. Author manuscript; available in PMC: 2021 Aug 1.

Published in final edited form as: Comput Toxicol. 2020 Aug 1;15(August 2020):1–100126. doi: 10.1016/j.comtox.2020.100126

Table 6.

Estimated prediction intervals by dataset.

	Regression Type	POD Type	Data	RMSE	Minimum Prediction Interval Width (fold = UB/LB)	1 mkd LB	1 mkd UB	10 mkd LB	10 mkd UB	100 mkd LB	100 mkd UB
1	ECDF of MLR model residuals	LEL	full dataset	NA	126	0.08	10.06	0.80	100.60	7.98	1005.98
2	ACM	LEL	CHR	0.628	284	0.06	17.02	0.59	170.16	5.88	1701.6
3	MLR	LEL	full cell dataset	0.622	276	0.06	16.56	0.6	165.61	6.04	1656.14
4	RR	LEL	full dataset	0.599	213	0.07	14.93	0.67	149.29	6.7	1492.86
5	MLR	LEL	CHR	0.593	208	0.07	14.53	0.69	145.3	6.88	1452.98
6	MLR	LEL	SUB	0.592	207	0.07	14.46	0.69	144.64	6.91	1446.43
7	MLR	LEL	full dataset	0.589	204	0.07	14.27	0.7	142.7	7.01	1426.98
8	MLR	LEL	high leverage points removed	0.582	198	0.07	13.83	0.72	138.26	7.23	1382.61
9	MLR	LEL	high Cooks distance plot points removed	0.582	198	0.07	13.83	0.72	138.26	7.23	1382.61
10	ACM	LEL	DEV	0.573	166	0.08	13.28	0.75	132.76	7.53	1327.58
11	ACM	LEL	full cell dataset	0.566	161	0.08	12.86	0.78	128.63	7.77	1286.29
12	ACM	LOAEL	DEV	0.562	158	0.08	12.63	0.79	126.33	7.92	1263.28
13	MLR	LOAEL	full cell dataset	0.559	156	0.08	12.46	0.8	124.63	8.02	1246.29
14	ACM	LEL	SUB	0.549	149	0.08	11.91	0.84	119.13	8.39	1191.3
15	MLR	LOAEL	SUB	0.526	119	0.09	10.74	0.93	107.38	9.31	1073.84
16	RR	LOAEL	full dataset	0.516	103	0.1	10.26	0.97	102.65	9.74	1026.46
17	ACM	LOAEL	CHR	0.515	102	0.1	10.22	0.98	102.18	9.79	1021.84
18	MLR	LEL	high Cooks distance points removed	0.511	100	0.1	10.04	1	100.36	9.96	1003.56
19	MLR	LEL	all potential outliers removed	0.511	100	0.1	10.04	1	100.36	9.96	1003.56
20	MLR	LOAEL	full dataset	0.508	99	0.1	9.9	1.01	99.01	10.1	990.06
21	MLR	LOAEL	high Cooks distance plot points removed	0.504	97	0.1	9.72	1.03	97.23	10.28	972.35
22	ACM	LOAEL	full cell dataset	0.504	97	0.1	9.72	1.03	97.23	10.28	972.35
23	MLR	LOAEL	CHR	0.502	96	0.1	9.64	1.04	96.36	10.38	963.61
24	MLR	LOAEL	high leverage points removed	0.5	96	0.1	9.55	1.05	95.5	10.47	954.95
25	ACM	LOAEL	SUB	0.5	96	0.1	9.55	1.05	95.5	10.47	954.95
26	MLR	LEL	DEV	0.496	85	0.11	9.38	1.07	93.79	10.66	937.87
27	MLR	LOAEL	DEV	0.466	68	0.12	8.19	1.22	81.91	12.21	819.11
28	MLR	LOAEL	high Cooks distance points removed	0.447	58	0.13	7.52	1.33	75.18	13.3	751.8
29	MLR	LOAEL	all potential outliers removed	0.447	58	0.13	7.52	1.33	75.18	13.3	751.8

Three different estimates of prediction interval are used: the 2.5^th to 97.5^th percentiles from the ECDF of the MLR model for the full LEL dataset; the RMSE from the MLR model for the full LEL dataset; and, the MLR model for the full LEL dataset with all potential outliers removed. The minimum prediction interval width is the upper bound of the interval divided by the lower bound of the interval. For context, the lower and upper bounds of a prediction interval for 1, 10, and 100 mg/kg/day “true” POD values are shown. LB and UB = lower bound and upper bound, respectively; mkd = mg/kg/day.