Document Jv87g6KmXK5oEBko5pwE0mBr

39 ff UNITED STATES ENVIRONMENTAL PROTECTION AGENCY WASHINGTON, D.C. 20460 1133 OFFICE OF PREVENTION, PESTICIDES AND TOXIC SUBSTANCES 21 October 2002 MEMORANDUM: SUBJECT: Focussed statistical analyses of APFO data on >and preweaning loss g?* FROM: Elizabeth H. Margosches, Ph.D., Statistician Existing Chemicals Assessment Branch J . Risk Assessment Division (7403M) / CD CD -rn TO " O O cn *~4fn TO: Katherine Anitole, Ph.D., Toxicologist Existing Chemicals Assessment Branch Risk Assessment Division (7403M) *TJ CD fK> cn no On 30 August 2002 several members of industry met with EPA staff to discuss results seen in the study by York (2002) and some other studies that might have bearing on them. It was agreed that certain additional analyses would be carried out. York (2002) reported there were no statistically significant differences among the treatment groups in numbers of dams delivering litters, the duration of gestation, averages for implantation sites per delivered litter, gestation index, numbers of dams with stillborn pups, dams with all pups dying, liveborn and stillborn pups, viability index, pup sex ratios and body weights for either the FO or FI parental generations and their litters. According to p. 45 of the report, these analyses were carried out using analysis of variance or, if the group variances were not comparable, the Kmskal-Wallis test (nonparametric), or, for count data, a chi-square for homogeneity. The additional analyses related to an index of prenatal mortality (taken as (implantations minus liveborn)/implantations) and one of preweaning mortality (taken as (liveborn minus those alive on day 22)/liveborn). These quantities are proportions within each litter and the variance of a sample proportion is related to the true proportion. When the denominators are nearly equal, the analyses can be carried out using data transformed in a standard fashion, using arcsin(.)l/2(see Gaylor, 1978). Analysis of variance of the numbers of implantations, and those numbers properly transformed for being counts ((i)'/2+(i+l)14) assured that this condition was pretty well fulfilled. To illustrate the effect of the transformation of the proportions, plots and analyses are provided both with and without the transformation, although the untransformed statistics should not be used. All analyses were implemented using the computer program Statistix (Statistix 7, Analytical Software, 2000). In light of the other tests already carried out by York (2002), the high dose prenatal mortality index was statistically compared only to the control. Plots of the index for control and four positive doses (p. 1 of the 36 analysis pages) showed that, in both F0 (red squares) and FI (blue circles), the treatments did not appear to differ. The comparison was carried out using Student's t-test. No difference was seen between high dose and control (p. 3). The preweaning mortality index was examined across all dose groups, within generation. Here again a plot of the index across all treatments (p. 