Closed-form elasticity and elementary-effect sensitivity analysis of the universal survival curve model for...

The universal survival curve (USC) joins the linear-quadratic (LQ) description of the shoulder region to the log-linear multi-target asymptote at a transition dose, and is increasingly invoked to justify ablative fractionation. Which input actually controls predicted survival has not been established analytically. We derive closed-form elasticities, rank the inputs by two independent methods, and quantify the consequences for stereotactic schedules.

Continuity of value and gradient at the transition dose fixes the quadratic coefficient and the transition dose in terms of the three cell-line parameters. Elasticities were derived in closed form, verified against central differences, and ranked independently by Morris elementary-effect screening over a fifteen per cent envelope. Biologically effective doses were compared for six clinical schedules and nine non-small-cell lung cancer cell lines.

Dose dominated, with mean absolute elasticity 7.89, followed by the mean inactivation dose 6.64, the quasi-threshold dose 1.15 and the radiosensitivity coefficient 0.104. Morris screening reproduced this ordering. The two agreed for conventional fractionation but diverged sharply above the transition dose, the LQ formulation overstating biologically effective dose by 42 per cent for 54 Gy in three fractions and by 97 per cent for a single 30 Gy fraction.

Within the USC model and the in vitro data examined, predicted survival is governed by delivered dose and the characteristic dose rather than by the radiosensitivity coefficient, so parameter-estimation effort should target the terminal slope of the survival curve; the analysis ranks the inputs of each model but does not adjudicate between the models.