A Practical Approach, Second Edition=Ronald D. Ho.pdf

STATISTICAL ANALYSIS FOR DEVELOPMENTAL AND REPRODUCTIVE TOXICOLOGISTS 701Table 17.2p-values for testing homogeneity, control versus dosage groups, and trend,using the litter-based analysis and mixed-effects model approachesControl vs. DoseLSD (t-test)DunnettApproach Homogeneity µ 1 = µ 2 µ 1 = µ 3 µ 1 = µ 2 µ 1 = µ 3 TrendLitter-based analysis .244 .138 .198 .215 .332 .198Mixed-effect model .185 .093 .161 .163 .276 .161freedom. The p value is greater than the 5% significance level. The comparison could stop here,but for the purpose of illustration, the dosage group comparisons and trend test are performed. Forthe mixed-effects model, the maximum likelihood estimates of the variance parameters areˆσ 2 = 0.196 and ˆσ f 2 = 0.277. The estimated intralitter correlation is ˆφ = 0.277/(0.196+0.277) = 0.586,indicating the presence of litter effect. The two methods give very similar results; however, themixed-effect modeling approach appears more powerful because it uses individual fetal data thataccounts for litter effects in the analysis.III. ANALYSIS OF BINARY RESPONSE DATABinary endpoints can also be measured either at the parent level, such as success or failure ofpregnancy, or at the individual fetal level, such as presence or absence of a particular malformationtype. The binary responses from individual dams are independent, while the binary responses fromthe fetuses in a litter are correlated. Statistical methods for the analyses of the parental and fetalresponses are different.A. Independent Binary Response DataGiven a typical reproductive experiment, if n i represents the total number of animals from the ithgroup and y i is the number of animals found to present a particular response of interest, the datacan be summarized asDose d 1 d 2 … d g TotalNo. of responses y 1 y 2 … y g yTotal n 1 n 2 … n g nProportions p 1 p 2 … p g py and n are the row marginal totals, p = y/n, and p i = y i /n i is the observed incidence rate in the ithgroup.An asymptotic chi-square test for homogeneity is commonly used to compare incidence rates(proportions) among several groups:2χ g −1=g∑i=12( yi− nip)np( 1 − p)For pairwise comparisons, the chi-square test is often used with the continuity correction. It canbe simplified as( 05= | y − n p | − . )np( 1 − p)2 i 1χ 11i2© 2006 by Taylor & Francis Group, LLC