title: Hazard ratio funnel plots for survival comparisons.
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.
  
  
  METHODS
  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 chi(2) statistics. Simulated results and a real example are presented.
  
  
  CONCLUSIONS
  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.
authors: Trent Cancer Registry, and NIHR Research Design Service for East Midlands, Nottingham, UK. paul.silcocks@nhs.net
authors: P
authors: P
authors: Silcocks
mesh_terms: D003626:Data Display; D006801:Humans; D015233:Models, Statistical; D016016:Proportional Hazards Models; D016019:Survival Analysis