Active learning-based multistage sequential decision-making model with application on common bile duct stone evaluation

Abstract

Multistage sequential decision-making occurs in many real-world applications such as healthcare diagnosis and treatment. One concrete example is when the doctors need to decide to collect which kind of information from subjects so as to make the good medical decision cost-effectively. In this paper, an active learning-based method is developed to model the doctors' decision-making process that actively collects necessary information from each subject in a sequential manner. The effectiveness of the proposed model, especially its two-stage version, is validated on both simulation studies and a case study of common bile duct stone evaluation for pediatric patients.

Keywords: Active learning; incomplete data; ordinal logistic model; sequential decision.

Figure 1.

The framework of the proposed multistage sequential decision-making model, where K is the number of stages, ${\pi }_i^{(j)}$ is the probability of patient i having disease estimated in stage j, $U_j$ and $L_j$ is the cutoff points on the estimated probability in stage j, and $C_K$ is the single cutoff point in the last stage, K.

Figure 2.

Mean coefficients estimation comparison among ground truth (black line), mean coefficients estimated from baseline approached individually (blue and yellow line), and mean coefficients estimated from proposed method jointly (red line). (a) for 4 β coefficients in stage 1 and (b) for 3 β coefficients in stage 2. This plot demonstrates that both methods have little bias on parameter estimation.

Figure 3.

Standard deviation of coefficients estimation from two methods.

Figure 4.

Relative efficiency of the proposed method with respect to the baseline method.

Figure 5.

Mean prediction metrics for 2 stages with coefficients estimated from baseline approach individually (blue and green line), and coefficients estimated from proposed method jointly (red and black line). Note that the blue and black lines are too close to each other to distinguish them from each other visually. The red line is almost higher than the green line in every dimension, demonstrating the advantages of the proposed method.

Figure 6.

Coefficients comparison between coefficients obtained from 2 methods for features in stages 1.