A method for determining groups in cumulative incidence curves in competing risk data.

The cumulative incidence function is the standard method for estimating the marginal probability of a given event in the presence of competing risks. One basic but important goal in the analysis of competing risk data is the comparison of these curves, for which limited literature exists. We proposed a new procedure that lets us not only test the equality of these curves but also group them if they are not equal. The proposed method allows determining the composition of the groups as well as an automatic selection of their number. Simulation studies show the good numerical behavior of the proposed methods for finite sample size. The applicability of the proposed method is illustrated using real data.

Joint modeling of longitudinal and competing-risk data using cumulative incidence functions for the failure submodels accounting for potential failure cause misclassification through double sampling.

Most of the literature on joint modeling of longitudinal and competing-risk data is based on cause-specific hazards, although modeling of the cumulative incidence function (CIF) is an easier and more direct approach to evaluate the prognosis of an event. We propose a flexible class of shared parameter models to jointly model a normally distributed marker over time and multiple causes of failure using CIFs for the survival submodels, with CIFs depending on the "true" marker value over time (i.e., removing the measurement error). The generalized odds rate transformation is applied, thus a proportional subdistribution hazards model is a special case. The requirement that the all-cause CIF should be bounded by 1 is formally considered. The proposed models are extended to account for potential failure cause misclassification, where the true failure causes are available in a small random sample of individuals. We also provide a multistate representation of the whole population by defining mutually exclusive states based on the marker values and the competing risks. Based solely on the assumed joint model, we derive fully Bayesian posterior samples for state occupation and transition probabilities. The proposed approach is evaluated in a simulation study and, as an illustration, it is fitted to real data from people with HIV.

Association between hypogammaglobulinaemia and severe infections during induction therapy in ANCA-associated vasculitis: from J-CANVAS study.

OBJECTIVES: To investigate the association between decreased serum IgG levels caused by remission-induction immunosuppressive therapy of antineutrophil cytoplasmic antibody-associated vasculitis (AAV) and the development of severe infections. METHODS: We conducted a retrospective cohort study of patients with new-onset or severe relapsing AAV enrolled in the J-CANVAS registry, which was established at 24 referral sites in Japan. The minimum serum IgG levels up to 24 weeks and the incidence of severe infection up to 48 weeks after treatment initiation were evaluated. After multiple imputations for all explanatory variables, we performed the multivariate analysis using a Fine-Gray model to assess the association between low IgG (the minimum IgG levels <500 mg/dl) and severe infections. In addition, the association was expressed as a restricted cubic spline (RCS) and analysed by treatment subgroups. RESULTS: Of 657 included patients (microscopic polyangiitis, 392; granulomatosis with polyangiitis, 139; eosinophilic granulomatosis with polyangiitis, 126), 111 (16.9%) developed severe infections. The minimum serum IgG levels were measured in 510 patients, of whom 77 (15.1%) had low IgG. After multiple imputations, the confounder-adjusted hazard ratio of low IgG for the incidence of severe infections was 1.75 (95% confidence interval: 1.03-3.00). The RCS revealed a U-shaped association between serum IgG levels and the incidence of severe infection with serum IgG 946 mg/dl as the lowest point. Subgroup analysis showed no obvious heterogeneity between treatment regimens. CONCLUSION: Regardless of treatment regimens, low IgG after remission-induction treatment was associated with the development of severe infections up to 48 weeks after treatment initiation.

Evaluating the association between latent classes and competing risks outcomes with multiphenotype data.

Latent class analysis is an intuitive tool to characterize disease phenotype heterogeneity. With data more frequently collected on multiple phenotypes in chronic disease studies, it is of rising interest to investigate how the latent classes embedded in one phenotype are related to another phenotype. Motivated by a cohort with mild cognitive impairment (MCI) from the Uniform Data Set (UDS), we propose and study a time-dependent structural model to evaluate the association between latent classes and competing risk outcomes that are subject to missing failure types. We develop a two-step estimation procedure which circumvents latent class membership assignment and is rigorously justified in terms of accounting for the uncertainty in classifying latent classes. The new method also properly addresses the realistic complications for competing risks outcomes, including random censoring and missing failure types. The asymptotic properties of the resulting estimator are established. Given that the standard bootstrapping inference is not feasible in the current problem setting, we develop analytical inference procedures, which are easy to implement. Our simulation studies demonstrate the advantages of the proposed method over benchmark approaches. We present an application to the MCI data from UDS, which uncovers a detailed picture of the neuropathological relevance of the baseline MCI subgroups.

