Shared Frailty Term Research Articles

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.

Flexible modelling of a bivariate degradation process with a shared frailty and an application to fatigue crack data

Examples of units with two performance characteristics that degrade over time are ubiquitous in reliability engineering. In this article, we develop a flexible model for bivariate degradation data pertaining to units in which the degradation processes corresponding to the performance characteristics are likely dependent on each other. The proposed model has two features: the degradation processes are marginally modelled by gamma processes, and the dependence between them is modelled by a shared frailty term that is assumed to follow the generalized gamma distribution. We show that this model is far more flexible and efficient than many of the commonly used models for capturing dependence between the performance characteristics. A computational technique for the maximum likelihood estimation, based on Monte Carlo simulation, is developed for the proposed model. Then, the method of estimation is evaluated through an elaborate Monte Carlo simulation study. The joint reliability function of the unit with two performance characteristics and its estimation are also discussed in this general setting. The proposed model is extended to the case of multiple performance characteristics. Finally, a case study is presented in which a real degradation data pertaining to fatigue cracks is analysed through the proposed model to demonstrate its usefulness.

Indirect Treatment Comparison of First-Line CDK4/6-Inhibitors in Post-Menopausal Patients with HR+/HER2- Metastatic Breast Cancer.

Background: CDK4/6-inhibitors have demonstrated similar efficacy and are considered an effective first-line endocrine treatment of patients with hormone-receptor positive (HR+)/human-epidermal-growth-factor-receptor-2 negative (HER2-) metastatic breast cancer (MBC) in the endpoint of progression-free survival (PFS). Amongst these, palbociclib was first to achieve regulatory approval, followed subsequently by ribociclib and abemaciclib. However, recent updates of overall survival (OS) showed inconsistencies in the OS benefit for palbociclib compared with the other two CDK4/6-inhibitors. With the lack of head-to-head comparison studies, our study sought to compare indirect survival outcomes between CDK4/6-inhibitors in this setting using a novel reconstructive algorithm. Methods: Phase III randomized trials comparing first-line aromatase inhibitor with/without a CDK4/6-inhibitor in post-menopausal patients with HR+/HER2- MBC were identified through systemic review and literature search of online archives of published manuscripts and conference proceedings. A graphical reconstructive algorithm was utilized to retrieve time-to-event data from reported Kaplan-Meier OS and PFS plots to allow for comparison of survival outcomes. Survival analyses were conducted with Cox proportional-hazards model with a shared-frailty term. Results: Three randomized phase III trials-PALOMA-2, MONALEESA-2 and MONARCH-3-comprising 1827 patients were included. Indirect pairwise comparisons of all CDK4/6-inhibitors showed no significant PFS differences (all p > 0.05). Likewise, indirect treatment comparison between ribociclib vs. palbociclib (one-stage: HR = 0.903, 95%-CI: 0.746-1.094, p = 0.297), abemaciclib vs. palbociclib (one-stage: HR = 0.843, 95%-CI: 0.690-1.030, p = 0.094) and abemaciclib vs. ribociclib (one-stage: HR = 0.933, 95%-CI: 0.753-1.157, p = 0.528) failed to demonstrate a significant OS difference. Conclusions: Findings from this indirect treatment comparison suggest no significant PFS or OS differences between CDK4/6-inhibitors in post-menopausal patients with HR+/HER2- MBC.

The Pareto type I joint frailty-copula model for clustered bivariate survival data

Clustered bivariate survival data arise in various fields, such as biology and medicine, when individuals in a dataset are clustered and exhibit two survival outcomes. Recently, the joint frailty-copula model was proposed to analyze clustered bivariate survival outcomes by accommodating the between-cluster heterogeneity via a shared frailty term. In this model, researchers fitted the baseline hazard functions via the nonparametric model, the spline model, or the Weibull model. However, when a population has extremely large survival time, the baseline hazard functions are better modeled by a heavy-tailed distribution. In this paper, we adopt the Pareto type I distribution for the joint frailty-copula model, which is one of the most popular heavy-tailed distributions. We show that the moments of the Pareto type I joint frailty copula model diverge to infinity owing to the heavy right-tail. We develop statistical inference methods based on three types of censoring schemes: (i) bivariate random censoring, (ii) semi-competing risks, and (iii) competing risks. We develop maximum likelihood estimation procedures, and make our computational tools available for users. Simulations are performed to check the accuracy of the proposed method. We finally analyze a real dataset for illustration.

