0.60-0.77). Post-discharge stroke was uncommon (0.3% in females and 0.5% in males). Despite the methodological challenges involved in the collection of survey data, this international multi-centre prospective cohort study demonstrated that PANSC following index hospitalization was high. Symptom prevalence was higher and took longer to resolve in females than in males. This supported the fact that while males were sicker during acute illness, females were disproportionately affected by PANSC.

Development and External Validation of Models to Predict Need for Nursing Home Level of Care in Community-Dwelling Older Adults With Dementia

Most older adults living with dementia ultimately need nursing home level of care (NHLOC). To develop models to predict need for NHLOC among older adults with probable dementia using self-report and proxy reports to aid patients and family with planning and care management. This prognostic study included data from 1998 to 2016 from the Health and Retirement Study (development cohort) and from 2011 to 2019 from the National Health and Aging Trends Study (validation cohort). Participants were community-dwelling adults 65 years and older with probable dementia. Data analysis was conducted between January 2022 and October 2023. Candidate predictors included demographics, behavioral/health factors, functional measures, and chronic conditions. The primary outcome was need for NHLOC defined as (1) 3 or more activities of daily living (ADL) dependencies, (2) 2 or more ADL dependencies and presence of wandering/need for supervision, or (3) needing help with eating. A Weibull survival model incorporating interval censoring and competing risk of death was used. Imputation-stable variable selection was used to develop 2 models: one using proxy responses and another using self-responses. Model performance was assessed by discrimination (integrated area under the receiver operating characteristic curve [iAUC]) and calibration (calibration plots). Of 3327 participants with probable dementia in the Health and Retirement Study, the mean (SD) age was 82.4 (7.4) years and 2301 (survey-weighted 70%) were female. At the end of follow-up, 2107 participants (63.3%) were classified as needing NHLOC. Predictors for both final models included age, baseline ADL and instrumental ADL dependencies, and driving status. The proxy model added body mass index and falls history. The self-respondent model added female sex, incontinence, and date recall. Optimism-corrected iAUC after bootstrap internal validation was 0.72 (95% CI, 0.70-0.75) in the proxy model and 0.64 (95% CI, 0.62-0.66) in the self-respondent model. On external validation in the National Health and Aging Trends Study (n = 1712), iAUC in the proxy and self-respondent models was 0.66 (95% CI, 0.61-0.70) and 0.64 (95% CI, 0.62-0.67), respectively. There was excellent calibration across the range of predicted risk. This prognostic study showed that relatively simple models using self-report or proxy responses can predict need for NHLOC in community-dwelling older adults with probable dementia with moderate discrimination and excellent calibration. These estimates may help guide discussions with patients and families in future care planning.

Predicting the Temperature-Driven Development of Stage-Structured Insect Populations with a Bayesian Hierarchical Model

The management of forest pests relies on an accurate understanding of the species’ phenology. Thermal performance curves (TPCs) have traditionally been used to model insect phenology. Many such models have been proposed and fitted to data from both wild and laboratory-reared populations. Using Hamiltonian Monte Carlo for estimation, we implement and fit an individual-level, Bayesian hierarchical model of insect development to the observed larval stage durations of a population reared in a laboratory at constant temperatures. This hierarchical model handles interval censoring and temperature transfers between two constant temperatures during rearing. It also incorporates individual variation, quadratic variation in development rates across insects’ larval stages, and “flexibility” parameters that allow for deviations from a parametric TPC. Using a Bayesian method ensures a proper propagation of parameter uncertainty into predictions and provides insights into the model at hand. The model is applied to a population of eastern spruce budworm (Choristoneura fumiferana) reared at 7 constant temperatures. Resulting posterior distributions can be incorporated into a workflow that provides prediction intervals for the timing of life stages under different temperature regimes. We provide a basic example for the spruce budworm using a year of hourly temperature data from Timmins, Ontario, Canada. Supplementary materials accompanying this paper appear on-line.

