# 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 