UC Riverside

We investigate the estimation issues for count data in dose response model. In

this thesis, we are considering logistic dose response model for a mixture experiment

with two drugs. We propose two new methods of estimation of parameters for this

model by forming the observation pairs. The standard maximum likelihood estima-

tion method uses the numerical methods for solving the estimating equations. This

method requires an initial set of values for the parameters in the model. The standard

procedure normally uses the initial values as zero or some convenient numbers without

any justication. We present two very systematic methods of nding the initial values

of parameters of the maximum likelihood estimating equations (MLEE). Our methods

are based on two criterion functions, the log-likelihood and the other function . We

then use the initial values and the corresponding criterion function to obtain the nal

solution of MLEE. We demonstrate that when we consider only two doses from the

data, we do have an exact analytic expression for the solution of estimating equations.

We use that fact to obtain the initial values of parameters in these models. Then we

have used the search algorithm for performing the optimization to nd the nal esti-

mates. The proposed methods are transparent in the selection of the initial values of

parameters. The proposed methods are computer intensive like bootstrap and jack-

knife methods popular among statisticians. We have also compared our estimates with

the estimates obtained by SAS and R. The proposed methods compare favorably with SAS and R in terms numerical values of the estimates and the performance time of the

estimates. We illustrate our methods with a data set (Giltinan, 1998). We present also

some simulated data to illustrate our methods.