A sum of profiles model and its application in experimental design.

Verbyla and Venables (1988) consider a sum of profiles model superimposed on an experimental design model and give an algorithm for solving the maximum likelihood equations for the estimates of the growth polynomials fitted to the factorial effects. Their method thus, gives numerical values of the estimates and their standard errors. We present a method of estimation that provides general algebraic formulae for the estimates and their standard errors for a very general factorial model applicable in any complete block design. The model is then easily extended to the case of an incomplete block design, where the treatment and block contrasts are generally not orthogonal. This involves using contrasts of adjusted treatment and block totals as opposed to the treatment and block totals in a complete block design. This extension is then applied to a problem of estimating relative potency of drugs in a bioassay, where it is assumed that the relative potency of the drug is dependent on time. In the classical literature on bioassays, one assumes that the relative potency is time invariant. This is not necessarily true. In microbiological assays several drugs such as penicillin, exhibit relative potency changes over time. Estimation of relative potency requires estimation of several contrasts, such as preparation, regression and validity contrasts. By assuming appropriate growth curve polynomials for these contrasts, the relative potency is determined as a ratio of two polynomials in time. Standard errors for the coefficients of these polynomials are also obtained.Ph.D.Biological SciencesBiostatisticsHealth and Environmental SciencesPharmaceutical sciencesPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/131379/2/9909844.pd