# Table 1 PROB of the CPCAT (decreasing trend)

c a $$\mu _0=25$$ $$\mu _0=50$$ $$\mu _0=75$$ $$\mu _0=100$$ $$\mu _0=125$$ $$\mu _0=150$$
0.1 0.9 0 0.001 0 0.006 0.017 0.049
0.5 0.9 0.012 0.038 0.082 0.128 0.168 0.257
1 0.9 0.059 0.098 0.169 0.173 0.27 0.329
5 0.9 0.163 0.184 0.241 0.22 0.266 0.271
10 0.9 0.201 0.215 0.203 0.222 0.237 0.253
0.1 0.8 0.009 0.337 0.866 0.998 1 1
0.5 0.8 0.157 0.474 0.733 0.905 0.966 0.988
1 0.8 0.221 0.475 0.654 0.807 0.871 0.912
5 0.8 0.253 0.321 0.391 0.425 0.439 0.492
10 0.8 0.206 0.258 0.291 0.282 0.323 0.346
0.1 0.7 0.565 1 1 1 1 1
0.5 0.7 0.597 0.962 0.997 0.993 0.998 0.997
1 0.7 0.546 0.873 0.938 0.947 0.959 0.959
5 0.7 0.368 0.474 0.553 0.594 0.597 0.622
10 0.7 0.257 0.357 0.394 0.39 0.409 0.427
0.1 0.6 0.999 1 1 1 1 1
0.5 0.6 0.945 0.994 0.993 0.997 0.991 0.995
1 0.6 0.846 0.949 0.942 0.945 0.943 0.943
5 0.6 0.479 0.565 0.578 0.628 0.618 0.609
10 0.6 0.334 0.407 0.425 0.46 0.457 0.478
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 