Variable Selection for Length-Biased and Interval-Censored Failure Time Data

Length-biased failure time data occur often in various biomedical fields, including clinical trials, epidemiological cohort studies and genome-wide association studies, and their analyses have been attracting a surge of interest. In practical applications, because one may collect a large number of candidate covariates for the failure event of interest, variable selection becomes a useful tool to identify the important risk factors and enhance the estimation accuracy. In this paper, we consider Cox’s proportional hazards model and develop a penalized variable selection technique with various popular penalty functions for length-biased data, in which the failure event of interest suffers from interval censoring. Specifically, a computationally stable and reliable penalized expectation-maximization algorithm via two-stage data augmentation is developed to overcome the challenge in maximizing the intractable penalized likelihood. We establish the oracle property of the proposed method and present some simulation results, suggesting that the proposed method outperforms the traditional variable selection method based on the conditional likelihood. The proposed method is then applied to a set of real data arising from the Prostate, Lung, Colorectal and Ovarian cancer screening trial. The analysis results show that African Americans and having immediate family members with prostate cancer significantly increase the risk of developing prostate cancer, while having diabetes exhibited a significantly lower risk of developing prostate cancer.

Abstract 17590: Association of Intensive vs Standard Blood Pressure Lowering With 1-year and 2-year Changes in Cardiac Biomarker Levels: Findings From SPRINT

Background: The Systolic Blood Pressure Intervention Trial (SPRINT) demonstrated that intensive systolic blood pressure (SBP) lowering was associated with marked reductions in cardiovascular disease (CVD) endpoints. We recently reported that intensive SBP lowering was also associated with a small increase in high-sensitivity cardiac troponin T (hs-cTnT) and a large decrease in N-terminal pro-B-type natiuretic peptide (NT-proBNP) over 1-year. However, data on longer term biomarker changes with intensive versus standard SBP lowering have not been previously reported. Methods: hs-cTnT and NT-proBNP were measured at baseline, 1 year, and 2 years from stored specimens in SPRINT participants. Changes in biomarkers were evaluated continuously on the log scale with interval censoring of participants with CVD events. The effect of intensive SBP lowering on biomarker changes was assessed using linear regression models with treatment effects reported as geometric mean ratios. Results: Of 9,361 SPRINT participants, hs-cTnT and NT-proBNP were measured in 8,828 (baseline), 7,887 (Year 1), and 7,463 (Year 2) free of CVD events. Intensive SBP lowering led to a 3% increase in log-transformed hs-cTnT from baseline to Year 1, but there was no significant change observed from baseline to Year 2. In contrast, intensive SBP lowering led to a consistent 10% decrease in NT-proBNP from baseline to Year 1 and to Year 2. NT-proBNP levels increased slightly from Year 1 to Year 2 in both treatment arms such that the 1-Year treatment effect for intensive SBP lowering was maintained to Year 2 (see Table). Conclusions: Intensive SBP lowering was associated with a transient, modest increase in hscTnT at Year 1 that was no longer present at Year 2. In contrast, intensive SBP lowering was associated with a persistent reduction in NT-proBNP at both 1 and 2 years follow-up. These findings highlight the complex responses of cardiac biomarkers to intensive SBP lowering.

Survival analysis with censored data: a further twist on ignorability conditions

A key assumption for the application of methods concerning censored data is that the random nature of the censoring mechanism should be ignorable when making likelihood-based inferences. The constant-sum property is an ignorability assumption that is critical for the correct use of a simplified version of the likelihood function and for the identifiability of the survival function [Oller R, Gómez G, Calle ML. Interval censoring: identifiability and the constant-sum property. Biometrika. 2007;94(1):61–70]. It has been proven to be weaker than the assumption of independence between the lifetime variable and the assessment process that leads to censored data. An important caveat is that the theoretical framework established in the class of constant-sum censoring models requires full knowledge of the support of the lifetime variable. In the present work we investigate the consequences of a wrong specification of the support. One might naively expect that this information is not necessary and that, for instance, the estimation of the survival function would assign null or almost null probabilities to regions outside the support. We reveal via examples that this premise is generally true but there are also several exceptions. To shed light on this issue, we introduce a new ignorability condition that extends the constant-sum property and removes the knowledge of the support from the equation. We also show that the independence assumption is stronger than the new extended constant-sum condition.