Background: In medical publications, effectiveness of health interventions for chronic diseases is usually expressed as absolute risk reduction (ARR), number-needed-to-treat (NNT) or relative risk reduction (RRR). These measures are estimated at one point in time and require the hazard rates to be constant over time in order to yield information that is representative for the whole interventions period. Measurement at one point in time may not be adequate if the relative hazard for the event of interest (typically death) varies with time. Individual patient data are required to estimate hazard rates and relative hazards. However, survival curves may be used to make inferences about relative hazards. Crossings and/or convergences of survival curves after they have diverged clearly indicates the relative hazard is not constant.
Objectives: To explore how frequent survival curves do converge and/or cross in medical research and to investigate determinants of convergences and crossings.
Design: Review of all publications that included survival graph during 2007 in five major peer-reviewed medical journals. The following data were extracted: type of disease, type of exposure, number of comparator groups, number of pairwise comparisons, type of primary and secondary end-points, sample size, maximum follow-up time, survival curve convergences, survival curve crossings, type of epidemiologic study design, result of log-rank test (if reported), and country in which the study was undertaken.
Sample: 177 publications from Annals of Internal Medicine (AIM), British Medical Journal (BMJ), Journal of the American Medical Association (JAMA), New England Journal of Medicine (NEJM) and The Lancet.
Results: 78% of the publications had survival curve convergences and 42% survival curve crossings. The proportion of survival curve convergences and crossings varied across disease type, intervention type, number of comparator groups, number of pairwise comparisons, types of primary and secondary endpoints, sample size, study design and length of follow-up time. In multivariate logistic regression, survival curve convergence was positively associated with more than one pairwise comparison (OR 3.7, 95% CI 1.3-10.8) and death as a secondary endpoint (OR 8.1, 95% CI 1.1-65.5). No association was found between survival curve crossings and any of the explanatory variables.
Conclusion: Survival curve convergences and crossings are common phenomena in medical research. The phenomena seem not to be associated with particular study characteristics. The results warrant care in making inferences about the effectiveness of interventions for chronic diseases on the basis of measurement at a single point in time.