Estimating disease incidence rates and transition probabilities in elderly patients using multi-state models: a case study in fragility fracture using a Bayesian approach.

BACKGROUND: Multi-state models are complex stochastic models which focus on pathways defined by the temporal and sequential occurrence of numerous events of interest. In particular, the so-called illness-death models are especially useful for studying probabilities associated to diseases whose occurrence competes with other possible diseases, health conditions or death. They can be seen as a generalization of the competing risks models, which are widely used to estimate disease-incidences among populations with a high risk of death, such as elderly or cancer patients. The main advantage of the aforementioned illness-death models is that they allow the treatment of scenarios with non-terminal competing events that may occur sequentially, which competing risks models fail to do. METHODS: We propose an illness-death model using Cox proportional hazards models with Weibull baseline hazard functions, and applied the model to a study of recurrent hip fracture. Data came from the PREV2FO cohort and included 34491 patients aged 65 years and older who were discharged alive after a hospitalization due to an osteoporotic hip fracture between 2008-2015. We used a Bayesian approach to approximate the posterior distribution of each parameter of the model, and thus cumulative incidences and transition probabilities. We also compared these results with a competing risks specification. RESULTS: Posterior transition probabilities showed higher probabilities of death for men and increasing with age. Women were more likely to refracture as well as less likely to die after it. Free-event time was shown to reduce the probability of death. Estimations from the illness-death and the competing risks models were identical for those common transitions although the illness-death model provided additional information from the transition from refracture to death. CONCLUSIONS: We illustrated how multi-state models, in particular illness-death models, may be especially useful when dealing with survival scenarios which include multiple events, with competing diseases or when death is an unavoidable event to consider. Illness-death models via transition probabilities provide additional information of transitions from non-terminal health conditions to absorbing states such as death, what implies a deeper understanding of the real-world problem involved compared to competing risks models.

Sieve estimation of a class of partially linear transformation models with interval-censored competing risks data.

In this paper, we consider a class of partially linear transformation models with interval-censored competing risks data. Under a semiparametric generalized odds rate specification for the cause-specific cumulative incidence function, we obtain optimal estimators of the large number of parametric and nonparametric model components via maximizing the likelihood function over a joint B-spline and Bernstein polynomial spanned sieve space. Our specification considers a relatively simpler finite-dimensional parameter space, approximating the infinite-dimensional parameter space as n → ∞, thereby allowing us to study the almost sure consistency, and rate of convergence for all parameters, and the asymptotic distributions and efficiency of the finite-dimensional components. We study the finite sample performance of our method through simulation studies under a variety of scenarios. Furthermore, we illustrate our methodology via application to a dataset on HIV-infected individuals from sub-Saharan Africa.

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates, with application to analysis of biomarker correlates in vaccine trials.

This article studies generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly-robust augmented inverse probability weighted complete-case (AIPW) approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.

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On restricted optimal treatment regime estimation for competing risks data.

It is well accepted that individualized treatment regimes may improve the clinical outcomes of interest. However, positive treatment effects are often accompanied by certain side effects. Therefore, when choosing the optimal treatment regime for a patient, we need to consider both efficacy and safety issues. In this article, we propose to model time to a primary event of interest and time to severe side effects of treatment by a competing risks model and define a restricted optimal treatment regime based on cumulative incidence functions. The estimation approach is derived using a penalized value search method and investigated through extensive simulations. The proposed method is applied to an HIV dataset obtained from Health Sciences South Carolina, where we minimize the risk of treatment or virologic failures while controlling the risk of serious drug-induced side effects.

Competing risks predictions with different time scales under the additive risk model.

