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

 True model: negative binomial GLMM; competing modeling strategies: Poisson, ZIP, NMM for arcsinhtransformed 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.