12)suggested no differences. This comparison was carried out using Analysis of Variance (p. 20 for P or F0, p. 26 for FI), followed by a Scheffe comparison of the individual treatment means (p. 21 and p. 27, respectively). Using the Scheffe basis permitted all contrasts of means to be considered in follow-up comparisons while controlling for an overall error rate. While the order o f treatment-group means appeared to differ between F0 and F I, in neither case were there any significant pairwise differences between the dose groups and the responses did not have any trend in dose. Gaylor, D.W. 1978. Methods and Concepts of Biometrics Applied to Teratology. In: J.G. Wilson and F.C. Fraser, ed., Handbook of Teratology. Voi. 4. New York: Plenum Press, pp. 429-444. Statistix Version 7.0 [computer software]. Analytical Software. 1985, 2000. cc: J. Seed TRPREB(arcsin(sqrt( 1-live/implant)) Data (proportions lost prior to birth) transformed to stabilize variances Scatter Plot of TRPREB vs DOSE oo o e 8 1! 81 i oa 0 o 6 O 1s a 12 DOSE 18 24 O GEN O F1 8 P 8 O I a 30 Scatter Plot of PREBIRTH vs DOSE NI3 I GEN O F1 P DOSE STATISTIX 7 .0 TWO-SAMPLE T TESTS FOR TRPREB BY DOSE CONT-HIGHONLY, 10/15/02, 4:03:39 PM P DOSE MEAN SAMPLE SIZE S. D. S.E. 0 30 DIFFERENCE 0.2020 0.2825 -0.0805 28 29 0.1941 0.2945 0.0367 0.0547 NULL HYPOTHESIS: DIFFERENCE = 0 ALTERNATIVE HYP: DIFFERENCE <> 0 ASSUMPTION T DF P 951 Cl FOR DIFFERENCE EQUAL VARIANCES UNEQUAL VARIANCES -1.21 -1.22 55 0.2299 48.6 0.2273 (-0.2134, 0.0524) (-0.2129, 0.0518) TESTS FOR EQUALITY OF VARIANCES F 2.30 NUM DF 28 DEN DF 27 P 0.0166 CASES INCLUDED 57 MISSING CASES 3 TRPREB = transformed (loss prior to birth) In parents (p. 3) and FI (p. 8), control and high dose groups not significantly different under assumption of unequal variances (or equal ones). The test for variance equality is sensitive to normality assumptions, and these data are not normally distributed. The indication the variances are unequal may not be correct for P (see the box and whiskers plot p. 4) although it's likely for FI (see p. 9) -3- TRPREB Box and Whisker Plot P 0 30 DOSE 57 cases 3 missing cases -4- The Box and Whisker Plot procedure computes box plots that graphically present measurements o f central tendency and variability. A series o f box plots can be displayed side by side, which can dramatically illustrate differences between groups. Each box plot is composed o f a box and two whiskers. The box encloses the middle half of the data. The box is bisected by a line at the value for the median. The vertical lines at the top and the bottom o f the box are called the whiskers, and they indicate the range o f "typical" data values. Whiskers always end at the value o f an actual data point and can't be longer than 114 times the size of the box. Extreme values are displayed as for possible outliers and "O" for probable outliers. Possible outliers are values that are outside the box boundaries by more than 114 times the size o f the box. Probable outliers are values that are outside the box boundaries