A case‐cohort approach for multi‐state models in hospital epidemiology

Analysing the determinants and consequences of hospital‐acquired infections involves the evaluation of large cohorts. Infected patients in the cohort are often rare for specific pathogens, because most of the patients admitted to the hospital are discharged or die without such an infection. Death and discharge are competing events to acquiring an infection, because these individuals are no longer at risk of getting a hospital‐acquired infection. Therefore, the data is best analysed with an extended survival model – the extended illness‐death model. A common problem in cohort studies is the costly collection of covariate values. In order to provide efficient use of data from infected as well as uninfected patients, we propose a tailored case‐cohort approach for the extended illness‐death model. The basic idea of the case‐cohort design is to only use a random sample of the full cohort, referred to as subcohort, and all cases, namely the infected patients. Thus, covariate values are only obtained for a small part of the full cohort. The method is based on existing and established methods and is used to perform regression analysis in adapted Cox proportional hazards models. We propose estimation of all cause‐specific cumulative hazards and transition probabilities in an extended illness‐death model based on case‐cohort sampling. As an example, we apply the methodology to infection with a specific pathogen using a large cohort from Spanish hospital data. The obtained results of the case‐cohort design are compared with the results in the full cohort to investigate the performance of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

病例队列研究设计中相对危险度的估计及其应用

目的:系统介绍病例队列研究设计的基本原理,以及风险比（ HR）的常用估计方法及其应用。 方法:首先,介绍病例队列研究设计的基本原理;其次,对Prentice法、Self-Prentice法和Barlow法加权Cox比例风险回归模型进行描述和说明;最后,以上海市女性健康队列研究为例,分析全队列数据与...     

Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time-dependent hazards and delayed entry

In the analysis of survival data, there are often competing events that preclude an event of interest from occurring. Regression analysis with competing risks is typically undertaken using a cause-specific proportional hazards model. However, modern alternative methods exist for the analysis of the subdistribution hazard with a corresponding subdistribution proportional hazards model. In this paper, we introduce a flexible parametric mixture model as a unifying method to obtain estimates of the cause-specific and subdistribution hazards and hazard-ratio functions. We describe how these estimates can be summarized over time to give a single number comparable to the hazard ratio that is obtained from a corresponding cause-specific or subdistribution proportional hazards model. An application to the Women's Interagency HIV Study is provided to investigate injection drug use and the time to either the initiation of effective antiretroviral therapy, or clinical disease progression as a competing event.     

Simulating competing risks data in survival analysis

Competing risks analysis considers time‐to‐first‐event (‘survival time’) and the event type (‘cause’), possibly subject to right‐censoring. The cause‐, i.e. event‐specific hazards, completely determine the competing risk process, but simulation studies often fall back on the much criticized latent failure time model. Cause‐specific hazard‐driven simulation appears to be the exception; if done, usually only constant hazards are considered, which will be unrealistic in many medical situations. We explain simulating competing risks data based on possibly time‐dependent cause‐specific hazards. The simulation design is as easy as any other, relies on identifiable quantities only and adds to our understanding of the competing risks process. In addition, it immediately generalizes to more complex multistate models. We apply the proposed simulation design to computing the least false parameter of a misspecified proportional subdistribution hazard model, which is a research question of independent interest in competing risks. The simulation specifications have been motivated by data on infectious complications in stem‐cell transplanted patients, where results from cause‐specific hazards analyses were difficult to interpret in terms of cumulative event probabilities. The simulation illustrates that results from a misspecified proportional subdistribution hazard analysis can be interpreted as a time‐averaged effect on the cumulative event probability scale. Copyright © 2009 John Wiley & Sons, Ltd.     

A proportional hazards regression model for the subdistribution with right-censored and left-truncated competing risks data

With competing risks failure time data, one often needs to assess the covariate effects on the cumulative incidence probabilities. Fine and Gray proposed a proportional hazards regression model to directly model the subdistribution of a competing risk. They developed the estimating procedure for right-censored competing risks data, based on the inverse probability of censoring weighting. Right-censored and left-truncated competing risks data sometimes occur in biomedical researches. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with right-censored and left-truncated data. We adopt a new weighting technique to estimate the parameters in this model. We have derived the large sample properties of the proposed estimators. To illustrate the application of the new method, we analyze the failure time data for children with acute leukemia. In this example, the failure times for children who had bone marrow transplants were left truncated.     

