Survival curve fitting using the Gompertz function: a methodology for conducting cost-effectiveness analyses on mortality data

The analysis of published survival curves can be the basis for incremental cost-effectiveness evaluations in which two treatments are compared with each other in terms of cost per life-year saved. The typical case is when a new treatment becomes available which is more effective and more expensive than the corresponding standard treatment. When effectiveness is expressed using the end-point of mortality, cost-effectiveness analysis can compare the (incremental) cost associated with the new treatment with the (incremental) clinical benefit measured in terms of number of life-years gained. The (incremental) cost-effectiveness ratio is therefore quantified as cost per life-year gained. This pharmacoeconomic methodology requires that the total patients years for the treatment and the control groups are estimated from their respective survival curves. We describe herein a survival-curve fitting method which carries our this estimation and a computer program implementing the entire procedure. Our method is based on a non-linear least-squares analysis in which the experimental points of the survival curve are fitted to the Gompertz function. The availability of a commercial program (PCNONLIN) is needed to carry out matrix handling calculations. Our procedure performs the estimation of the best-fit parameters from the survival curve data and then integrates the Gompertz survival function from zero-time to infinity. This integration yields the value of the area under the survival curve (AUC) which is an estimate of the number of patients years totalled in the population examined. If this AUC estimation is performed separately for the two survival curves of two treatments being compared, the difference between the two AUCs permits to determine the incremental number of patient years gained using the more effective of the two treatments as opposed to the other. The cost-effectiveness analysis can consequently be carried out. An example of application of this methodology is presented in detail.