Additive Hazards Model for Competing Risks Analysis of the Case-Cohort Design (original) (raw)
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Analysis and design of randomised clinical trials involving competing risks endpoints
Trials, 2011
Background: In randomised clinical trials involving time-to-event outcomes, the failures concerned may be events of an entirely different nature and as such define a classical competing risks framework. In designing and analysing clinical trials involving such endpoints, it is important to account for the competing events, and evaluate how each contributes to the overall failure. An appropriate choice of statistical model is important for adequate determination of sample size. Methods: We describe how competing events may be summarised in such trials using cumulative incidence functions and Gray's test. The statistical modelling of competing events using proportional cause-specific and subdistribution hazard functions, and the corresponding procedures for sample size estimation are outlined. These are illustrated using data from a randomised clinical trial (SQNP01) of patients with advanced (non-metastatic) nasopharyngeal cancer. Results: In this trial, treatment has no effect on the competing event of loco-regional recurrence. Thus the effects of treatment on the hazard of distant metastasis were similar via both the cause-specific (unadjusted csHR = 0.43, 95% CI 0.25-0.72) and subdistribution (unadjusted subHR 0.43; 95% CI 0.25-0.76) hazard analyses, in favour of concurrent chemo-radiotherapy followed by adjuvant chemotherapy. Adjusting for nodal status and tumour size did not alter the results. The results of the logrank test (p = 0.002) comparing the cause-specific hazards and the Gray's test (p = 0.003) comparing the cumulative incidences also led to the same conclusion. However, the subdistribution hazard analysis requires many more subjects than the cause-specific hazard analysis to detect the same magnitude of effect. Conclusions: The cause-specific hazard analysis is appropriate for analysing competing risks outcomes when treatment has no effect on the cause-specific hazard of the competing event. It requires fewer subjects than the subdistribution hazard analysis for a similar effect size. However, if the main and competing events are influenced in opposing directions by an intervention, a subdistribution hazard analysis may be warranted.
Competing risks analyses: objectives and approaches
European Heart Journal, 2014
Studies in cardiology often record the time to multiple disease events such as death, myocardial infarction, or hospitalization. Competing risks methods allow for the analysis of the time to the first observed event and the type of the first event. They are also relevant if the time to a specific event is of primary interest but competing events may preclude its occurrence or greatly alter the chances to observe it. We give a non-technical overview of competing risks concepts for descriptive and regression analyses. For descriptive statistics, the cumulative incidence function is the most important tool. For regression modelling, we introduce regression models for the cumulative incidence function and the cause-specific hazard function, respectively. We stress the importance of choosing statistical methods that are appropriate if competing risks are present. We also clarify the role of competing risks for the analysis of composite endpoints.
Statistics review 11: assessing risk
Critical care (London, England), 2004
Relative risk and odds ratio have been introduced in earlier reviews (see Statistics reviews 3, 6 and 8). This review describes the calculation and interpretation of their confidence intervals. The different circumstances in which the use of either the relative risk or odds ratio is appropriate and their relative merits are discussed. A method of measuring the impact of exposure to a risk factor is introduced. Measures of the success of a treatment using data from clinical trials are also considered.
American Journal of Epidemiology, 1996
The authors propose a method to perform a combined analysis of matched and unmatched case-control studies that is based on an adaptation of logistic regression and can be performed using standard software. This methodology can be used to do pooled analyses of studies with different designs. Likelihood ratio tests can be performed to assess association, heterogeneity, or trend. The standard errors of the coefficients allow the derivation of a Wald test and the calculation of confidence intervals. Another application is to compare relative risk estimators for the same risk factors studied in different phases of a disease in an effort to explore factors that may be more important in one phase than in another. Interaction terms of risk factors with variables that code the different pooled studies can be used for this purpose. The advantage of using this method is that a formal statistical comparison can be performed in which the regression coefficients of the interaction terms estimate the relative differences in risk (odds ratio ratios) between the studies. This estimation can be adjusted for other confounder factors. Two examples of application using data from case-control studies on cervical cancer and colorectal cancer are presented to illustrate the use of this epidemiologic method. Am J Epidemiol Abbreviations: CIN III, cervical intraeprthellal neoplasia grade III; ICC, invasive cervical cancer.
