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Figure S1: Densities used in the simulation studies in the two class case. Left: Yinline image N(3, 1), Yinline image N(4, 0.82). Middle: Yinline image Gamma(25,0.2), Yinline image Gamma(35,0.2). Right: Noncentral t distributions Yinline image t(4,7) and Yinline image t(5,10)

Figure S2: Densities used in the simulation studies in the three class case. Left: Yinline image N(5, 1), Yinline image N(6, 1), Yinline image N(7,1) . Middle: Yinline image Gamma(25, 0.2), Yinline image Gamma(35,0.2), Yinline image Gamma(45,0.2). Right: Noncentral t distributions Yinline image t(4, 7), Yinline image t(5, 10) and Y3∼ t(6, 12)

Figure S3: Empirical ROC curve and CNS ROC curve for the liver cancer data when the H and LD group are combined to single ‘diseased’ group.

Figure S4: The projections of the ROC surface on the sides of the unit cube are equivalent of a pairwise ROC analysis. The corresponding ROC curves for each pair of disease status for the liver data are shown.

Figure S5: Projections of the empirical and CNS ROC surfaces on the sides of the unit cube for the liver data. Up: Corresponding ROC curves in the case of an upper LOD that causes approximately 10% censoring. Down: Corresponding ROC curves in the case of an upper LOD that causes approximately 30% censoring.

Table S1: Simulation results for 1000 repetitions for the bigamma scenario. The likelihood approach assumes the correct model for both populations. The coverage is derived by using the percentile bootstrap with 200 samples for each repetition. (True AUC equals to 0.9037)

Table S2: Simulation results for 1000 repetitions for the scenario of two populations that follow a noncentral t distribution. The likelihood approach falsely assumes the normal model for both populations. The coverage is derived by using the percentile bootstrap with 200 samples for each repetition. (True AUC equals to 0.7355)

Table S3: Simulation results for 1000 repetitions for the trigamma scenario. The likelihood approach assumes the correct model for the three populations. The coverage is derived by using the percentile bootstrap with 200 samples for each repetition. (True VUS equals to 0.7747)

Table S4: Simulation results for 1000 repetitions for the scenario of three noncentral t distributions. The likelihood approach falsely assumes the normal model for the three populations. The coverage is derived by using the percentile bootstrap with 200 samples for each repetition. (True VUS equals to 0.4185)

Table S5: Simulation results for 1000 repetitions for the binormal scenario with unequal sample sizes for the two populations (100 and 300 for Y0 and Y1 respectively). The likelihood approach assumes the correct model for both populations. The coverage is derived by using the percentile bootstrap with 200 samples for each repetition. (True AUC equals to 0.7826)

Table S6: Simulation results for 1000 repetitions for the bigamma scenario with unequal sample sizes for the two populations (100 and 300 for Yqand Y\, respectively). The likelihood approach assumes the correct model for both populations. The coverage is derived by using the percentile bootstrap with 200 samples for each repetition. The case of 50% is not presented for left censoring since the level of censoring for Yo is over 90%. (True AUC equals to 0.9037)

Table S7: Simulation results for 1000 repetitions for the scenario where the two populations follow two noncentral tdistributions. The sample sizes for the two populations (100 and 300 for Yqand Y\respectively). The likelihood approach falsely assumes normality for both populations. The coverage is derived by using the percentile bootstrap with 200 samples for each repetition. (True AUC equals to 0.7355)

Table S8: Simulation results for 1000 repetitions in the case of a lower LOD when 5 or 6 or 7 knots are used with the proposed method (CNS(5), CNS(6), and CNS(7) respectively). The sample size for each of the two populations equals to 100. (Results that correspond to CNS(6) are restated here for convenience)

Table S9: Simulation results for 1000 repetitions in the case of a lower LOD when 5 or 6 or 7 knots are used with the proposed method (CNS(5), CNS(6), and CNS(7) respectively). The sample size for each of the two populations equals to 200. (Results that correspond to CNS(6) are restated here for convenience)

Table S10: Simulation results for 1000 repetitions in the case of a lower LOD when 5 or 6 or 7 knots are used with the proposed method (CNS(5), CNS(6), and CNS(7) respectively). The sample sizes are 100 and 300 for Y0 and Y1 respectively. (Results that correspond to CNS(6) are restated here for convenience)

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