Patient death as a censoring event or competing risk event in models of nursing home placement

Participant death is often observed in studies that examine predictors of events, such as hospitalization or institutionalization, in older adult populations. The Cox proportional hazards modeling of the target event, whereby death is treated as a censoring event, is the standard analysis in this competing risks situation. However, the assumption of noninformative censoring applied to a frequently occurring competing event like death may be invalid and complicate interpretation in terms of the probability of the event. Multiple cause‐specific hazard (CSH) models can be estimated, but ambiguities may arise when interpreting covariate effects across multiple CSH models and in terms of the cumulative incidence function (CIF). Alternatively, one can model the proportional hazards of the subdistribution of the CIF and evaluate the covariate effects on the CIF directly. We examine and compare these two approaches with nursing home (NH) placement data from a randomized controlled trial of a counseling and support intervention for spouse‐caregivers of patients with Alzheimer's disease. CSHs for NH placement (where death is treated as a censoring event) and death (where NH placement is treated as a censoring event) and subdistribution hazards of the CIF for NH placement are modeled separately. In the presence of multiple covariates, the intervention effect is significant in both approaches, but the interpretation of the covariate effects requires joint evaluation of all estimated models. Copyright © 2009 John Wiley & Sons, Ltd.     

Methodological challenges in using point-prevalence versus cohort data in risk factor analyses of nosocomial infections

Purpose

To explore the impact of length-biased sampling on the evaluation of risk factors of nosocomial infections (NIs) in point-prevalence studies.

Evaluating competing adverse and beneficial outcomes using a mixture model

A competing risk framework occurs when individuals have the potential to experience only one of the several mutually exclusive outcomes. Standard survival methods often overestimate the cumulative incidence of events when competing events are censored. Mixture distributions have been previously applied to the competing risk framework to obtain inferences regarding the subdistribution of an event of interest. Often the competing event is treated as a nuisance, but it may be of interest to compare adverse events against the beneficial outcome when dealing with an intervention. In this paper, methods for using a mixture model to estimate an adverse-benefit ratio curve (ratio of the cumulative incidence curves for the two competing events) and the ratio of the subhazards for the two competing events are presented. A parametric approach is described with some remarks for extending the model to include uncertainty in the event type that occurred, left truncation in order to allow for time-dependent analyses, and uncertainty in the timing of the event resulting in interval censoring. The methods are illustrated with data from an HIV clinical cohort examining whether individuals initiating effective antiretroviral therapy have a greater risk of antiretroviral discontinuation or switching compared with HIV RNA suppression.     

Marginal structural models for case-cohort study designs to estimate the association of antiretroviral therapy initiation with incident AIDS or death

To estimate the association of antiretroviral therapy initiation with incident acquired immunodeficiency syndrome (AIDS) or death while accounting for time-varying confounding in a cost-efficient manner, the authors combined a case-cohort study design with inverse probability-weighted estimation of a marginal structural Cox proportional hazards model. A total of 950 adults who were positive for human immunodeficiency virus type 1 were followed in 2 US cohort studies between 1995 and 2007. In the full cohort, 211 AIDS cases or deaths occurred during 4,456 person-years. In an illustrative 20% random subcohort of 190 participants, 41 AIDS cases or deaths occurred during 861 person-years. Accounting for measured confounders and determinants of dropout by inverse probability weighting, the full cohort hazard ratio was 0.41 (95% confidence interval: 0.26, 0.65) and the case-cohort hazard ratio was 0.47 (95% confidence interval: 0.26, 0.83). Standard multivariable-adjusted hazard ratios were closer to the null, regardless of study design. The precision lost with the case-cohort design was modest given the cost savings. Results from Monte Carlo simulations demonstrated that the proposed approach yields approximately unbiased estimates of the hazard ratio with appropriate confidence interval coverage. Marginal structural model analysis of case-cohort study designs provides a cost-efficient design coupled with an accurate analytic method for research settings in which there is time-varying confounding.     