Introduction to Competing Risk Model in the Epidemiological Research
International Journal of Epidemiologic Research
Background and aims: Chronic kidney disease (CKD) is a public health challenge worldwide, with adverse consequences of kidney failure, cardiovascular disease (CVD), and premature death. The CKD leads to the end-stage of renal disease (ESRD) if late/not diagnosed. Competing risk modeling is a major issue in epidemiology research. In epidemiological study, sometimes, inappropriate methods (i.e. Kaplan-Meier method) have been used to estimate probabilities for an event of interest in the presence of competing risks. In these situations, competing risk analysis is preferred to other models in survival analysis studies. The purpose of this study was to describe the bias resulting from the use of standard survival analysis to estimate the survival of a patient with ESRD and to provide alternate statistical methods considering the competing risk. Methods: In this retrospective study, 359 patients referred to the hemodialysis department of Shahid Ayatollah Ashrafi Esfahani hospital in Tehra...
Evaluating and Interpreting Epidemiological Risk
Hospital Pharmacy, 2000
This special feature sets forth the basic skills pharmacists need to evaluate the primary literature with regard to epidemiological risk. The author discusses (1) the three key types of observational study designs used in epidemiological literature; (2) common measures of association and and their utility; (3) calculation of attributable risk, relative risk, and odds ratio; (4) the limitations of using relative risk and odds ratio; and (5) inappropriate use of risk in the primary literature.
Competing risk analysis using R: an easy guide for clinicians
Bone Marrow Transplantation, 2007
In the last decade with widespread use of quantitative analyses in medical research, close co-operation between statisticians and physicians has become essential from the experimental design through all phases of complex statistical analysis. On the other hand, easy-to-use statistical packages allow clinicians to perform basic statistical analyses themselves. Since the software they most commonly use does not perform in depth competing risk analysis, we recommend an add-on package for the R statistical software. We provide all the instructions for downloading it from internet and illustrate how to use it for analysis of a sample dataset of patients who underwent haematopoietic stem cell transplantation for acute leukaemia.
Contemporary Clinical Trials Communications
Introduction : Com pet ing risks arise when sub jects are ex posed to mul ti ple mu tu ally ex clu sive fail ure events, and the oc cur rence of one fail ure hin ders the oc cur rence of other fail ure events. In the pres ence of com pet ing risks, it is im por tant to use meth ods ac count ing for com pet ing events be cause fail ure to ac count for these events might re sult in mis lead ing in fer ences. Methods and Objective : Us ing data from a mul ti site ret ro spec tive ob ser va tional lon gi tu di nal study done in Ethiopia, we per formed sen si tiv ity analy ses us ing Fine-Gray model, Cause-specific Cox (Cox-CSH) model, Cause-specific Ac cel er ated Fail ure Time (CS-AFT) model, ac count ing for death as a com pet ing risk to de termine base line co vari ates that are as so ci ated with a com pos ite of un favourable re ten tion in care out comes in peo ple liv ing with Hu man Im mune Virus who were on both Iso ni azid pre ven tive ther apy (IPT) and an ti retro viral ther apy (ART). Non-cause spe cific (non-CSH) model that does not ac count for com pet ing risk was also performed. The com pos ite out come com prises of loss to fol low-up, stopped treat ment and death. Age, World Health Or gan i sa tion (WHO) stage, gen der, and CD4 count were the con sid ered base line co vari ates. Results : We in cluded 3578 pa tients in our analy sis. WHO stage III-or-IV was sig nif i cantly as so ci ated with the com pos ite of un favourable out comes, Sub-hazard ra tio (SHR) = 1.31, 95% con fi dence in ter val (CI):1.04-1.65 for the sub-distribution haz ard model, haz ard ra tio [HR] = 1.31, 95% CI:1.05-1.65, for the Cox-CSH model, and HR = 0.81, 95% CI:0.69-0.96, for the CS-AFT model. Gen der and WHO stage were found to be sig nif icantly as so ci ated with the com pos ite of un favourable out comes, HR = 1.56, 95% CI:1.27-1.90, HR = 1.28, 95% CI: 1.06-1.55 for males and WHO stage III-or-IV, re spec tively for the non-CSH model. Conclusions : Re sults show that WHO stage III-or-IV is sig nif i cantly as so ci ated with un favourable out comes. The re sults from com pet ing risk mod els were con sis tent. How ever, re sults ob tained from the non-CSH model were in con sis tent with those ob tained from com pet ing risk analy sis mod els.
