How good are the estimates of the hazard ratio When calculated indirectly? An empirical investigation

Article type
Authors
D'Amico R, Torri V, Floriani I, Tinazzi A, Liberati A
Abstract
Background: The calculation of the hazard ratio (HR) estimated indirectly extracting data from the survival curves requires the knowledge of some information at various time-points such as: a) number of patients at risk; b) number of patients censored and c) range of the lengths of follow up (LFU) (1). When none of this information is reported, assumptions are required regarding: a) maximum and minimum LFU; b) rate of censoring at various time-points and c) numbers of time intervals to be considered.

Objective: To assess the performance of the indirect estimate of the HR under different assumptions.

Methods: Three randomised clinical trials involving patients with different prognoses were considered. For each study, patients from both arms were randomly selected with replacements and a survival curve was obtained. Several HRs were calculated: a) using the individual data and b) using the indirect method under different assumptions. This process was repeated 1000 times. The distributions of the logHRs obtained by the indirect methods were compared to the distribution of the logHRs obtained by using the individual data.

Results: Our preliminary results indicate that means and variances of the distribution of the logHRs estimates derived through the indirect method were similar to those derived from individual data regardless of the number of time intervals and the assumption of the maximum and minimum FU.

Conclusion: When the survival curves are clearly reported HRs estimates obtained through indirect method appears to be a good approximation of those obtained via the individual data. Further investigation to assess the robustness of the indirect estimates under departures from the proportional hazard hypothesis are warranted and will be discussed during the presentation. 1. Parmar MKB, Torri V, Stewart L. Extracting summary statistics to perform meta-analyses of the published literature for survival endpoint. Statistics in Medicine 1998; 17:2815-2834