Correction to 'Bayesian inference reveals positive but subtle effects of experimental fishery closures on marine predator demographics'.

Correction to 'Bayesian inference reveals positive but subtle effects of experimental fishery closures on marine predator demographics'.

Assessment of preparation time and 1-year Invisalign aligner attachment survival using flowable and packable composites:

To compare preparation time and 1-year Invisalign aligner attachment survival between a flowable composite (FC) and a packable composite (PC). Fifty-five participants (13 men and 42 women, mean age ± SD: 24.2 ± 5.9 years) were included in the study. Ipsilateral quadrants (ie, maxillary and mandibular right, or vice versa) of attachments were randomly assigned to the FC group (Filtek Z350XT Flowable Restorative) and the PC group (Filtek Z350XT Universal Restorative) by tossing a coin. The primary outcome was preparation time. The secondary outcome was time to the first damage of an attachment. Preparation times were compared using the paired t-test, and the survival data were analyzed by the Cox proportional hazards model with a shared frailty term, with α = .05. The preparation times were significantly shorter with the FC (6.22 ± 0.22 seconds per attachment) than with the PC (32.83 ± 2.16 seconds per attachment; P < .001). The attachment damage rates were 14.79% for the FC and 9.70% for the PC. According to the Cox models, attachment damage was not significantly affected by the attachment material, sex, arch, tooth location, attachment type, presence of overbite, or occurrence of tooth extraction. The use of a FC may save time as compared with the use of a PC. With regard to attachment survival, there was no significant difference between the two composites. None of the covariates of attachment materials (sex, arch, tooth location, attachment type, presence of overbite, oir occurrence of tooth extraction) affected attachment damage.

Fitting a shared frailty illness-death model to left-truncated semi-competing risks data to examine the impact of education level on incident dementia

BackgroundSemi-competing risks arise when interest lies in the time-to-event for some non-terminal event, the observation of which is subject to some terminal event. One approach to assessing the impact of covariates on semi-competing risks data is through the illness-death model with shared frailty, where hazard regression models are used to model the effect of covariates on the endpoints. The shared frailty term, which can be viewed as an individual-specific random effect, acknowledges dependence between the events that is not accounted for by covariates. Although methods exist for fitting such a model to right-censored semi-competing risks data, there is currently a gap in the literature for fitting such models when a flexible baseline hazard specification is desired and the data are left-truncated, for example when time is on the age scale. We provide a modeling framework and openly available code for implementation.MethodsWe specified the model and the likelihood function that accounts for left-truncated data, and provided an approach to estimation and inference via maximum likelihood. Our model was fully parametric, specifying baseline hazards via Weibull or B-splines. Using simulated data we examined the operating characteristics of the implementation in terms of bias and coverage. We applied our methods to a dataset of 33,117 Kaiser Permanente Northern California members aged 65 or older examining the relationship between educational level (categorized as: high school or less; trade school, some college or college graduate; post-graduate) and incident dementia and death.ResultsA simulation study showed that our implementation provided regression parameter estimates with negligible bias and good coverage. In our data application, we found higher levels of education are associated with a lower risk of incident dementia, after adjusting for sex and race/ethnicity.ConclusionsAs illustrated by our analysis of Kaiser data, our proposed modeling framework allows the analyst to assess the impact of covariates on semi-competing risks data, such as incident dementia and death, while accounting for dependence between the outcomes when data are left-truncated, as is common in studies of aging and dementia.

