Fig. 1

AUCs for the mean ± SD with the training sample size and changes in the sampling times. a–d The instability of the prediction models built by the LR algorithm (red line) and RF algorithm (blue line) based on different single sampling times and sample sizes. a-l show that the prediction models built by the LR algorithm were better than those built by the RF algorithm. AUCs above 100 samplings showed that the performances of the prediction models built using the LR algorithm could be slightly improved as the training sample size increased, but the RF algorithm demonstrated the opposite performance. SDs of the AUCs from the prediction models built by both algorithms with different sample sizes displayed wide ranges. a-l separately represent the sampling times: 1, 1, 1, 1, 5, 10, 50, 100, 300, 600, 1200, and 2100 (related data are shown in Table 2). AUC area under the curve, LR logistic regression, RF random forest, SD standard deviations