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Table 3 Area under the curve (AUC) for comparison of mean logarithmic score LS ¯ ( r ) of true vs. wrong modeling strategy ( r  = 1,…,100 iterations per simulation scenario)

From: Bayesian model selection techniques as decision support for shaping a statistical analysis plan of a clinical trial: An example from a vertigo phase III study with longitudinal count data as primary endpoint

k, degree of

 

AUC

overdispersion

Model

n  = 20

n  = 50

n  = 100

0.5

Poi

1

1

1

0.5

ZIP

1

1

1

0.5

arcsinh

0.796

0.781

0.953

0.5

ZINB

0.498

0.498

0.499

1

Poi

1

1

1

1

ZIP

1

1

1

1

arcsinh

0.683

0.831

0.883

1

ZINB

0.497

0.501

0.499

5

Poi

0.999

1

1

5

ZIP

0.999

1

1

5

arcsinh

0.673

0.796

0.877

5

ZINB

0.526

0.513

0.509

10

Poi

0.903

0.988

1

10

ZIP

0.909

0.990

1

10

arcsinh

0.733

0.826

0.913

10

ZINB

0.562

0.526

0.515

20

Poi

0.675

0.831

0.920

20

ZIP

0.686

0.837

0.925

20

arcsinh

0.773

0.902

0.966

20

ZINB

0.628

0.564

0.548

50

Poi

0.526

0.567

0.644

50

ZIP

0.548

0.582

0.658

50

arcsinh

0.799

0.914

0.985

50

ZINB

0.742

0.667

0.512

  1. True model: negative binomial GLMM; competing modeling strategies: Poisson, ZIP, NMM for arcsinh-transformed counts, ZINB. Sample size: n = 20, 50, 100 patients per group; degree of overdispersion: k  = 0.5, 1, 5, 10, 20, 50. AUC can be interpreted as a summary measure for the goodness of discrimination between the true negative binomial model generating the longitudinal data and rival models which should be taken into consideration in practice. For k→∞, the difference between a negative binomial and the alternative Poisson model dissolves because of convergence in distribution; therefore, AUC →0.5 and both model alternatives approximate with respect to their forecasting ability.