In the analysis for competing risks data, regression modeling of the cause-specific hazard functions has been usually conducted using the same time scale for all event types. However, when the true time scale is different for each event type, it would be appropriate to specify regression models for the cause-specific hazards on different time scales for different event types. Often, the proportional hazards model has been used for regression modeling of the cause-specific hazard functions. However, the proportionality assumption may not be appropriate in practice. In this article, we consider the additive risk model as an alternative to the proportional hazards model. We propose predictions of the cumulative incidence functions under the cause-specific additive risk models employing different time scales for different event types. We establish the consistency and asymptotic normality of the predicted cumulative incidence functions under the cause-specific additive risk models specified on different time scales using empirical processes and derive consistent variance estimators of the predicted cumulative incidence functions. Through simulation studies, we show that the proposed prediction methods perform well. We illustrate the methods using stage III breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.

Finite-sample adjustments in variance estimators for clustered competing risks regression.

The marginal Fine-Gray proportional subdistribution hazards model is a popular approach to directly study the association between covariates and the cumulative incidence function with clustered competing risks data, which often arise in multicenter randomized trials or multilevel observational studies. To account for the within-cluster correlations between failure times, the uncertainty of the regression parameters estimators is quantified by the robust sandwich variance estimator, which may have unsatisfactory performance with a limited number of clusters. To overcome this limitation, we propose four bias-corrected variance estimators to reduce the negative bias of the usual sandwich variance estimator, extending the bias-correction techniques from generalized estimating equations with noncensored exponential family outcomes to clustered competing risks outcomes. We further compare their finite-sample operating characteristics through simulations and two real data examples. In particular, we found the Mancl and DeRouen (MD) type sandwich variance estimator generally has the smallest bias. Furthermore, with a small number of clusters, the Wald t -confidence interval with the MD sandwich variance estimator carries close to nominal coverage for the cluster-level effect parameter. The t -confidence intervals based on the sandwich variance estimator with any one of the three types of multiplicative bias correction or the z -confidence interval with the Morel, Bokossa and Neerchal (MBN) type sandwich variance estimator have close to nominal coverage for the individual-level effect parameter. Finally, we develop a user-friendly R package crrcbcv implementing the proposed sandwich variance estimators to assist practical applications.

A competing risk analysis of colorectal cancer recurrence after curative surgery.

BACKGROUND: This study examines the effect of prognostic patient and disease characteristics on colorectal cancer (CRC) recurrence after curative resection. We used competing risk analysis with death as a competing risk. This method provides the clinician a perspective into a patient's actual risk of experiencing a recurrence. METHODS: A retrospective cohort study of patients diagnosed with CRC who underwent curative resection for CRC from 2003-2007 at the Royal University Hospital in Saskatoon was completed. The outcome of interest was the first CRC recurrence, either local or distant metastasis. Demographic data, tumor characteristics, adjuvant treatment and follow-up data, date of local recurrence or metastasis were recorded from the medical record. Univariate analysis was completed to look at the relationship between each of the prognostic indicators and recurrence. Multivariable modelling (subdistribution regression modelling) was done to identify the main risk factors in determining recurrence. RESULTS: Of 148 patients, 38 (25.7%) experienced a recurrence, 16 (10.8%) died without evidence of recurrence, and 94 (63.5%) experienced neither outcome. The median follow-up was 30.5 months (interquartile range 10.6-50). In univariable subdistribution regression, T-stage, N-stage, vascular invasion and positive margins were all predictive of cancer recurrence, with p ≤ 0.001, with subdistribution hazard ratios for T4 stage at 11.93, T3 stage at 2.46, N2 stage at 10.58, and presence of vascular invasion at 4.27. N-stage remained as the sole predictor in multivariable regression. Cumulative incidence function (CIF) of recurrence at 48 months after surgery was 15%, 27% and 90% for N1/2, N3 and N4 respectively. CONCLUSION: The highest CIF of recurrence was associated with T4 stage, N2 stage, and vascular invasion. Patient's age, tumour location, type, or histological grade were not found to have a significant effect on the success of CRC surgery in precluding a recurrence.