by more than 3 times the size of the box. Copyright 2000 Analytical Software -5- STATISTIX 7.0 TWO-SAMPLE T TESTS FOR PREBIRTH BY DOSE 10/15/02, 3:34:53 PM P DOSE MEAN SAMPLE SIZE S.D. S.E. 0 30 DIFFERENCE 0.0727 0.1274 -0.0547 28 29 0.0826 0.1942 0.0156 0.0361 NULL HYPOTHESIS: DIFFERENCE = 0 ALTERNATIVE HYP: DIFFERENCE <> 0 ASSUMPTION T DF P 95% Cl FOR DIFFERENCE EQUAL VARIANCES UNEQUAL VARIANCES -1.38 -1.39 55 0.1747 38.1 0.1719 (-0.1344, 0.0250) (-0.1342, 0.0248) TESTS FOR EQUALITY OF VARIANCES F -- 5.52 NUM DF -- 28 DEN DF -- 27 P -- 0.0000 CASES INCLUDED 57 MISSING CASES 3 PREBIRTH = loss prior to birth -6- PREBIRTH Box and Whisker Plot P 0 30 DOSE 57 cases 3 missing cases -7- STATISTIX 7.0 TWO-SAMPLE T TESTS FOR TRPREB BY DOSE CONT-HIGHONLY, 10/15/02, 4:05:52 PM R DOSE MEAN SAMPLE SIZE S.D. S.E. 0 30 DIFFERENCE 0.2497 0.2521 -2.41E-03 28 29 0.1483 0.2223 0.0281 0.0413 NOLL HYPOTHESIS: DIFFERENCE = 0 ALTERNATIVE HYP: DIFFERENCE <> 0 ASSOMPTION T DF P 95% CI FOR DIFFERENCE EQUAL VARIANCES UNEQUAL VARIANCES -0.05 -0.05 55 0.9619 49.1 0.9616 (-0.1032, 0.0984) (-0.1028, 0.0980} TESTS FOR EQUALITY OF VARIANCES F -- 2.23 NUM DF -- 28 DEN DF -- 27 P -- 0.0201 CASES INCLUDED 57 MISSING CASES 3 -8- TRPREB Box and Whisker Plot & 1. 0 - 0.8 0.6 0.4 0.2 0.0 0 DOSE 57 cases 3 missing cases -9- STATISTIX 7.0 TWO-SAMPLE T TESTS FOR PREBIRTH BY DOSE 10/15/02, 3:27:53 PM Fl DOSE MEAN SAMPLE SIZE S.D. S.E. 0 30 DIFFERENCE 0.0801 0.0998 -0.0197 28 29 0.0600 0.1258 0.0113 0.0234 NULL HYPOTHESIS: DIFFERENCE = 0 ALTERNATIVE HYP: DIFFERENCE <> 0 ASSUMPTION T DF P 95% CI FOR DIFFERENCE EQUAL VARIANCES UNEQUAL VARIANCES -0.75 -0.76 55 0.4563 40.4 0.4524 (-0.0723, 0.0329) (-0.0722, 0.0328) TESTS FOR EQUALITY OF VARIANCES F ------ 4.39 NUM DF -- 28 DEN DF -- 27 P -- 0.0001 CASES INCLUDED 57 MISSING CASES 3 -10- PREBIRTH Box and Whisker Plot Pi 0.8 0.6 - 0.4- 0. 2 - 0.0- 30 DOSE 57 cases 3 missing cases -ll- T R P R E W (arcsin(sqrt(1-d ay22 /live)) Data (proportions of live births lost prior to weaning) transformed to stabilize variances Scatter Plot of TRPREW vs DOSE GEN O F1 P TRPREW 1.6 o 1.2 0.8 0.4 0.0 0 Box and Whisker Plot o o 1 3 10 DOSE 283 cases 16 missing cases 30 p. 12 and pp. 13-15 illustrate two ways of looking at the transformed preweaning loss, to clarify the conclusions of the analysis of variance on pp. 20 and 26. -13- TRPREW Box and Whisker Plot 0 1 3 10 30 DOSE 142 cases Parent(FO) 8 missing cases -14- TRPREW Box and Whisker Plot 0 1 3 10 30 DOSE 141 casesFl8 missing cases -15- Scatter Plot of PREWEAN vs DOSE GEN O F1 P P R E W E A N (1-day22/live) DOSE PREWEAN 1.2 o 0.8 0.4 0.0 0 Box and Whisker Plot o 0 * 0* o * 1 3 10 DOSE 283 cases F0&F1 16 missing cases o o o * 30 -17- PREWEAN Box and Whisker Plot 0 1 3 10 30 DOSE 142 cases Parent(FO) 8 missing cases -18- PREWEAN 0.35 0.28 0.21 0.14 0.07 0.00 Box and Whisker Plot 3 DOSE 141 casesFi8 missing cases 10 30 -19 STATISTIX 7.0 ONE-WAY AOV FOR TRPREW BY DOSE SOURCE DF SS MS F P BETWEEN 4 WITHIN 137 TOTAL 141 0.31524 9.85073 10.1660 0.07881 0.07190 1.10 0.3611 CHI-SQ DF BARTLETT'S TEST OF ------ ---- EQUAL VARIANCES 32.85 4 P 0.0000 COCHRAN'S Q LARGEST VAR / SMALLEST VAR 0.3314 6.0991 COMPONENT OF VARIANCE FOR BETWEEN GROUPS 2.433E-04 EFFECTIVE CELL SIZE 28.4 DOSE MEAN SAMPLE SIZE GROUP STD DEV 0 1 3 10 30 TOTAL 0.1378 0.1532 0.1162 0.0661 0.2089 0.1362 28 27 29 29 29 142 0.3110 0.3150 0.1632 0.1403 0.3465 0.2681 CASES INCLUDED 142 MISSING CASES 8 10/16/02, 3:23:20 PM r? -20- STATISTIX 7.0 .. SCHEFFE COMPARISON OF MEANS OF TRPREW BY DOSE 10/16/02, 3:21:29 PM F DOSE MEAN HOMOGENEOUS GROUPS 30 0.2089 I 1 0.1532 I 0 0.1378 I 3 0.1162 I 10 0.0661 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.438 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. -21- Residuals One-Way AOV Residual Plot Using dose alone somewhat underestimates the pattern of preweaning loss. -22- STATISTIX 7.0 ONE-WAY AOV FOR PREWEAN BY DOSE ALLDOSESD22, 10/17/02, 8:51:04 AM r SOURCE DF SS MS F P BETWEEN 4 WITHIN 137 TOTAL 141 0.10272 3.38109 3.48380 0.02568 0.02468 1.04 0.3887 CHI-SQ DF BARTLETT 'S TEST OF ----- -- EQUAL VARIANCES 70.93 4 P -- 0.0000 COCHRAN'S Q LARGEST VAR / SMALLEST VAR 0.3627 15.017 COMPONENT OF VARIANCE FOR BETWEEN GROUPS 3.520E-05 EFFECTIVE CELL SIZE 28.4 DOSE MEAN SAMPLE SIZE GROUP STD DEV 0 1 3 10 30 TOTAL 0.0591 0.0638 0.0372 0.0221 0.1005 0.0564 28 27 29 29 29 142 0.1889 0.1914 0.0641 0.0549 0.2126 0.1571 CASES INCLUDED 142 MISSING CASES 8 -23- STATISTIX 7.0 ALLDOSESD22, 10/17/02, 8:52:43 AM SCHEFFE COMPARISON OF MEANS OF PREWEAN BY DOSE P DOSE MEAN HOMOGENEOUS GROUPS 30 0.1005 I 1 0.0638 I 0 0.0591 I 3 0.0372 I 10 0.0221 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.438 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. -24- Residuals One-Way AOV Residual Plot -25- STATISTIX 7.0 ALLDOSESD22 10/17/02, 9:01:05 AM ONE-WAY AOV FOR TRPREW BY DOSE SOURCE DF SS MS F P BETWEEN 4 WITHIN 136 TOTAL 140 0.04543 2.65791 2.70334 0.01136 0.01954 0.58 0.6768 CHI-SQ DF BARTLETT'S TEST OF ----- ---- EQUAL VARIANCES 6.38 4 P 0.1726 COCHRAN'S Q LARGEST VAR / SMALLEST VAR 0.3339 2.3935 COMPONENT OF VARIANCE FOR BETWEEN GROUPS -2.903E-04 EFFECTIVE CELL SIZE 28.2 DOSE MEAN SAMPLE SIZE GROUP STD DEV 0 1 3 10 30 TOTAL 0.0593 0.0710 0.1114 0.0878 0.0721 0.0803 28 28 28 28 29 141 0.1168 0.1299 0.1807 0.1308 0.1323 0.1398 CASES INCLUDED 141 MISSING CASES 8 -26- STATISTIX 7.0 ALLDOSESD22, 10/17/02, 9:02:27 AM SCHEFFE COMPARISON OF MEANS OF TRPREW BY DOSE Fi DOSE MEAN HOMOGENEOUS GROUPS 3 0.1114 I 10 0.0878 I 30 0.0721 I 1 0.0710 I 0 0.0593 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.438 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. -27- Residuals One-Way AOV Residual Plot 0.6 0.3 0.0 -0.3 - 0.6 0.058 0.067 0.076 0.085 0.094 Fitted values:arcsin(sqrt(1 -day22/live)) F1 dams; F2 pups 0.103 0.112 -28- STATISTIK 7.0 ONE-WAY AOV FOR PREWEAN BY DOSE ALLDOSESD22, 10/17/02, Fl SOURCE DF SS MS F P BETWEEN 4 WITHIN 136 TOTAL 140 0.01010 0.33704 0.34714 0.00253 0.00248 1.02 0.3999 CHI - DF P BARTLETT'S TEST OF --- EQUAL VARIANCES 32.45 4 0.0000 COCHRAN'S Q LARGEST VAR / SMALLEST VAR 