Multi-stage Mixed Effects Models With Applications To Risk Assessment

The description and evaluation of dose-response relationship is a critical component of riskassessment. According to the rapid development of molecular biology, the mechanism ofcausing disease has been more and more clearly. So through combining the traditionalmulti-stage models with disease mechanism, biologically based dose-response models could beestablished in order to improve the accuracy of risk assessment.Since it's hardly to obtain the complete data for multi-stage models from a single study,this paper applied the thought of meta analysis to the evaluation of dose-response relationship,and focused on the structure of meta-regression models as well as strategy of modelconstructing.In this search, the model structures and parameter estimation methods of three types ofmeta regression model, linear, general linear and nonlinear, were introduced. According to theguidelines of systematic review, twenty-six papers about male reproductive toxicity of leadwere carefully collected to establish a database. With these data, biologically based multi-stagemixed effects models were constructed. The main ideas were as follows: First, linear metaregression model was established in which the mean difference of testes weight was defined asdependent variable, age and body weight was defined as two covariates. Comparing with thesingle random effect model, the estimate value of between-study variance was significantlyreduced. Thus, it indicated considering covariates in meta analysis were necessary. Second, several stages of mixed effects model about corresponding variables were constructed under thepath of blood-brain barrier and blood-testis barrier. The model structures included were logistic,exponential, linear as well as hyperbola, and they were all reasonable for the explanation ofbiological relationship. Third, an interactive effects model of logistic form was trying toestablish among exposure variables and blood lead, but according to the result of randomeffects model, there was no significant interactive effect between exposure dose and exposuretime.Due to lack of original data, it's hard to carry out direct parameter estimation methods ofnonlinear meta regression model at present. Parametric bootstrap technique was used forparameter estimation and hypotheses test in this paper, and the results would be acceptable after500 iterations.Based on the conclusions above, the following strategies of constructing multi-stage mixedeffects models were suggested by the author:1. A fixed effects model should be estimated first according to the scatter plot, and thecoefficients of the model would be identified as the initial values for next iterations whenrandom or mixed effects model were further constructed.2. Dose-response models in risk assessment might be not only mathematically based, theyshould be endowed with biological meanings also.3. Since in some instance, the variance of response variable might be changeable along withthe alteration of explanatory variable, in the procedure of model constructing, a fixedeffects model should be considered firstly, then the random effects model or randomcoefficient model when necessary. The best fit model should be chosen by comparing thealterations of between-study variance and residual variance, as well as their relationshipswith covariates.4. With sufficient collected data, it might be possible to study the interactive effects amongcovariates. This would be quite useful for the explanation of disease mechanism.5. As at present, there's no appropriate software to carry out the WIGLS or REML estimate directly for nonlinear meta regression model, the parametric bootstrap would be a suitableway for parameter estimation and hypotheses test if the population distribution of observedvariable was already known.