Lead-Time Simple Exponential Smoothing as a Configurable, Uncertainty-Aware Framework for Adaptive Radiotherapy Monitoring

Abstract

Lead-time simple exponential smoothing (LT-SES) is developed as a configurable, uncertainty-aware framework for adaptive radiotherapy monitoring, in which a prospectively selected smoothing parameter alpha determines how strongly new observations update the current level. Using the standard innovations formulation of SES, closed-form expressions were derived for the predictive mean and variance of the remaining-course aggregate, enabling prediction intervals and conditional threshold probabilities to be updated after each fraction. OAR mean-dose time series from 32 prostate and 23 HN treatment courses were evaluated at prespecified $\alpha$-values from 0.1 to 1.0 across remaining-course horizons of 5, 10, 15, and 20 fractions, with a running-mean benchmark. Two parotid time series illustrated threshold probabilities, probability maps, and probability-weighted rank scores for $\alpha$ = 0.25, 0.50, and 1.0. Prediction intervals widened with forecast horizon and with increasing $\alpha$. Undercoverage was greatest for the running-mean benchmark and the lowest positive $\alpha$-values, especially at longer horizons, whereas $\alpha \ge 0.4$ produced wider intervals with coverage generally above nominal. In the parotid examples, lower $\alpha$-values provided greater stability, while higher $\alpha$-values responded more rapidly to short-term variation and sustained level shifts. Probability weighting produced greater numerical separation than the conventional scalar comparator and identified the sustained-shift time series several fractions before the scalar ratio crossed unity. LT-SES contextualizes projected scalar threshold differences using time series-specific interfractional innovation scale and remaining-course uncertainty. Its probability-scale outputs and rank scores provide a relative, uncertainty-aware complement to conventional scalar dose-metric monitoring.

22 pages and 8 figures plus 18 pages and 5 figures of Supplementary material