PubMed · 8636737
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D S Sitar, M Cheang. 1996. Error in statistics program.. https://doi.org/10.1016/0895-4356(95)00035-6
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In order to determine a biological response to ultraviolet radiation, calculations of biologically weighted dose rates are required, which in turn involve the integral over wavelength of an action spectrum multiplied by appropriate surface flux data. To determine a biologically weighted dose rate accurately, a reasonable wavelength resolution is required, involving a full radiative transfer solution to be performed for each wavelength in order to obtain the surface flux information. If biologically weighted dose rates are needed as a function of ozone variation, then the number of radiative transfer solutions quickly makes a large number of ozone variations cumbersome. This paper shows that the perturbation theory developed for atmospheric radiative transfer by Box and co-workers can predict surface fluxes and hence biologically weighted dose rates for a large range of ozone variations very efficiently. The method is then extended to calculate radiation amplification factors. Results for biologically weighted dose rates are presented for a large range of solar zenith angles and ozone loadings using perturbation theory and a full radiative transfer code and show that the perturbation predictions never deviate very far from the radiative transfer solutions.
PURPOSE: One important task in population pharmacokinetic/pharmacodynamic model building is to identify the relationships between the parameters and demographic factors (covariates). The purpose of this study is to present an automated procedure that accomplishes this. The benefits of the proposed procedure over other commonly used methods are (i) the covariate model is built for all parameters simultaneously, (ii) the covariate model is built within the population modeling program (NONMEM) giving familiar meaning to the significance levels used, (iii) it can appropriately handle covariates that varies over time and (iv) it is not dependent on the quality of the posterior Bayes estimates of the individual parameter values. For situations in which the computer run-times are a limiting factor, a linearization of the non-linear mixed effects model is proposed and evaluated. METHODS: The covariate model is built in a stepwise fashion in which both linear and non-linear relationships between the parameters and covariates are considered. The linearization is basically a linear mixed effects model in which the population predictions and their derivatives with respect to the parameters are fixed from a model without covariates. The stepwise procedure as well as the linearization was evaluated using simulations in which the covariates were taken from a real data set. RESULTS: The covariate models identified agreed well with what could be expected based on the covariates that were actually supported in each of the simulated data sets. The predictive performance of the linearized model was close to that of the non-linearized model. CONCLUSIONS: The proposed procedure identifies covariate models that are close to the model supported by the data set as well as being useful in the prediction of new data. The linearized model performs nearly as well as the non-linearized model.
PURPOSE: To facilitate the use of the collimator scatter correction factor, Sc, parametrization methods that relate Sc to the field size by fitting were investigated. MATERIALS AND METHODS: Sc was measured with a mini-phantom for five types of dual photon energy accelerators with energies varying between 6 and 25 MV. Using these Sc-data six methods of parametrizing Sc for square fields were compared, including a third-order polynomial of the natural logarithm of the field size normalized to the field size of 10 cm2. Also five methods of determining Sc for rectangular fields were considered, including one which determines the equivalent field size by extending Sterling's method. RESULTS: The deviations between measured and calculated Sc-values were determined for all photon beams and methods investigated in this study. The resulting deviations of the most accurate method varied between 0.07 and 0.42% for square fields and between 0.26 and 0.79% for rectangular fields. A recommendation is given as to how to limit the number of fields for which Sc should be measured in order to be able to accurately predict it for an arbitrary field size.