Survival path model outperforms conventional static machine learning models in long-term dynamic prognosis prediction for patients with intermediate stage hepatocellular carcinoma

Abstract

Motivation: Patients with intermediate stage hepatocellular carcinoma (HCC) require repeated disease monitoring, prognosis assessment, and treatment planning. A novel machine learning model called survival path mapping (SP) model was developed, while its performance as compared with conventional machine learning models remains unknown. Between January 2007 and December 2018, the time-series data of 2644 intermediate stage HCC patients from four medical centers in China were reviewed and included. Static machine learning models by Gaussian Naive Bayes (GNB), support vector machine (SVM), and random forest (RF) for the prediction of survivorship were built based on data at initial admission. Longitudinal data divided into different time slices were utilized for the construction of the SP model. The time-dependent c-index was compared between models.

Results: The training set, internal testing set, and external testing set consisted of 1560, 670, and 414 HCC patients, respectively. The survival path model had superior or non-inferior performance in prognosis prediction compared to GNB and RF models since the 12th month after initial diagnosis in the training set and the external testing set. The survival path model had higher time-dependent c-index over all conventional ML models since the 6th month in the external testing cohort. In conclusion, the survival path model had superior performance in long-term dynamic prognosis prediction compared to conventional static machine learning models for intermediate stage HCC.

Availability and implementation: The parameters of models are provided in the manuscript.

Figure 1.

Flowchart of study design. Times-series data of 2230 patients with intermediate stage HCC were included in this study and were separated into training set (n = 1560) and internal testing set (n = 670), respectively. (A) The time-series data were converted into data of time slices (ts). (B) In building of conventional static ML models, the data of time slice no. 1 were extracted. The conventional models were built based on framework of Bayesian, random forest, or SVM to separately predict survival status of HCC patients at 6, 12, 24, 36, 48 months based on data of time slices no. 1. The construction of survival path model was based on time-series data from ts no. 1 to no. 9. The time-dependent c-index of different category of models in prediction of survival based on data of different time slices (ts 1–9) were compared. The results were also validated in a multicentric cohort (n = 414).

Figure 2.

Scatter plot of the correlation between the survival outcome and key features/variables using PCA. The scatter plot describes the correlations between the survival outcome and 16 key features/variables of intermediate-stage liver after dimensionality reduction using PCA. In all subgraphs, the data points for “death” and “survival” overlap, suggesting that using variables from a single time point alone is insufficient to accurately predict whether a patient will have died at a specific time point. An outlier point with PC1 more than two times of the maximal value of the rest patients in PC1 at time slice no. 7 was removed to gain a better visualization of the relationship between the distribution of points and the outcomes.

Figure 3.

The survival path model constructed based on the training set. The numbers above each node separated by slash refers to the node name, sample size, and median OS of the patients at the specific node, respectively. The “NA” refers to the condition that median OS was not reached.

Figure 4.

Comparison of the time-dependent c-index between different models. The change of time-dependent c-index along with different evaluation time for the four machine learning models in the training set, internal testing set, and multicentric testing set were compared. *** The SP model demonstrated superior c-index compared to other machine learning models, with P-value $<$.0009.