Risk-adjusted CUSUM control charts for shared frailty survival models with application to hip replacement outcomes: a study using the NJR dataset

BackgroundContinuous monitoring of surgical outcomes after joint replacement is needed to detect which brands’ components have a higher than expected failure rate and are therefore no longer recommended to be used in surgical practice. We developed a monitoring method based on cumulative sum (CUSUM) chart specifically for this application.MethodsOur method entails the use of the competing risks model with the Weibull and the Gompertz hazard functions adjusted for observed covariates to approximate the baseline time-to-revision and time-to-death distributions, respectively. The correlated shared frailty terms for competing risks, corresponding to the operating unit, are also included in the model. A bootstrap-based boundary adjustment is then required for risk-adjusted CUSUM charts to guarantee a given probability of the false alarm rates. We propose a method to evaluate the CUSUM scores and the adjusted boundary for a survival model with the shared frailty terms. We also introduce a unit performance quality score based on the posterior frailty distribution. This method is illustrated using the 2003-2012 hip replacement data from the UK National Joint Registry (NJR).ResultsWe found that the best model included the shared frailty for revision but not for death. This means that the competing risks of revision and death are independent in NJR data. Our method was superior to the standard NJR methodology. For one of the two monitored components, it produced alarms four years before the increased failure rate came to the attention of the UK regulatory authorities. The hazard ratios of revision across the units varied from 0.38 to 2.28.ConclusionsAn earlier detection of failure signal by our method in comparison to the standard method used by the NJR may be explained by proper risk-adjustment and the ability to accommodate time-dependent hazards. The continuous monitoring of hip replacement outcomes should include risk adjustment at both the individual and unit level.

Early Post-treatment Prostate-specific Antigen at 4 Weeks and Abiraterone and Enzalutamide Treatment for Advanced Prostate Cancer: An International Collaborative Analysis

BackgroundDeclines in prostate-specific antigen (PSA) levels at 12wk are used to evaluate treatment response in metastatic castration-resistant prostate cancer (mCRPC). PSA fall by ≥30% at 4wk (PSA4w30) has been reported to be associated with better outcome in a single-centre cohort study. ObjectiveTo evaluate clinical relevance of early PSA decline in mCRPC patients treated with next-generation hormonal treatments (NGHTs) such as abiraterone and enzalutamide. Design, setting, and participantsThis was a retrospective multicentre analysis. Eligible patients received NGHT for mCRPC between 6 January 2006 and 31 December 2017 in 13 cancer centres worldwide, and had PSA levels assessed at baseline and at 4 and/or 12wk after treatment. PSA response was defined as a ≥30% decline (progression as a ≥25% increase) from baseline. Outcome measurements and statistical analysisAssociation with overall survival (OS) was analysed using landmark multivariable Cox regression adjusting for previous chemotherapy, including cancer centre as a shared frailty term. Results and limitationsWe identified 1358 mCRPC patients treated with first-line NGHT (1133 had PSA available at 4wk, and 948 at both 4 and 12wk). Overall, 583 (52%) had a PSA4w30; it was associated with longer OS (median: 23; 95% confidence interval [CI]: 21–25) compared with no change (median: 17; 95% CI: 15–18) and progression (median: 13; 95% CI: 10–15). A PSA12w30 was associated with lower mortality (median OS 22 vs 14; hazard ratio=0.57; 95% CI=0.48–0.67; p<0.001). PSA4w30 strongly correlated with PSA12w30 (ρ=0.91; 95% CI=0.90–0.92; p<0.001). In total, 432/494 (87%) with a PSA4w30 achieved a PSA12w30. Overall, 11/152 (7%) patients progressing at 4wk had a PSA12w30 (1% of the overall population). ConclusionsPSA changes in the first 4wk of NGHT therapies are strongly associated with clinical outcome from mCRPC and can help guide early treatment switch decisions. Patient summaryProstate-specific antigen changes at 4wk after abiraterone/enzalutamide treatment are important to determine patients’ outcome and should be taken into consideration in clinical practice.

