Author + information
- Judith A. Finegold, MBBS∗ ( and )
- Darrel P. Francis, MA, MD
- ↵∗International Centre for Circulatory Health, National Heart and Lung Institute, Imperial College London, 59 North Wharf Road, London W2 1LA, United Kingdom
We thank Dr. Messori and colleagues for asking for clarification on the Methods used in our recent paper.
We should clarify that our Figure 2 used an average weighted solely by the sample size of the 5 trials, because this seemed appropriate weighting for combining rates across trials. The reason for this graph was to take the same approach used previously by our group (1) to address the frequently raised question of whether lifespan gain really does expand progressively with time, even though many commentators simply state that “one has to implant x devices to obtain a benefit” without specifying a time window. Figure 2 shows that no single value is correct for all time windows. Nothing from Figure 2 is used elsewhere in our paper.
For the lifespan gain calculations in the main paper, we used hazard ratios published by the trialists themselves, because these came from the entire trial period, which maximized the information extracted from the data. All 5 trials provided a hazard ratio, but not all provided the 95% confidence interval. We could not, therefore, calculate the ideal inverse-variance–weighted average using the reciprocal of the confidence interval width and instead used an unweighted average of the 5 hazard ratios. Lifespan gains were calculated using a life table with annual deaths calculated from 2 competing hazards. One hazard was amenable to reduction by cardiac resynchronization therapy device implantation; the other was not and instead increased annually by a scale factor of 1.1.
The second inquiry was how the Gompertz method was used to calculate lifespan gain in the post-trial period. We did not attempt to fit Kaplan-Meier survival curves to the Gompertz equation because, as Dr. Messori and colleagues rightly point out, this is mathematically and statistically complex. It would additionally be unwise to attempt to extract from the trial data the Gompertz coefficient, which quantifies rising mortality hazard with aging (equivalent to longer after randomization). First, trials typically do not report survival for sufficiently long periods for curves to show appreciable convexity (mortality acceleration), that is, the Gompertz coefficient has not yet manifested. Second, because of staggered enrollment, at later times from randomization there are fewer patients being followed, so random noise dominates the Kaplan-Meier curves, which further imperils any attempt to extract the Gompertz coefficient. We therefore set the Gompertz exponent eβ at β=0.095 per year to scale up the hazard of non–cardiac resynchronization therapy–preventable mortality by a factor of 1.1 every year, based on the U.S. national census data of 2003.
We thank Dr. Messori and colleagues for helping ensure our methods are clear and, as always, welcome any further questions via the Journal or directly.
Please note: Dr. Francis is supported by the British Heart Foundationhttp://dx.doi.org/10.13039/501100000274 (FS/10/038) and is a consultant to Medtronic and Sorin.
- American College of Cardiology Foundation