A multi-state model for evolution of intensive care unit patients: prediction of nosocomial infections and deaths

Nosocomial (hospital-acquired) infections are very frequent in intensive care units (ICU). The risk of death after severe infection is high, but the precise rate of death in ICU attributable to nosocomial infection is not known. The goal of this project was to build a statistical model to predict the occurrence of nosocomial infections in ICU and the outcome of the patients. We collected data on 676 consecutive patients admitted to an ICU for more than 24 hours between 1993 and 1996. The following data were collected for each patient: history; clinical examination at entry; subsequent infections; outcome. A multi-state heterogeneous semi-Markov model was determined and then validated; the initial data set was randomly split into two groups: two-thirds (450 patients) to build the model and one-third (226 patients) to validate it. The model defined five states: ICU admission; first simple infection; first complicated infection; death, and discharge from the ICU. Transitions between these states determined nine different events. The global model of patient histories can be divided into nine survival models, each corresponding to one of these events. The possible events from a given state were considered to be competing. Since many risk factors induced non-proportional hazard functions, piecewise exponential models were used to model event occurrence. The effect of continuous covariates on hazard functions has been described with a non-parametric method that enables non-linear relations to be shown. Among other things, the model allows patients' post-admission histories to be predicted from data available at ICU admission. The bootstrap estimator of the attributable risk of death due to simple or complicated nosocomial infections is 44.2 percent (95 percent CI 26.0-61.6 percent). We were also able to characterize the most highly exposed patients, those who comprise the high-risk group on whom prevention efforts must be focused.     

Comparing Modeling Approaches for Discrete Event Simulations With Competing Risks Based on Censored Individual Patient Data: A Simulation Study and Illustration in Colorectal Cancer

ObjectivesThis study aimed to provide detailed guidance on modeling approaches for implementing competing events in discrete event simulations based on censored individual patient data (IPD).MethodsThe event-specific distributions (ESDs) approach sampled times from event-specific time-to-event distributions and simulated the first event to occur. The unimodal distribution and regression approach sampled a time from a combined unimodal time-to-event distribution, representing all events, and used a (multinomial) logistic regression model to select the event to be simulated. A simulation study assessed performance in terms of relative absolute event incidence difference and relative entropy of time-to-event distributions for different types and levels of right censoring, numbers of events, distribution overlap, and sample sizes. Differences in cost-effectiveness estimates were illustrated in a colorectal cancer case study.ResultsIncreased levels of censoring negatively affected the modeling approaches’ performance. A lower number of competing events and higher overlap of distributions improved performance. When IPD were censored at random times, ESD performed best. When censoring occurred owing to a maximum follow-up time for 2 events, ESD performed better for a low level of censoring (ie, 10%). For 3 or 4 competing events, ESD better represented the probabilities of events, whereas unimodal distribution and regression better represented the time to events. Differences in cost-effectiveness estimates, both compared with no censoring and between approaches, increased with increasing censoring levels.ConclusionsModelers should be aware of the different modeling approaches available and that selection between approaches may be informed by data characteristics. Performing and reporting extensive validation efforts remains essential to ensure IPD are appropriately represented.     

External comparisons with the case-cohort design

The case-cohort design can be an economic alternative to the standard cohort design. Prentice (Biometrika 1986;73:1-11) showed how the case-cohort design can be used to obtain relative risk estimates for comparisons within the cohort being studied. In this paper, the authors consider ways in which the case-cohort design can be used for comparing risk in exposure groups within the cohort to the risk in an external population. The problem reduces to estimating the number of expected cases at each exposure level in the total cohort, when exposure status is available only for members of a subcohort, i.e., a random sample of the total cohort. The authors describe theoretical and empirical properties of several variations of the design and analysis of case-cohort studies. Empirical properties were examined by replicating the selection of the subcohort in a study of second cancer risk after chemotherapy for a first cancer. Use of a case-cohort design in that study would have saved five-sixths of the cost of gathering covariate information at the price of only an 11% loss in efficiency relative to a full cohort study.     

