A semiparametric approach to analysing dose-response data

In the analysis of a quantal dose-response experiment with grouped data, the most commonly used parametric procedure is logistic regression, commonly referred to as 'logit analysis'. The adequacy of the fit by the logistic regression curve is tested using the chi-square lack-of-fit test. If the lack-of-fit test is not significant, then the logistic model is assumed to be adequate and estimation of effective doses and confidence intervals on the effective doses can be made. When the tolerance distribution of the dose-response data is not known and cannot be assumed by the user, one can use non-parametric methods, such as kernel regression or local linear regression, to estimate the dose-response curve, effective doses and confidence intervals. This research proposes another alternative based on semi-parametric regression to analysing quantal dose-response data called model-robust quantal regression (MRQR). MRQR linearly combines the parametric and non-parametric predictions with the use of a mixing parameter. MRQR uses logistic regression as the parametric portion of the model and local linear regression as the non-parametric portion of the model. Our research has shown that the MRQR procedure can improve the fit of the dose-response curve by producing narrower confidence intervals for predictions while providing improved precision of estimates of the effective doses with respect to either logistic or local linear regression results.