Quantifying diagnostic accuracy improvement of new biomarkers for competing risk outcomes.

The net reclassification improvement (NRI) and the integrated discrimination improvement (IDI) were originally proposed to characterize accuracy improvement in predicting a binary outcome, when new biomarkers are added to regression models. These two indices have been extended from binary outcomes to multi-categorical and survival outcomes. Working on an AIDS study where the onset of cognitive impairment is competing risk censored by death, we extend the NRI and the IDI to competing risk outcomes, by using cumulative incidence functions to quantify cumulative risks of competing events, and adopting the definitions of the two indices for multi-category outcomes. The "missing" category due to independent censoring is handled through inverse probability weighting. Various competing risk models are considered, such as the Fine and Gray, multistate, and multinomial logistic models. Estimation methods for the NRI and the IDI from competing risk data are presented. The inference for the NRI is constructed based on asymptotic normality of its estimator, and the bias-corrected and accelerated bootstrap procedure is used for the IDI. Simulations demonstrate that the proposed inferential procedures perform very well. The Multicenter AIDS Cohort Study is used to illustrate the practical utility of the extended NRI and IDI for competing risk outcomes.

Fine-Gray subdistribution hazard models to simultaneously estimate the absolute risk of different event types: Cumulative total failure probability may exceed 1.

The Fine-Gray subdistribution hazard model has become the default method to estimate the incidence of outcomes over time in the presence of competing risks. This model is attractive because it directly relates covariates to the cumulative incidence function (CIF) of the event of interest. An alternative is to combine the different cause-specific hazard functions to obtain the different CIFs. A limitation of the subdistribution hazard approach is that the sum of the cause-specific CIFs can exceed 1 (100%) for some covariate patterns. Using data on 9479 patients hospitalized with acute myocardial infarction, we estimated the cumulative incidence of both cardiovascular death and non-cardiovascular death for each patient. We found that when using subdistribution hazard models, approximately 5% of subjects had an estimated risk of 5-year all-cause death (obtained by combining the two cause-specific CIFs obtained from subdistribution hazard models) that exceeded 1. This phenomenon was avoided by using the two cause-specific hazard models. We provide a proof that the sum of predictions exceeds 1 is a fundamental problem with the Fine-Gray subdistribution hazard model. We further explored this issue using simulations based on two different types of data-generating process, one based on subdistribution hazard models and other based on cause-specific hazard models. We conclude that care should be taken when using the Fine-Gray subdistribution hazard model in situations with wide risk distributions or a high cumulative incidence, and if one is interested in the risk of failure from each of the different event types.

Subjective cognitive complaints and permanent work disability: a prospective cohort study.

PURPOSE: Work disability (WD) is a medico-legal concept that refers to disability benefits (DB) granted due to diseases. We assessed whether subjective cognitive complaints (SCC)-presenting as self-rated difficulties of concentration, memory, clear thinking, and decision making-predict permanent WD in knowledge-intensive occupations. METHODS: In this prospective cohort study with up to 7-year follow-up, we combined the SCC questionnaire results with reliable registry data on the DBs of 7161 professional/managerial employees (46% females). We excluded employees who were on long-term sickness absence (SA) or had received a DB at baseline. The exposure variable was the presence of SCC. Age and SA before the questionnaire as a proxy measure of general health were treated as confounders and the analyses were conducted by gender. The outcome variable was a granted DB. The cumulative incidence function illustrates the difference between SCC categories, and the Fine-Gray model estimates the predictors of WD during the 8-year follow-up. RESULTS: The annual incidence of DB was 0.15% in the entire cohort: 0.18% among the females, and 0.12% among the males (p = 0.795). The most common primary reasons for permanent WD were mental (36%) and musculoskeletal (20%) disorders. SCC predicted DB in both genders when controlling for age and prior SA. Hazard ratios were 2.9 with a 95% confidence interval 1.4-6.0 for the females and 3.7 (1.8-7.9) for the males. CONCLUSION: Subjective cognitive complaints predict permanent WD in knowledge-intensive occupations. This finding has implications for supporting work ability and preventing work disability among employees with cognitively demanding tasks.