Misspecified regression model for the subdistribution hazard of a competing risk

We consider a competing risks setting, when evaluating the prognostic influence of an exposure on a specific cause of failure. Two main regression models are used in such analyses, the Cox cause-specific proportional hazards model and the subdistribution proportional hazards model. They are exemplified in a real data example focusing on relapse-free interval in acute leukaemia patients. We examine the properties of the estimator based on the latter model when the true model is the former. An explicit relationship between subdistribution hazards ratio and cause-specific hazards ratio is derived, assuming a flexible parametric distribution for latent failure times.     

Estimating and testing for center effects in competing risks

The problems of fitting Gaussian frailties proportional hazards models for the subdistribution of a competing risk and of testing for center effects are considered. In the analysis of competing risks data, Fine and Gray proposed a proportional hazards model for the subdistribution to directly assess the effects of covariates on the marginal failure probabilities of a given failure cause. Katsahianbiet al. extended their model to clustered time to event data, by including random center effects or frailties in the subdistribution hazard. We first introduce an alternate estimation procedure to the one proposed by Katsahian et al. This alternate estimation method is based on the penalized partial likelihood approach often used in fitting Gaussian frailty proportional hazards models in the standard survival analysis context, and has the advantage of using standard survival analysis software. Second, four hypothesis tests for the presence of center effects are given and compared via Monte-Carlo simulations. Statistical and numerical considerations lead us to formulate pragmatic guidelines as to which of the four tests is preferable. We also illustrate the proposed methodology with registry data from bone marrow transplantation for acute myeloid leukemia (AML).     

Semiparametric accelerated failure time cure rate mixture models with competing risks

Modern medical treatments have substantially improved survival rates for many chronic diseases and have generated considerable interest in developing cure fraction models for survival data with a non‐ignorable cured proportion. Statistical analysis of such data may be further complicated by competing risks that involve multiple types of endpoints. Regression analysis of competing risks is typically undertaken via a proportional hazards model adapted on cause‐specific hazard or subdistribution hazard. In this article, we propose an alternative approach that treats competing events as distinct outcomes in a mixture. We consider semiparametric accelerated failure time models for the cause‐conditional survival function that are combined through a multinomial logistic model within the cure‐mixture modeling framework. The cure‐mixture approach to competing risks provides a means to determine the overall effect of a treatment and insights into how this treatment modifies the components of the mixture in the presence of a cure fraction. The regression and nonparametric parameters are estimated by a nonparametric kernel‐based maximum likelihood estimation method. Variance estimation is achieved through resampling methods for the kernel‐smoothed likelihood function. Simulation studies show that the procedures work well in practical settings. Application to a sarcoma study demonstrates the use of the proposed method for competing risk data with a cure fraction.     

Determinants and outcomes of serious attempted suicide: a nationwide study in Finland, 1996-2003

Suicide is among the 10 leading causes of death. Attempted suicide is 10-40 times more frequent than completed suicide and is the strongest single predictor of subsequent suicide. The current study population included all persons in Finland who were hospitalized with a diagnosis of attempted suicide between 1996 and 2003 (N = 18,199). Information on background variables and mortality was obtained by register linkage. The risk of repeated attempted suicide was 30% and the risk of suicide was 10%. The risks of repeated attempted suicide, completed suicide, and death from any cause were high immediately after discharge from the hospital. Analysis of competing causes of death revealed that while alcohol-related disorder was not associated with suicide, it markedly increased the risk of other violent death: The subdistribution hazards rate (SHR) was 2.61 (95% confidence interval (CI): 2.12, 3.21). Schizophrenia-related disorders (SHR = 1.87, 95% CI: 1.57, 2.21) and mood disorders (SHR = 1.72, 95% CI: 1.47, 2.01) were associated with the risk of suicide. The risks of suicide and all-cause mortality were extremely high immediately after hospitalization for attempted suicide.     

