# br In order to obtain the CR the consistency

In order to obtain the CR, the consistency index (CI) is first cal-culated as

where the
eigenvalue λmax represents the sum of each criteria

weight in the pairwise comparison multiplied by the relative prior-ity vector. Then the CR is the ratio of the CI and the random index (RI) (see Table 5):

Fig. 1. AHP decision model for primary treatment in first decision step in non-metastatic case.

Fig. 2. AHP decision model for secondary treatment therapy in second decision step including metastatic cases.

Table 5

Table 6

Pairwise comparison of criteria with respect to goal in first decision step.

Goal
Stage-related risk
Breast
Biomarker breast
Patient-related risk
nth Root of the
Priority vector (PV)

cancer-related risk
cancer risk

product (GM)

Table 7

Weights of criteria with respect to goal in first decision step for five experts and aggregation for overall experts.

Goal: selecting effective treatment plan for breast cancer
Stage risk
Breast cancer risk
Biomarker breast cancer risk
Patient risk

To avoid any discrepancy, this N,N-Dimethylsphingosine study considers a threshold value of 10% for consistency ratio and confirms that there are no CRs exceeding this threshold value. If the comparison matrices were found to be inconsistent during the interview process, then experts were asked to revise their input, and a new comparison matrix was developed and corresponding CR value calculated. In this study, the GM was employed to combine the opinion of several oncologists as experts.

In order to rank the alternatives, a ranking algorithm is de-veloped, as will be presented in Section 5, rather than using the AHP methodology, due to the enormous number of alternatives and their comparisons in the AHP. Instead of developing a gen-eral treatment strategy that could be derived using the AHP, in this study, we aim to determine a patient-tailored strategy using a multi-criteria ranking algorithm.

In this section, we present the weights of criteria and subcri-teria obtained from the AHP models developed for both decision steps. Tables 6 to 8 represent the AHP results for the first deci-sion step, while Tables S.1-S.6 (in supplementary document) and Table 9 present the AHP results for the second decision step.

Table 6 shows an expert’s pairwise comparison of criteria with respect to the goal (selecting an effective primary treatment plan) and the priority vector of each criteria. The CR value of 0.01 in Table 6 implies that the input by this expert is consistent. Table 7 shows the weight of four main criteria with respect to the goal for five experts and the aggregated value overall for the experts obtained by the geometric mean. In Table 7, rhizome is observed that the cancer stage-related risk has the highest weight of 48% among all criteria considered for the primary treatment. Breast cancer-related risk has a weight of 28%, biomarker breast cancer-related risk has a weight of 18%, and patient risk has a weight of 7% of im-portance in selecting treatment alternatives for primary treatment. Table 8 shows a summary of AHP weights of criteria and subcri-teria for primary treatment. Table 9 shows a summary of breast cancer treatment selection criteria and corresponding weights for selecting an effective secondary treatment plan (see supplemen-tary material for detailed AHP results for the second decision step

and corresponding Tables S.1 to S.6 that provide expert’s pairwise comparison of criteria.)

In Table 6, we have n = 4 risk factors. The geometric mean of each risk factor weight is obtained by taking the nth root of the product of each row, as shown in the “nth root of the product (GM)” column. In Table 6, the sum of GMs is 5.13. Then the pri-ority vector is obtained by dividing each GM by 5.13, i.e. GMs are normalized. For example, priority vector value of the stage risk cri-teria is 2.55/5.13 = 0.50.