Additive and Multiplicative Hazards Regression Models In Competing Risks Analysis: Application To The Canadian Heart Health Survey

Background: In survival analysis, an event whose occurrence influences the occurrence of another event is termed a competing risk event. The Cox hazards model is applicable in standard survival analysis with a single event. To correctly assess covariate effects in competing risks analysis, the Fine & Gray (F-G) subdistribution hazards and the Cox cause-specific hazards models are appropriate. Equally, additive hazards models can be used to examine the covariate effects in a competing risks framework. Objectives: (i) To examine the additive and multiplicative hazards models in the competing risks setting by applying the said models to the Canadian Heart Health Survey data; (ii) To determine the risk factors for cardiovascular disease using the competing risks approach; (iii) To compare the risk factors identified by the additive and multiplicative hazards models in the context of competing risks. Methods: The observational Canadian Heart Health Survey database collected between 1986 and 1995 is the baseline data used in this study. Two competing outcomes, cardiovascular disease (CVD) and non-CVD-related deaths, are analyzed with the Cox cause-specific and the F-G multiplicative hazards models. Similarly, the additive hazards models of Aalen and that of Lin & Ying (L-Y) are modeled for the outcomes using the competing risks approach. Results: There were 13,996 eligible subjects in my data, and 7,071 (50.5%) of them were women. After a median follow-up time of 15 years (interquartile range = 5.52 years), a total of 1,536 deaths were observed, and 549 (35.7%) of these were CVD related deaths. Factors like male gender, old age, and alcohol abstinence significantly increased the risk of CVD mortality in the additive and multiplicative hazards models. Former alcohol users compared to current alcohol users have a 53% (P-value= 0.002) and a 55% (P-value= 0.001) increased risk of CVD mortality in the Cox cause-specific and the F-G models, respectively. In the L-Y additive model, former alcohol users compared to current users increased CVD mortality by adding 16 new cases per 10,000 person-years (P-value = 0.008). Conclusion: The results from my study suggest that covariate effects in the Cox cause-specific and the F-G subdistribution hazards models may be identical in terms of magnitude and direction. The numerical results from the multiplicative and the additive hazards models give different interpretation of the covariate effects, and using both the additive and multiplicative models together would boost understanding of the data

Different competing risks models applied to data from the Australian Orthopaedic Association National Joint Replacement Registry

Purpose: Here we describe some available statistical models and illustrate their use for analysis of arthroplasty registry data in the presence of the competing risk of death, when the influence of covariates on the revision rate may be different to the influence on the probability (that is, risk) of the occurrence of revision. Patients and methods: Records of 12,525 patients aged 75–84 years who had received hemiarthroplasty for fractured neck of femur were obtained from the Australian Orthopaedic Association National Joint Replacement Registry. The covariates whose effects we investigated were: age, sex, type of prosthesis, and type of fixation (cementless or cemented). Extensions of competing risk regression models were implemented, allowing the effects of some covariates to vary with time. Results: The revision rate was significantly higher for patients with unipolar than bipolar prostheses (HR = 1.38, 95% CI: 1.01–1.89) or with monoblock than bipolar prostheses (HR = 1.45, 95% CI: 1.08–1.94). It was significantly higher for the younger age group (75–79 years) than for the older one (80–84 years) (HR = 1.28, 95% CI: 1.05–1.56) and higher for males than for females (HR = 1.37, 95% CI: 1.09–1.71). The probability of revision, after correction for the competing risk of death, was only significantly higher for unipolar prostheses than for bipolar prostheses, and higher for the younger age group. The effect of fixation type varied with time; initially, there was a higher probability of revision for cementless prostheses than for cemented prostheses, which disappeared after approximately 1.5 years. Interpretation: When accounting for the competing risk of death, the covariates type of prosthesis and sex influenced the rate of revision differently to the probability of revision. We advocate the use of appropriate analysis tools in the presence of competing risks and when covariates have time-dependent effects.Marianne H Gillam, Amy Salter, Philip Ryan, and Stephen E Grave

Improving statistical analysis of prospective clinical trials in stem cell transplantation. An inventory of new approaches in survival analysis

The CLINT project is an European Union funded project, run as a specific support action, under the sixth framework programme. It is a 2 year project aimed at supporting the European Group for Blood and Marrow Transplantation (EBMT) to develop its infrastructure for the conduct of trans-European clinical trials in accordance with the EU Clinical Trials Directive, and to facilitate International prospective clinical trials in stem cell transplantation. The initial task is to create an inventory of the existing biostatistical literature on new approaches to survival analyses that are not currently widely utilised. The estimation of survival endpoints is introduced, with an emphasis on recent developments which complements standard analysis. The issues raised are new regression models that allow the estimation of time dependent effect for cause specific hazard, cumulative incidence and more generally mean response. New development in multi state model, with notably, recent regression models that assess the influence of covariates directly on transition probabilities are detailed. Some recent test for comparing cumulative incidence function across treatment arm are introduced. The estimation of centre effect in multi centric studies is also documented. Sample size calculation in the presence of competing risks are then presented. We close with the inventory of available packages and macro in R that implement the previous survival models

Analyzing Competing Risk Data Using the R timereg Package

In this paper we describe flexible competing risks regression models using the comp.risk() function available in the timereg package for R based on Scheike et al. (2008). Regression models are specified for the transition probabilities, that is the cumulative incidence in the competing risks setting. The model contains the Fine and Gray (1999) model as a special case. This can be used to do goodness-of-fit test for the subdistribution hazardsâ proportionality assumption (Scheike and Zhang 2008). The program can also construct confidence bands for predicted cumulative incidence curves. We apply the methods to data on follicular cell lymphoma from Pintilie (2007), where the competing risks are disease relapse and death without relapse. There is important non-proportionality present in the data, and it is demonstrated how one can analyze these data using the flexible regression models.

Analyzing Competing Risk Data Using the R timereg Package

In this paper we describe flexible competing risks regression models using the comp.risk() function available in the timereg package for R based on Scheike et al. (2008). Regression models are specified for the transition probabilities, that is the cumulative incidence in the competing risks setting. The model contains the Fine and Gray (1999) model as a special case. This can be used to do goodness-of-fit test for the subdistribution hazards’ proportionality assumption (Scheike and Zhang 2008). The program can also construct confidence bands for predicted cumulative incidence curves.We apply the methods to data on follicular cell lymphoma from Pintilie (2007), where the competing risks are disease relapse and death without relapse. There is important non-proportionality present in the data, and it is demonstrated how one can analyze these data using the flexible regression models

Competing risks methods

Competing risks data usually arises in studies in which the failure of an individual may be classified into one of k (k > 1) mutually exclusive causes of failure. When competing risks are present, classical survival analysis techniques may not be appropriate to use. The main goal of this paper is to review the specific methods to deal with competing risks. To this aim, we first focus on how to specify a competing risks model, which is the structure of observed data in this framework, and how components of the model are estimated from a given random sample. In addition, we discuss how to correctly interpret probabilities in the presence of competing risks, and regression models are considered in detail. To conclude, we illustrate the problem with data from a bladder cancer study