Logistic regression with uncertain disturbance and its application in risk forecast for postoperative complications of renal cell carcinoma with tumor thrombus

Forecasting postoperative complications in patients with renal cell carcinoma and tumor thrombus is clinically important but mathematically challenging, because the available data are limited, temporally unstable, and strongly affected by epistemic uncertainty. To address this problem, this paper proposes an uncertain logistic regression model with an uncertain disturbance term. The model parameters are estimated by uncertain maximum likelihood, and the residual is further analyzed through uncertain Bayesian rule and uncertain hypothesis testing. A retrospective cohort of 491 patients is used for the case study, including 418 patients from 2023 and earlier as the training set and 73 patients from 2024 as the temporal test set. Seven clinically meaningful risk factors are identified, including age, body mass index, tumor thrombus grade, venous-wall adherence, tumor diameter, lymph-node status, and metastasis status. Compared with the probabilistic logistic regression benchmark, the proposed method reduces the maximum forecast deviation from 0.1537 to 0.1350 and decreases the misjudgment ratio from 0.1644 to 0.1507. For the 90% uncertain interval, the empirical coverage obtained by uncertainty theory is 87%, whereas the corresponding probabilistic interval covers only 25% of the residuals. These results suggest that the proposed model is useful for conservative retrospective risk analysis under epistemic uncertainty, but they should not be interpreted as evidence of confirmed clinical decision support value. Further external and prospective validation is still required before any clinical deployment.