Table 2 PROB of the CPCAT (increasing trend)

c

a

$$\mu _0=25$$

$$\mu _0=50$$

$$\mu _0=75$$

$$\mu _0=100$$

$$\mu _0=125$$

$$\mu _0=150$$

0.1

1.1

0

0

0

0.004

1

1

0.5

1.1

0.015

0.035

0.07

0.098

0.995

0.994

1

1.1

0.067

0.096

0.127

0.167

0.95

0.959

5

1.1

0.191

0.199

0.211

0.234

0.591

0.595

10

1.1

0.2

0.207

0.2

0.209

0.438

0.445

0.1

1.2

0.002

0.101

0.608

0.935

1

1

0.5

1.2

0.11

0.311

0.594

0.789

0.998

0.998

1

1.2

0.154

0.384

0.544

0.697

0.942

0.947

5

1.2

0.239

0.319

0.379

0.42

0.601

0.61

10

1.2

0.225

0.251

0.289

0.291

0.451

0.453

0.1

1.3

0.178

0.985

1

1

1

1

0.5

1.3

0.38

0.831

0.977

0.99

0.994

0.993

1

1.3

0.402

0.744

0.891

0.943

0.946

0.947

5

1.3

0.276

0.427

0.481

0.516

0.596

0.609

10

1.3

0.259

0.292

0.345

0.348

0.458

0.443

0.1

1.4

0.9

1

1

1

1

1

0.5

1.4

0.724

0.989

0.998

0.998

0.993

0.995

1

1.4

0.677

0.906

0.953

0.937

0.945

0.943

5

1.4

0.382

0.484

0.532

0.601

0.594

0.625

10

1.4

0.288

0.359

0.396

0.413

0.446

0.463

1. Parameter $$c>(<)1$$ indicates generalized Poisson distribution with over-(under-)-dispersion ($$\sigma ^2=c\cdot \mu$$) or Poisson distribution ($$c=1$$). Parameter a indicates the value of the true LOEC via $$\mu _2=a\cdot \mu _0$$. Parameter $$\mu _0$$ denotes the mean reproduction of the control group