next up previous
Next: Results. Up: Statistical Methods Previous: Facility Comparison Analyses.

Dose-Response Analyses.

These analyses are based on Eq. 1 with a multiplicative main effects model for the variable A, B, S, L, IG, and F. The effect of dose is represented with an exponential relative risk function or an additive excess relative risk (ERR) function. The main effects model with exponential relative risk is expressed as

 

where , A = (age -52.5)/100, and D is external dose in Sv. In Eq. 3 B, S, L, IG, and F are factors and A and D are continuous variates. Score [38] test statistics for external dose are presented for selected cause of death categories using all ten dose groups. Additional summary results---parameter estimates, standard errors, and likelihood ratio test (LRT) statistics---are given for each cause of death category with the highest dose group deleted (low dose analysis). The score test for D in Eq. 3 is identical [39] to that obtained for D variable in Eq. 4 below, and can be compared to the standard normal distribution to evaluate the strength of the dose-response relation. These analyses are then repeated using adjusted doses. The score test and low dose exponential relative risk are used as a screening procedure to identify cause-of-death categories that may show a strong association with dose.

Most summary statistics (estimates and SEs) for relative risk parameters are expressed in log percent (L%) units, i.e. they are given in logarithmic units multiplied by 100---see [13] Chapter 22,[15] and the Appendix. For the ERR estimates likelihood based intervals are given---see [16,17].

More detailed results are presented for several cause of death categories using a main effects model with the additive excess relative risk (ERR) function to describe the dose-response relation for external radiation, e.g.

 

The main effects model provides an overall descriptive summary of the the effects of each stratification variables on cause specific mortality. Thus inclusion of these potential confounding variables (A,B,S,L) and exposure variables (F and IG) provides a broader context in which to evaluate the relative importance of the estimated effect of external radiation. A saturated model for the confounding variables AG,B,S, and L was also considered and was found to have little effect on the dose parameter estimate. Detailed results are given for all cancer in the Appendix (see Table AVII). The score statistic for a linear dose term for the main effects model and the saturated model (i.e. stratified analysis) were routinely calculated and no important difference for any cause of death categories were found.

A detailed analysis for all cancer mortality that uses the Akaike Information Criteria (AIC) to contrast the effectiveness of several exponential and ERR models is presented [18,19]. For Poisson data the AIC = Deviance + (number of parameters), combines a measure of the discrepancy between the fitted values and the data (as measured by the deviance) and the simplicity of the model as reflected in the number of parameters. McCullagh and Nelder---see Sec 3.9--- [20] discuss a general approach to model selection which includes the AIC and note situations when = 2 (used here) provides a reasonable choice. Ostrouchov and Frome [21] discuss various approaches to model selection based on AIC and related criteria where the objective is to find a subset of models that adequately describe a large ADS. See global modal search at (Computational Statistics.)



next up previous
Next: Results. Up: Statistical Methods Previous: Facility Comparison Analyses.