MULTI-FORTE will output the final results only to the printer or a disk file. However, intermediate results may be dumped from the screen by pressing command-S to stop the printing and command-shift-4 (Imagewriter only, screen set to 2-bit black and white). Be careful, command-C or command-. will cause an exit from the program after pressing return to continue (This may produce only a beep if you have Automac III or another macro program looking for this key combination. You should disable this macro key combination as it is not possible to stop the program with the combination active). After dumping the screen to the printer pressing command-S (or return) will cause the program to continue.
After the program has converged the output will be saved to a scratch file for printing or to the disk file as designated previously (.OUT file) by the user for later analysis. The print-out is headed by the owner message, version number and the system date and time. The title, fitting algorithm, model (if supplied in S/R MODEL), weighting information, DT (if appropriate), PC, number of iteration loops, and damping (if appropriate) are printed next. For simulations, the elapsed time is displayed for comparison purposes.
The next section displays the final parameter values. The number, name, final fitted value, standard deviation (SD), percent coefficient of variation (CV), inputted lower limit and upper limit are displayed for each parameter. A warning is given if any of the parameter values are within 5% of the upper or lower limit.. A coefficient of variation of greater than 50% can indicate that the model selected has too many parameters, or that the data are insufficient or too 'noisy'. The SD or CV information is more an indication of how good the fit is or how noisy the data appears and does not give much information about the population statistics of the parameters.
If a Bayesian analysis was selected the population mean and standard deviation inputted, the square root of the weight for the parameter (1/standard deviation), and the weighted residual are printed. The weighted residual is calculated as (parameter value-population mean value) times the square root of the weight. Thus the weighted residual squared is the contribution of this parameter to the overall WSS.
The model fit can be evaluated in part by looking at the next output. The sum of the weighted squared residuals (WSS), the unweighted coefficient of determination (R2), and the unweighted correlation coefficient (R) between the observed and calculated y-values. The mean error (ME), mean absolute error (MAE) and root mean squared error (RMSE) are useful parameters for determining how useful the model might be at predicting future results. Akaike's information criterion (AIC), Schwarz criteria (SC), and log likehood (LL) are useful criteria for determining which model is best (Note always use the same weighting scheme when making this determination.
AIC = N • ln (WSS) + 2 • M
SC = N • ln (WSS) + M • ln(N)
LL = -N/2 • [ln (2 • π) + ln (WSS/N) + 1] (from xycoon.com)
where N = number of data points (weighted); WSS = the weighted sum of squares; and M = the number of adjustable parameters.
The lowest value of AIC, SC, the smallest value of WSS, and the value of R2 closest to 1.000 indicate a best fit [Akaike, 1973; Yamaoka, 1978]. The AIC value can be quite useful in evaluating the number of terms in a given model type (e.g. two or three exponentials, 4 or 6 parameters). If the same weighting scheme is used the model with the lower AIC value is generally the more significant. This result can also be determined by comparison of the F value obtained by comparing the two models [Mandel, 1964; Boxenbaum, 1974];
where WSSj is the sum of the weighted squared residuals obtained with the jth set of parameters. For example, j may refer to the one compartment model and the k to the two compartment fit.
In Boomer, the Model and Parameter Definition section is next. In this section all the constants and parameters are displayed with name, value, type, from, to, dep, start, and stop information in a compact tabular form. Careful analysis of this section should help to ensure that the model has been entered correctly. With other version of Multi-Forte constants included in the model are printed by way of confirmation. This is followed by information about the fitted data. Data for each line is presented as data number, time (x or independent value), calculated and observed concentration (y or dependent value), (weight), and weighted residual. The weight value is actually the square root of the weight used for each data point during the final calculation. The weighted residual is calculated as (observed value - calculated value) times the square root of the weight. Squaring and summing these values will give the WSS for this data set. At the end of each data set or line the calculated WSS, weighted R2, and unweighted R value are printed. This allows the analyst to determine which line is contributing most to the overall WSS in multi-line data sets. In the case of Bayesian analysis it allows the analyst to see the contribution of the concentration data and contrast this with the contribution of the fitted parameter values.
Post fitting information generated in the S/R MODELOUT will be printed at this point. In the demo model set, the AUC is calculated for data fit by models 1-4,13-16. Additional information is output for the two compartment - I.V. bolus model (#13). This includes calculated values for k10, k12, k21, V1, Vbeta, Vss, and total body clearance. The details of these calculations can be seen in the source code for this subroutine in the MODEL.DEMO text file. Boomer will calculate AUC, AUMC, and MRT information for each data set line.
Data can be optionally output in printer plots. These plots include linear and semi-log plots of observed and calculated y values versus x values, standardized weighted residuals versus x, and standardized weighted residuals versus calculated y values. The standardized weighted residuals are calculated as (observed y value - calculated y value) times the square root of the weight divided by the standard error. The standard error is calculated as the square root of WSS divided by the number of data points minus the number of parameters (or divided by just the number of point with a Bayesian analysis). The first two plots give the analyst a general 'feel' for the fit. Outliers may become obvious, systematic deviation between the observed and calculated data points may be obvious. The two residual plot can be very useful in the evaluation of the weighting scheme selected or the model selected. Non-random residuals may well mean a poor weighting scheme or a model with insufficient parameters (Draper and Smith 1966) [Draper, 1966].
Again, all of the above output can be directed to a disk file for inclusion, as a text file, into a report etc. Calculated values versus time or the standardized residuals versus time data can be saved as disk files for later enhancement with a plotting program such as DeltaGraph Pro (Mac graphing program). The data is saved as a text file with x and y values separated by a tab and each data pair separated with a carriage return.
Material on this website should be used for Educational or Self-Study Purposes Only
Copyright © 2001-2008 David W. A. Bourne (david@boomer.org)