Survival analysis for AdVerse events with VarYing follow-up times (SAVVY): Rationale and statistical concept of a meta-analytic study.

The assessment of safety is an important aspect of the evaluation of new therapies in clinical trials, with analyses of adverse events being an essential part of this. Standard methods for the analysis of adverse events such as the incidence proportion, that is the number of patients with a specific adverse event out of all patients in the treatment groups, do not account for both varying follow-up times and competing risks. Alternative approaches such as the Aalen-Johansen estimator of the cumulative incidence function have been suggested. Theoretical arguments and numerical evaluations support the application of these more advanced methodology, but as yet there is to our knowledge only insufficient empirical evidence whether these methods would lead to different conclusions in safety evaluations. The Survival analysis for AdVerse events with VarYing follow-up times (SAVVY) project strives to close this gap in evidence by conducting a meta-analytical study to assess the impact of the methodology on the conclusion of the safety assessment empirically. Here we present the rationale and statistical concept of the empirical study conducted as part of the SAVVY project. The statistical methods are presented in unified notation, and examples of their implementation in R and SAS are provided.

Modeling the cumulative incidence function of multivariate competing risks data allowing for within-cluster dependence of risk and timing.

We propose to model the cause-specific cumulative incidence function of multivariate competing risks data using a random effects model that allows for within-cluster dependence of both risk and timing. The model contains parameters that makes it possible to assess how the two are connected, e.g. if high-risk is related to early onset. Under the proposed model, the cumulative incidences of all failure causes are modeled and all cause-specific and cross-cause associations specified. Consequently, left-truncation and right-censoring are easily dealt with. The proposed model is assessed using simulation studies and applied in analysis of Danish register-based family data on breast cancer.

Semiparametric mixture cure model analysis with competing risks data: Application to vascular access thrombosis data.

The article is motivated by a nephrology study in Taiwan, which enrolled hemodialysis patients who suffered from vascular access thrombosis. After treatment, some patients were cured of thrombosis, while some may experience recurrence of either type (acute or nonacute) of vascular access thrombosis. Our major interest is to estimate the cumulative incidence probability of time to the first recurrence of acute thrombosis after therapy. Since the occurrence of one type of vascular access thrombosis precludes occurrence of the other type, patients are subject to competing risks. To account for the presence of competing risks and cured patients, we develop a mixture model approach to the regression analysis of competing-risks data with a cure fraction. We make inference about the effects of factors on both the cure rate and cumulative incidence function (CIF) for a failure of interest, which are separately specified in the logistic regression model and semiparametric regression model with time-varying and time-invariant effects. Based on two-stage method, we develop novel estimation equations using the inverse probability censoring weight techniques. The asymptotic properties of the estimators are rigorously studied and the plug-in variance estimators can be obtained for constructing interval estimators. We also propose a lack-of-fit test for assessing the adequacy of the proposed model and several tests for time-varying effects. The simulation studies and vascular access thrombosis data analysis are conducted to illustrate the proposed method.

Self-reported health problems in a health risk appraisal predict permanent work disability: a prospective cohort study of 22,023 employees from different sectors in Finland with up to 6-year follow-up.

PURPOSE: Work disability (WD) as a medico-legal concept refers to disability benefits (DB) that are granted due to diseases that permanently reduce work ability. We studied whether an occupational healthcare instrument for the prediction of sickness absence (SA) risk-a health risk appraisal (HRA)-also predicts permanent WD. METHODS: HRA results were combined with registry data on DB of 22,023 employees from different industry sectors. We analysed how the HRA risk categories predict DB and considered occupational group, gender, age, and prior SA as confounding variables. Cumulative incidence function illustrates the difference between the HRA risk categories, and the Fine-Gray model estimates the predictors of WD during 6-year follow-up. RESULTS: The most common primary reasons for permanent WD were musculoskeletal (39%) and mental disorders (21%). Self-reported health problems in the HRA, labelled as "WD risk factors", predicted DB when controlling for age and prior SA. Hazard ratios were 10.9 or over with the lower limit of the 95% confidence interval 3.3 or over among those with two simultaneous WD risk factors. 14% of the females and 17% of the males with three or more simultaneous WD risk factors had received a DB, whereas the respective figures among those without findings were 1.9% and 0.3%. CONCLUSIONS: Self-reported health problems in the HRA, especially multiple simultaneous WD risk factors, predict permanent WD among both genders across occupational groups. Screening WD risk with a self-administered questionnaire is a potential means for identifying high-risk employees for targeting occupational healthcare actions.