The analysis of case cohort design in the presence of competing risks with application to estimate the risk of delayed cardiac toxicity among Hodgkin Lymphoma survivors

The case‐cohort design is an economical solution to studying the association between an exposure and a rare disease. When the disease of interest has a delayed occurrence, then other types of event may preclude observation of the disease of interest giving rise to a competing risk situation. In this paper, we introduce a modification of the pseudolikelihood proposed by Prentice (Biometrika 1986; 73 :1–11) for the analysis of case‐cohort design, to accommodate the existence of competing risks. The modification is based on the Fine and Gray (J. Amer. Statist. Assoc. 1999; 94 :496–509) approach to enable the modeling of the hazard of subdistribution. We show through simulations that the estimate that maximizes this modified pseudolikelihood is almost unbiased. The predictive probabilities based on the model are close to the theoretical probabilities. The variance for the estimates can be calculated using the jackknife approach. An application of this method on the analysis of late cardiac morbidity among Hodgkin Lymphoma survivors is presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Premature death of adult adoptees: analyses of a case-cohort sample

Genetic and environmental influence on risk of premature death in adulthood was investigated by estimating the associations in total and cause-specific mortality of adult Danish adoptees and their biological and adoptive parents. Among all 14,425 non-familial adoptions formally granted in Denmark during the period 1924 through 1947, we selected the study population according to a case-cohort sampling design. As the case-control design, the case-cohort design has the advantage of economic data collection and little loss in statistical efficiency, but the case-cohort sample has the additional advantages that rate ratio estimates may be obtained, and re-use of the cohort sample in future studies of other outcomes is possible. Analyses were performed using Kalbfleisch and Lawless's estimator for hazard ratio, and robust estimation for variances. In the main analyses the sample was restricted to birth years of the adoptees 1924 and after, and age of transfer to the adoptive parents before 7 years, and age at death was restricted to 16 to 70 years. The results showed a higher mortality among adoptees, whose biological parents died in the age range of 16 to 70 years; this was significant for deaths from natural causes, vascular causes and all causes. No influence was seen from early death of adoptive parents, regardless of cause of death.     

Case-cohort studies: an effective design for the investigation of biomarkers as risk factors for chronic diseases--demonstrated by the example of the MONICA/KORA Augsburg Case-Cohort Study 1984-2002

As it is often not possible to determine specific measures of exposure in all participants of a prospective cohort study due to financial or other restrictions, new study designs have been developed. The aim of these designs is to obtain valid results even though expensive measurements are restricted to a limited number of participants of the original cohort study. The case-cohort study is a design that has recently become interesting as an alternative to the well known nested case-control study. The following article describes the case-cohort design considering as an example data from the MONICA/KORA Augsburg cohort study 1984-2002 and the outcomes of type 2 diabetes mellitus and acute myocardial infarction. Furthermore, results obtained in the full cohort for selected exposures are compared with results obtained in the case-cohort study.     

Depressed mood and cause-specific mortality: a 40-year general community assessment

PurposeThe current study describes how the excess mortality risk associated with depression translates into specific causes of death occurring during a 40-year follow-up period, with focus on deaths related to injuries, cardiovascular diseases, and cancer.MethodsData come from a cross-sectional survey (Community Mental Health Epidemiology Study) conducted in the early 1970s in Washington County, Maryland. Random sampling for the survey resulted in 2762 interviews. For the current analyses, baseline depressed mood was linked to current participant vital status through the use of death certificates.ResultsThe relative subdistribution hazards for cardiovascular deaths (3.08 [1.74–5.45]) and fatal injuries (4.63 [1.76–12.18]) were significant during the entire 40-year period for young adults (18–39 years old at baseline). The relative subdistribution hazard for cardiovascular deaths during the first 15 years of follow-up was pronounced in elderly (≥65 years) males (2.99 [1.67–5.37]) subjects. There were no significant associations between depressed mood and cancer deaths.ConclusionsIndividuals in the general community with depressed mood may be at increased risk of deaths as the result of cardiovascular disease and injury, even several decades after exposure assessment. Young adults with depressed mood appear to be particularly vulnerable to these associations.