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^ where the single-source transform Pj i i sjxi is given in Theorem 17.4.1. ik Unlike for the aggregate mean, for the aggregate variance we evidently need to perform n separate inversions to calculate viji tjxi for each i and then add to calculate V tjj; x in Eq. (17.24). (We assume that the within-level variances wiji tjxi , if included, are speci ed directly.) Hence, we suggest calculating only the conditional mean in real time to perform control, and occasionally calculating the conditional variance to evaluate the accuracy of the conditional mean.

is in uenced by knowledge of whether a particular dose saturates a physiological process such as excretion or whether it is likely to accumulate in a particular tissue, because these factors are likely to become increasingly important the longer a chronic study continues.

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^ The most complicated part of the conditional aggregate mean transform M sjj; x in ^ Eq. (17.25) is the matrix inverse I q s 1 in the transform of the single-source transition probability in Eq. (17.14). Since the matrix inverse calculation can be a computational burden when the number of levels is large, it is natural to seek approximations that avoid this matrix inverse. We describe such approximations in this section. The matrix inverse I q s 1 is a compact representation for the series PI n n 0 q s . For P tjx , it captures the possibility of any number of transitions up to time t. However, if the holding times in the levels are relatively long in the time scales relevant for control, then the mean for times t of interest will only be signi cantly affected by a very few transitions. Indeed, often only a single transition need be considered. The single-transition approximation is obtained by making the Markov chain absorbing after one transition. Hence, the single-transition approximation is simply Pjk tjx % Hjk tjx ; j T k; and Pjj tjx % Gjc tjx Hjj tjx 17:26

Antiviral ef cacy of pyrazofurin against selected RNA viruses Antiviral Res 1982, 2, 331 337 Marquez, V E; Lim, M I; Treanor, S P; Plowman, J; Priest, M A; Markovac, A; Khan, M S; Kaskar, B; Driscoll, J S Cyclopentenylcytosine a carbocyclic nucleoside with antitumor and antiviral properties J Med Chem 1988, 31, 1687 1694 De Clercq, E Carbocyclic adenosine analogues as S-adenosylhomocysteine hydrolase inhibitors and antiviral agents: recent advances Nucleosides Nucleotides 1998, 17, 625 634 Hasobe, M; Liang, H; Aultriche, D B; Borcherding, D R; Wolfe, M S; Borchardt, R T (10 R,20 S,30 R)-9-(20 ,30 -Dihydroxycyclopentan-10 -yl)-adenine and 3-deazaadenine analogs of aristeromycin which exhibit potent antiviral activity with reduced cytotoxicity Antiviral Chem Chemother 1993, 4, 245 248 Hasobe, M; Mckee, J G; Borchardt, R T.

for Hjk tjx in Eq. (17.9) and Gj tjx in Eq. (17.9). From Eq. (17.26) we see that no inversion is needed. Alternatively, we can develop a two-transition approximation. (Extensions to higher numbers are straightforward.) Modifying the proof of Theorem 17.4.1 in a straightforward manner, we obtain Pjk tjx % for j T k and Pjj tjx % Gjc tjx P

Behavior. Although the primary emphasis in toxicity testing has long been the estimation of morphologic changes, much recent interest has focused on more fundamental evaluations. One such aspect has been the evaluation of chemical effects on behavior. The categories of methods used in behavioral toxicology fall into two principal classes, stimulus-oriented behavior, and internally generated behavior. The former includes two types of conditioned behavior: operant conditioning, in which animals are trained to perform a task in order to obtain a reward or to avoid a punishment, and classical conditioning, in which an animal learns to associate a conditioning stimulus with a re ex action. Stimulus-oriented behavior also involves unconditioned responses in which the animal s response to a particular stimulus is recorded. Internally generated behavior includes observation of animal behavior in response to various experimental situations, and includes exploratory behavior, circadian activity, social behavior, and so on. The performance of animals treated with a particular chemical is compared with that of untreated controls as a measure of the effect of the chemical. Many of the variables associated with other types of testing must also be controlled in behavioral tests: sex, age, species, environment, diet, and animal husbandry. Behavior may vary with all of these. Norton describes a series of four tests that may form an appropriate series, inasmuch as they represent four different types of behavior; the series should therefore re ect different types of nervous system activity. They are as follows:

17:27

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