Does the use of preoperative bisphosphonates in patients with osteopenia and osteoporosis affect lumbar fusion rates? Analysis from a national spine registry.

OBJECTIVE: Bisphosphonates are used to increase bone strength in treating osteopenia and osteoporosis, but their use for increasing lumbar fusion rates has been controversial. The objective of this study was to determine if preoperative treatment with bisphosphonates affects the reoperation rates for nonunions (operative nonunion rates) following lumbar fusions in patients with osteopenia or osteoporosis. METHODS: The authors conducted a cohort study using data from the Kaiser Permanente Spine Registry. Patients (aged ≥ 50 years) with a diagnosis of osteopenia or osteoporosis who underwent primary elective lumbar fusions for degenerative disc disease, deformity, or spondylolisthesis were included in the cohort. Repeated spinal procedures at the index lumbar levels were noted through chart review. Reoperations for symptomatic nonunions (operative nonunions), time to nonunion, and the nonunion spine level(s) were also identified. The crude 2-year cumulative incidence of operative nonunions was calculated as 1 minus the Kaplan-Meier estimator. Cox proportional hazard regression was used to evaluate the association between preoperative bisphosphonate use and operative nonunion after adjustment for covariates. Analysis was stratified by osteopenia and osteoporosis diagnosis. RESULTS: The cohort comprised 1040 primary elective lumbar fusion patients, 408 with osteopenia and 632 with osteoporosis. Ninety-seven (23.8%) patients with osteopenia and 370 (58.5%) patients with osteoporosis were preoperative bisphosphonate users. For the osteopenia group, no operative nonunions were observed in patients with preoperative bisphosphonate, while the crude 2-year incidence was 2.44% (95% CI 0.63-4.22) in the nonuser group. For the osteoporotic group, after adjustment for covariates, no difference was observed in risk for operative nonunions between the preoperative bisphosphonate users and nonusers (HR 0.96, 95% CI 0.20-4.55, p = 0.964). CONCLUSIONS: To the authors' knowledge, this study presents one of the largest series of patients with the diagnosis of osteopenia or osteoporosis in whom the effects of preoperative bisphosphonates on lumbar fusions were evaluated using operative nonunion rates as an outcome measure. The results indicate that preoperative bisphosphonate use had no effect on the operative nonunion rates for patients with osteoporosis. Similar indications were not confirmed in osteopenia patients because of the low nonunion frequency. Further studies are warranted to the determine if preoperative and postoperative timing of bisphosphonate use has any effect on lumbar fusion rates.

Comparison of two treatments in the presence of competing risks.

Competing risks data arise frequently in clinical trials, and a common problem encountered is the overall homogeneity between two groups. In competing risks analysis, when the proportional subdistribution hazard assumption is violated or two cumulative incidence function (CIF) curves cross; currently, the most commonly used testing methods, for example, the Gray test and the Pepe and Mori test, may lead to a significant loss of statistical testing power. In this article, we propose a testing method based on the area between the CIF curves (ABC). The ABC test captures the difference over the whole time interval for which survival information is available for both groups and is not based on any special assumptions regarding the underlying distributions. The ABC test was also extended to test short-term and long-term effects. We also consider a combined test and a two-stage procedure based on this new method, and a bootstrap resampling procedure is suggested in practice to approximate the limiting distribution of the combined test and two-stage test. An extensive series of Monte Carlo simulations is conducted to investigate the power and the type I error rate of the methods. In addition, based on our simulations, our proposed TS, Comb, and ABC tests have a relatively high power in most situations. In addition, the methods are illustrated using two different datasets with different CIF situations.