Pharmacoepidemiology and drug safety, 2014
PurposeThe magnitude of risk for adverse drug reactions may be communicated by a measure of ‘exposure needed for one additional patient to be harmed’ (ENH). We present four ENH measures, based on four different counterfactual contrasts, as illustrated by the known effects of NSAID use on peptic ulcer bleeding.The magnitude of risk for adverse drug reactions may be communicated by a measure of ‘exposure needed for one additional patient to be harmed’ (ENH). We present four ENH measures, based on four different counterfactual contrasts, as illustrated by the known effects of NSAID use on peptic ulcer bleeding.MethodsThe four measures were basic ENH (estimating the excess risk when treating the entire source population versus treating no one), age-restricted ENH (the entire source population above, e.g. 50 years old treated versus no one above 50 years old treated), standardised ENH (a population of similar age and gender distribution as those actually treated versus same subjects not treated) and naturalistic ENH (those actually treated versus same subjects not treated).Data were derived from a case-control dataset on NSAIDs and severe peptic ulcer bleeding, collected in Funen County in 1995–2006. We incorporated prescription and census data to account for the source population's drug use.The four measures were basic ENH (estimating the excess risk when treating the entire source population versus treating no one), age-restricted ENH (the entire source population above, e.g. 50 years old treated versus no one above 50 years old treated), standardised ENH (a population of similar age and gender distribution as those actually treated versus same subjects not treated) and naturalistic ENH (those actually treated versus same subjects not treated).Data were derived from a case-control dataset on NSAIDs and severe peptic ulcer bleeding, collected in Funen County in 1995–2006. We incorporated prescription and census data to account for the source population's drug use.ResultsEstimates of basic, age-restricted, standardised and naturalistic ENH were 619 person-years (py) (95% confidence interval (CI): 558–684), 223 py (CI: 201–246), 131 py (CI: 118–144) and 162 py (CI: 151–173). The age-restricted ENH showed strong dependence on the chosen age limit.Estimates of basic, age-restricted, standardised and naturalistic ENH were 619 person-years (py) (95% confidence interval (CI): 558–684), 223 py (CI: 201–246), 131 py (CI: 118–144) and 162 py (CI: 151–173). The age-restricted ENH showed strong dependence on the chosen age limit.ConclusionThe differing counterfactual contrasts underlying the ENH result in widely different estimates. These differences reflect the clinical and epidemiological aspects of NSAID-related peptic ulcer bleeding. The ultimate choice of ENH measure will depend on epidemiological or clinical considerations and on availability of data. Copyright © 2014 John Wiley & Sons, Ltd.The differing counterfactual contrasts underlying the ENH result in widely different estimates. These differences reflect the clinical and epidemiological aspects of NSAID-related peptic ulcer bleeding. The ultimate choice of ENH measure will depend on epidemiological or clinical considerations and on availability of data. Copyright © 2014 John Wiley & Sons, Ltd.