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As the P-value calculation procedure takes into account only the best ranks for each factor, the method is very robust, which is important when using high-throughput data.

We also calculate powers of the five p-value calculation procedures together with the three test statistics at the nominal level α=0.05 when π T = π R and θ=0.6 with the following settings: n=30 and 60, π P =0.15 and 0.3, and π R =0.5,0.8 and 0.95 for the balanced allocation 1 1 1 and unbalanced allocation 1 2 3.

The approximate unconditional and bootstrap-resampling methods perform better than other p-value calculation procedures in the sense that their corresponding type I error rates are closer to the prespecified nominal level and their corresponding powers are larger than those of other p-value calculation procedures.

In terms of time-consuming and type I error rates and powers, the approximate unconditional method with score test statistic behaves the best among our considered p-value calculation procedures and test statistics.

Inspired by Tang and Tang [ 18], we also propose the exact unconditional, approximate unconditional and Bootstrap-resampling p-value calculation procedures for testing three-arm non-inferiority with small sample sizes.

Given θ=0.6 and 0.8, the corresponding p-values for testing H0:(π T − π P )/(π R − π P )≤ θ versus H1:(π T − π P )/(π R − π P )> θ based on the five p-value calculation procedures and three test statistics are reported in Table 2.

To investigate the sensitivity of various p-value calculation procedures (i.e., AM, SAM, EUM, AUM and BTM) to different test statistics, Figure 2 presents boxplots of their corresponding type I error rates against π P for test statistics T W, T R and T L. Examination of Figure 2 shows that there is no significant effect of π P on the type I error rate.

Let us analyze the calculation procedure of the intermediate (regular) baseline values using the proposed method.

The p-values were corrected for multiple comparisons using the Benjamini-Hochberg FDR calculation procedure [ 26].

The p-values were then corrected for multiple comparisons using the Benjamini-Hochberg FDR calculation procedure [ 26].

Algorithm 1 describes the drivers' initialization and route calculation procedures that are called in Algorithm 3. The route calculation procedure consists in using a shortest path algorithm with the z value of a link (Equation 3) as its weight.

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