The effect of dose on the antimalarial efficacy of artesunate-mefloquine against Plasmodium falciparum malaria: a protocol for systematic review and individual patient data (IPD) meta-analysis.

IntroductionAntimalarial posology based on weight bands leaves patients at the margins vulnerable to receiving either lower or higher weight-adjusted (mg/kg) dosages. This article aims to describe the protocol for systematic review and individual patient meta-analysis (MA) for a study of the distribution of artesunate and mefloquine dosage administered in patients with uncomplicated Plasmodium falciparum malaria treated with an artesunate-mefloquine (AS-MQ) regimen. Relationship between mg/kg dose and therapeutic outcomes will be assessed through a one-stage individual participant data (IPD) MA.Methods and analysisTherapeutic efficacy studies with the AS-MQ regimen will be identified by searching the following databases: PUBMED, EMBASE and Web of Science. The corresponding authors of the relevant studies will be requested to share the IPD for the purpose of this MA to a secured repository. All available studies will be standardised using a common data management protocol and pooled into a single database. The relationship between mg/kg dosage and treatment failures will be assessed using a Cox regression model with study sites considered as a shared frailty term. Safety parameters will be explored where available.Ethics and disseminationThis IPD MA met the criteria for waiver of ethical review as defined by the Oxford Tropical Research Ethics Committee as the research consisted of secondary analysis of existing anonymous data. The results of this analysis will be disseminated at conferences, WorldWide Antimalarial Resistance Network website and any peer-reviewed publication arising will be made open source.PROSPERO registration numberCRD42018103776.

A Semi-parametric Transformation Frailty Model for Semi-competing Risks Survival Data.

In the analysis of semi-competing risks data interest lies in estimation and inference with respect to a so-called non-terminal event, the observation of which is subject to a terminal event. Multi-state models are commonly used to analyse such data, with covariate effects on the transition/intensity functions typically specified via the Cox model and dependence between the non-terminal and terminal events specified, in part, by a unit-specific shared frailty term. To ensure identifiability, the frailties are typically assumed to arise from a parametric distribution, specifically a Gamma distribution with mean 1.0 and variance, say, σ2. When the frailty distribution is misspecified, however, the resulting estimator is not guaranteed to be consistent, with the extent of asymptotic bias depending on the discrepancy between the assumed and true frailty distributions. In this paper, we propose a novel class of transformation models for semi-competing risks analysis that permit the non-parametric specification of the frailty distribution. To ensure identifiability, the class restricts to parametric specifications of the transformation and the error distribution; the latter are flexible, however, and cover a broad range of possible specifications. We also derive the semi-parametric efficient score under the complete data setting and propose a non-parametric score imputation method to handle right censoring; consistency and asymptotic normality of the resulting estimators is derived and small-sample operating characteristics evaluated via simulation. Although the proposed semi-parametric transformation model and non-parametric score imputation method are motivated by the analysis of semi-competing risks data, they are broadly applicable to any analysis of multivariate time-to-event outcomes in which a unit-specific shared frailty is used to account for correlation. Finally, the proposed model and estimation procedures are applied to a study of hospital readmission among patients diagnosed with pancreatic cancer.

경쟁위험 생존자료에 대한 결합 프레일티모형

Competing-risks events are often observed in a clustered clinical study such as a multi-center clinical trial. We propose a joint modelling approach via a shared frailty term for competing risks survival data from a cluster. For the inference we use the hierarchical likelihood (or h-likelihood), which avoids an intractable integration. We derive the corresponding h-likelihood procedure. The proposed method is illustrated via the analysis of a practical data set.

