Tumor dynamics and survival
Early tumor measurements and PSA kinetics used to predict later outcomes with patients kept apart between training and test data, with attention to dropout, information time and simple benchmarks such as the last observed value.
Do early tumor measurements improve prediction of subsequent survival?
A patient-separated landmark analysis of public colorectal cancer data, including calibration, censoring, uncertainty and temporal-integrity sensitivity.
- In a public 150-patient colorectal-cancer subset, a week-16 landmark analysis (128 patients) used only tumor measurements available before the prediction time.
- Adding early tumor change raised held-out concordance from 0.532 to 0.581 (difference +0.049, 95% interval −0.005 to +0.106), and calibration stayed weak (slope 0.464).
- Early tumor change is a candidate for further study, not a survival surrogate or decision rule; a separate validation cohort and denser longitudinal data are needed.
Does a tumor-kinetic model add anything to a single early tumor change?
At 16, 24 and 32 weeks, a mixed-effects tumor-kinetic estimate added no held-out survival discrimination beyond the observed one-point change, and carrying the last value forward predicted the next measurement best.
- At 16, 24 and 32 weeks, a mixed-effects tumor-kinetic estimate changed held-out survival C-index by only +0.002 to +0.016 over the observed one-point change, and every interval included zero.
- For the next tumor measurement, carrying the last value forward was the most accurate rule at every landmark (MAE 0.42–0.61), beating both linear and quadratic mixed models.
- Kinetic terms correlated about 0.97 with the one-point change, so with this measurement density a simple change suffices; this is not an evaluation of mechanistic TGI models in general.
When patients stop being measured: how much does dropout change a tumor-shrinkage estimate?
Most tumor-scan dropout was death. A mixed model removed most of the survivor bias in 48-week shrinkage; a joint model and delta adjustment showed the 24-week arm difference was robust but the 48-week difference was fragile.
- In a public colorectal-cancer subset where most scan dropout was death, the mean of patients still scanned overstated 48-week shrinkage by about a third in the combination arm; a mixed-effects model removed most of that bias.
- The 24-week shrinkage and arm difference held under every dropout assumption tried, including a joint model and delta adjustments.
- The 48-week arm difference lost support if dropouts in the better-looking arm deteriorated about 0.5 per year faster than predicted; without recorded dropout reasons, the mechanism is not identified.