A combined Cox and logistic model provides accurate predictive performance in estimation of time-dependent probabilities for recurrence of intrahepatic cholangiocarcinoma after resection

Abstract

Background: Intrahepatic cholangiocarcinoma has heterogeneous outcomes after resection. There remains a need for broadly applicable recurrence-specific tool offering precise evaluation on curativeness of resection.

Methods: A four hospital-based clinical cohort involving 1,655 patients with intrahepatic cholangiocarcinoma who received surgical resection were studied. Cox and logistic models were networked into one system containing risk categories with distinctive probabilities of recurrence. Prediction of time-to-recurrence was performed by formulizing time-dependent risk probabilities. The model was validated in three clinical cohorts (n=332).

Results: From the training cohort, 10 and 11 covariates, including diabetes, cholelithiasis, albumin, platelet count, alpha fetoprotein, carbohydrate antigen 19-9, carcinoembryonic antigen, hepatitis B virus infection, tumor size and number, resection type, and lymph node metastasis, from Cox and logistic models were identified significant for recurrence-free survival (RFS). The combined Cox & logistic ranking system (CCLRS)-adjusted time-dependent probabilities were categorized into seven ranks (5-yr RFS for lowest and highest ranks were 75% vs. 0%; hazard ratio 18.5, 95% CI: 14.7-24.9, P<0.0001). The CCLRS was validated with a minimum area under curve value of 0.8086. Prediction of time-to-recurrence was validated to be excellent (Pearson r, 0.8204; P<0.0001).

Conclusions: The CCLRS allows precise estimation on risk of recurrence for intrahepatic cholangiocarcinoma after resection. It could be applicative when estimating time-dependent disease status and stratifying individuals who sole resection of the tumor would not be curative.

Keywords: Primary liver cancer; biliary malignancy; hepatectomy; nomogram; regression model; resection; surgery.

Figure 1

Outline of the study. A total of 1,323 patients with high quality of data were enrolled from 1,477 cases. Multivariable Cox and Logistic analyses identified 10 and 11 significant and independent prognostic covariates, respectively. Probability for Cox and logistic models was networked and adjusted into one probability to build a predictive signature, which was validated in three independent clinical cohorts.

Figure 2

Nomograms generated for prediction of recurrence in patients with ICC after resection from multivariate analyses and development of the CCLRS. All significant covariates from the multivariate analyses were located on the left row and a straight line is drawn up to the points (located in the first row in each nomogram) to determine the corresponding points. Total points were added up and a straight line is drawn down to RFS rates for Cox and predicted probability for logistic models (located at the last row in each nomogram) to determine the individualized predicted survival probability. In ROC curves, thin gray lines represent the reference line. (A) A nomogram to predict recurrence of ICC using Cox regression model. (B) A nomogram to predict recurrence of ICC using logistic regression model. (C) ROC curve for the Cox regression model. (D) ROC curve for the Logistic regression model. ICC, intrahepatic cholangiocarcinoma; CCLRS, combined Cox & logistic ranking system; RFS, recurrence-free survival; ROC, receiver operating characteristic.

Figure 3

Validation of the CCLRS. The results obtained from the training set were validated in two independent validation cohorts drawn from Renji Hospital (validation cohort 1) and Zhongshan Hospital (validation cohort 3). Independent evaluation of the validation cohort 2 was discarded due to small sample size; this cohort was included in the combined validation cohorts. Blue dotted and gray thin lines represent the reference lines in calibration plots and ROC curves. Shown are calibration plots comparing predicted and actual probability of recurrence-free survival in validation cohort 1 (A), validation cohort 3 (C), and combined validation cohort (E), and ROC curves for evaluation accuracy in validation cohort 1 (B), validation cohort 3 (D), and combined validation cohort (F). CCLRS, combined Cox & logistic ranking system; ROC, receiver operating characteristic.

Figure 4

Evaluation of model performance for rank-dependent predicted probabilities, probability-dependent actual outcomes, and estimated time-to-recurrence. Rank-dependent adjusted probabilities obtained from the CCLRS were assessed using Kaplan-Meier estimation for discriminative ability in both training cohort (A) and validation cohort (B). Patient-to-recurrence columns (patients with recurrence, marked in red; patients without recurrence, marked in blue) in training cohort (C) and validation cohort (D) were generated for validation of model fit. Estimation of time-to-recurrence was tested in the validation cohort and obtained Pearson r value of 0.8204 (P<0.0001; E). Size of each plot is in proportion to the number of overlapping patients. CCLRS, combined Cox & logistic ranking system.