Estimation of parameters for logistic regression model in dose response study with a single compound or mixture of compounds

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 estimation 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 justification. We present two very systematic methods of finding 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 Delta. We then use the initial values and the corresponding criterion function to obtain the final 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 find the final estimates. The proposed methods are transparent in the selection of the initial values of parameters. The proposed methods are computer intensive like bootstrap and jackknife 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.