0.5270 6.0289 COMPONENT OF VARIANCE FOR BETWEEN GROUPS 1.665E-06 EFFECTIVE CELL SIZE 28.2 DOSE MEAN SAMPLE SIZE GROUP STD DEV 0 1 3 10 30 TOTAL 0.0162 0.0205 0.0408 0.0236 0.0214 0.0245 28 28 28 28 29 141 0.0329 0.0425 0.0809 0.0358 0.0413 0.0498 CASES INCLUDED 141 MISSING CASES 8 4 AM -29- STATISTIX 7.0 ALLDOSESD22, 10/17/02, 8:57:42 AM SCHEFFE COMPARISON OF MEANS OF PREWEAN BY DOSE Fi DOSE MEAN HOMOGENEOUS GROUPS 3 0.0408 I 10 0.0236 I 30 0.0214 I 1 0.0205 I 0 0.0162 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.438 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. -30- Residuals CD CO ii T- q od 0.3 0.2- "P + -0.1 -0.2 -0.3- 1.6 One-Way AOV Residual Plot + + + ++ + + 2ll 2^6 1 Fitted valuesX10E-2:1-day22/live F1 generation dams; F2 pups + + P + ------------ 1-- ^ 4.1 -31- Statistix offers a number o f procedures to test hypotheses about the central values o f the population distributions from which the samples are drawn. These procedures are often referred to as tests o f location. Several of these tests are parametric and require the assumption that the data are normally distributed, Nonparametric tests are provided for situations where the assumption of normality is not appropriate. When their assumptions are appropriate, parametric tests are generally more powerful than their nonparametric equivalents, although nonparametric tests often compare quite well in performance. The parametric versions test hypotheses concerning the group means. The nonparametric procedures test central value hypotheses based on measures other than the mean. Copyright 2000 Analytical Software -32- STATISTIX 7.0 ALLDOSESD22, 10/17/02, 2:28:50 PM SCHEFFE COMPARISON OF MEANS OF TRIMPLANT BY DOSE P DOSE MEAN HOMOGENEOUS GROUPS 10 8.0142 I 1 8.0054 I 30 7.9451 I 0 7.9304 I 3 7.9130 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.438 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. pp. 33 and 35 show the numbers of implantations (transformed because they are counts) are essentially the same across treatment groups. -33- STATISTIX 7.0 ALLDOSESD22, 10/17/02, 2:27:40 PM SCHEFFE COMPARISON OF MEANS OF IMPLANT BY DOSE P DOSE MEAN HOMOGENEOUS GROUPS 10 15..621 I 1 15..593 I 30 15..345 I 0 15..286 I 3 15..241 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.438 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. -34- STATISTIX 7.0 ALLDOSESD22, 10/17/02, 4:03:39 PM SCHEFFE COMPARISON OF MEANS OF TRIMPLANT BY DOSE R DOSE MEAN HOMOGENEOUS GROUPS 1 8.0345 I 10 7.9177 I 30 7.8713 I 0 7.8501 I 3 7.8387 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.404 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. -35- STATISTIX 7.0 ALLDOSESD22, 10/17/02, 4:05:19 PM SCHEFFE COMPARISON OF MEANS OF IMPLANT BY DOSE P' DOSE MEAN HOMOGENEOUS GROUPS 1 15.709 I 10 15.298 I 30 15.086 I 0 15.036 I 3 14.982 I THERE ARE NO SIGNIFICANT PAIRWISE DIFFERENCES AMONG THE MEANS. CRITICAL F VALUE 2.404 REJECTION LEVEL 0.050 STANDARD ERRORS AND CRITICAL VALUES OF DIFFERENCES VARY BETWEEN COMPARISONS BECAUSE OF UNEQUAL SAMPLE SIZES. -36-