Hazard ratio funnel plots for survival comparisons. Issue 10 (18th June 2009) - Silcocks, P
Abstract : Background: Funnel plots are a form of control chart that give a snapshot of many institutions at a particular moment in time. This paper describes how funnel plots may be constructed for survival analyses based on hazard ratios obtained from a Cox regression model with adjustment for covariates and allowance for overdispersion. Method: Analysis of simulated and real survival data. Results: It describes how centred hazard ratio estimates adjusted for covariates can be obtained from a Cox regression and gives details of the necessary programming in Stata. Allowance for overdispersion can be made by multiplying the standard errors by a factor based on either the model or the log-rank χ 2 statistics. Simulated results and a real example are presented. Conclusion: Funnel plots based on hazard ratios are easier to interpret than multiple Kaplan–Meier survival plots, and in contrast to funnel plots based on survival at, say, 5 years, are less open to accusations of bias and use more information. The interpretation of such plots may be enhanced by using standard meta-analysis methods. Hazard ratio comparisons may now be added to the repertoire of techniques used by Cancer Registries, Primary Care Trusts, and other commissioners of healthcare.