Risk for Child Maltreatment Among Infants Discharged From a Neonatal Intensive Care Unit

Studies suggest that neonatal illness may cause increased risk for child maltreatment (CM), but these findings may be biased by observed and unobserved confounding factors (social, family, and maternal characteristics) including increased surveillance by health care providers. This study expands on previous research by examining and controlling for these potential study biases and confounders using a sibling discordance retrospective cohort study design. Infants born in a Level IV neonatal intensive care unit (NICU) were matched with non-NICU born sibling controls. Cox proportional hazard models with shared frailty terms were used to account for clustering and heterogeneity in CM survival time (time to CM event). Potentially key covariates were selected using the directed acyclic graph approach, and surveillance reports were identified and systematically included or excluded from analyses. Managing these sources of bias reduced but did not eliminate the association between neonatal illness and CM report risk. Risk was especially high during the first year of the NICU infant's life and among families with multiple well-known CM risk factors.

Randomized Trial of Partial vs. Stepwise Caries Removal

This randomized, multicenter clinical trial evaluated the effectiveness of 2 treatments for deep caries lesions — partial caries removal (PCR) and stepwise excavation (SW) — with respect to the primary outcome of pulp vitality for a 3-year follow-up period. Inclusion criteria were as follows: patients with permanent molars presenting deep caries lesions (lesion affecting ≥ 1/2 of the dentin on radiographic examination), positive response to a cold test, absence of spontaneous pain, negative sensitivity to percussion, and absence of periapical lesions (radiographic examination). Teeth randomly assigned to PCR (test) received incomplete caries removal and filling in a single session. Outcome success was evaluated by assessment of pulp vitality, determined by pulp sensitivity to a cold test and the absence of periapical lesions. Data were analyzed by a Weibull regression model with shared frailty term (survival analysis). At baseline, 299 treatments were executed: PCR, 152 and SW, 147. By the end of the 3-year follow-up period, 213 teeth had been evaluated. Adjusted survival rates were 91% for PCR and 69% for SW (p = 0.004). These results suggest that there is no need to re-open a cavity and perform a second excavation for pulp vitality to be preserved (Clinical trials registration NCT00887952).

Sample size in cluster‐randomized trials with time to event as the primary endpoint

In cluster-randomized trials, groups of individuals (clusters) are randomized to the treatments or interventions to be compared. In many of those trials, the primary objective is to compare the time for an event to occur between randomized groups, and the shared frailty model well fits clustered time-to-event data. Members of the same cluster tend to be more similar than members of different clusters, causing correlations. As correlations affect the power of a trial to detect intervention effects, the clustered design has to be considered in planning the sample size. In this publication, we derive a sample size formula for clustered time-to-event data with constant marginal baseline hazards and correlation within clusters induced by a shared frailty term. The sample size formula is easy to apply and can be interpreted as an extension of the widely used Schoenfeld's formula, accounting for the clustered design of the trial. Simulations confirm the validity of the formula and its use also for non-constant marginal baseline hazards. Findings are illustrated on a cluster-randomized trial investigating methods of disseminating quality improvement to addiction treatment centers in the USA.

Survival analysis with clustered observations of orthodontic brackets

Failures in the bonding of dental bracket are a big concern for orthodontists. Clinical experience suggests that some patients are more prone than others to experience failures. Therefore, it can be expected that in statistical analysis of orthodontic bracket failures, the usual assumption of independence between the observations is violated. An approach to overcome this problem is to apply the frailty model, in which the association between failure times is modelled with a random-effect term (i.e. frailty). We postulated that brackets of the same subject share the same frailty, that is, a latent common group effect, due to some unknown or unobserved covariates.The aim of this study was to investigate possible risk factors related to bracket failure using Cox proportional hazards model with a shared frailty term and to compare the results with those obtained using a basic Cox proportional hazards model.Survival data for 1677 brackets were obtained from a cohort of 54 females (mean age +/- SD: 13.3+/-4.8 yrs) and 46 males (mean age +/-SD: 13.1+/-3.8 yrs) over a eight-year period. Age, gender, vertical craniofacial morphology and anatomical location of brackets were entered into Cox models as covariates. The findings indicated that bracket failure was significantly affected by tooth position within the dental arch, with the highest failure risk in maxillary posterior region. Age, gender and vertical craniofacial morphology did not affect bracket failure. A Cox proportional hazards model with a shared frailty term represents a useful approach for modelling orthodontic bracket failures.