Reference Interval Estimation by Generalized Least Squares
Syntax
xrigls yvar xvar [if] [in] [, major_options minor_options]
options Description ------------------------------------------------------------------------- major_options alpha(#) specifies significance level for testing between FP functions centile(# [# ...]) defines the centiles of yvar|xvar cv models the S-curve as a coefficient of variation detail displays the final regression models fp([m:term] [s:term]) specifies fractional polynomial models minor_options covars([m:vars] [s:vars]) includes variables as predictors of the mean and/or SD curve cycles(#) determines the number of fitting cycles nograph suppresses the graph of the results noleave prevents the creation of new variables notidy preserves fractional polynomial transformations powers(powlist) defines powers for fractional polynomials ropts([m:mopts] [s:sopts]) determines regression options saving(filename[, replace]) saves the graph to a file se calculates standard errors of estimated centile curves -------------------------------------------------------------------------
where term is of the form [powers] # [# ...]|df #.
Description
xrigls calculates reference intervals for yvar based on the xvar- (e.g. age-) specific mean and standard deviation of yvar. yvar is assumed to be Normally distributed, conditional on xvar.
Options
+-------+ ----+ Major +------------------------------------------------------------
alpha(#) specifies the significance level for testing between degrees of FP for the mean and SD curves. Default : 0.05.
centile(# [#...]) defines the required centiles of yvar|xvar. Default is 3 and 97 (i.e. a 94% reference interval).
cv models the S-curve as a coefficient of variation.
detail displays the final regression models for the mean and SD curves.
fp([m:term [, s:term]{cmd:) specifies fractional polynomial models in xvar for the mean and SD curves. term is of form [powers] # [# ...]|df #. The phrase powers is optional. The powers should be separated by spaces, for example fp(m:powers 0 1, s:powers 2). If powers or df are not given for any curve, the default is cmd:fp(m:df 4,s:df 2)}. df # specifies that the degrees of freedom for the best-fitting FP model are to be at most # for the curve in question. The powers are then determined from the data.
+-------+ ----+ Minor +------------------------------------------------------------
covars([m:vars [, s:vars]{cmd:) includes variables as predictors in the regression model for the mean and/or SD (S) curves.
cycles(#) determines the number of fitting cycles (fit mean, calculate absolute residuals, fit absolute residuals, recalculate weights, etc.). The default value of # is 2: an initial (unweighted) fit for the mean is followed by an unweighted fit of the absolute residuals; weights are calculated, and one weighted fit for the mean, one weighted fit for the absolute residuals and a final weighted fit for the mean are carried out.
nograph suppresses a plot of yvar against xvar with fitted values and reference limits superimposed. The default is to have the graph.
noleave prevents the creation of new variables. The default (leave) causes new variables, appropriately labelled, containing the estimated mean, SD, Z- scores for yvar and also the centiles specified in centile(), to be created.
noselect specifies that the degree of FP will be that specified in the fp() option. The default is to select a lower order FP if the likelihood ratio test has P-value alpha().
notidy preserves the variables created in the routine representing the fractional polynomials powers of the xvar used in the analysis.
powers(powlist) specifies powers for FP models. Default powlist is -2, -1,-0.5, 0, 0.5, 1, 2, 3 (0 meaning log).
ropts([m:mopts] [,] [s:sopts]) determines the regression options for the mean and SD regression models. Example: ropt(m:nocons) suppresses the constant for the mean curve.
saving(filename[, replace] saves the graph to a file (see nograph).
se calculates the standard errors of the estimated centile curves.
Remarks
yvar is assumed to have a normal (Gaussian) distribution. If a constant SD is assumed, it is estimated by the residual mean square in the usual way. Otherwise, the SD is estimated by regression of the absolute residuals on an FP in xvar. The SD's are the predicted values from this regression, multiplied by the square root of pi/2 (i.e. 1.2533...). Since the correct regression for yvar should include weights proportional to the reciprocal of the squared SD, the regression for yvar is repeated using weights equal to the squared reciprocal of the fitted SDs. At each iteration, models of lower degree are also fitted. The FP with the lowest degree (k), for which the FP with degree k+1 is not a significantly better fit, is selected. The selection criteria between models may be specified.
xrigls displays the deviance (-2 * ln likelihood) for the entire model (including weights derived from the fitted SD). In general, the lower the deviance, the better the fit of the model.
Examples
. sysuse auto
. xrigls mpg weight, fp(m:1 3,s:2 2) centile(10 90) cycles(3)
The FP model with powers (1,3) is used for the mean, and the FP model with powers (2,2) for the SD. Three cycles are performed. The results are saved in new variables. A graph of the resulting 10th, 50th and 90th centiles (or 80% reference interval) is given.
. xrigls mpg weight, fp(m:df 2,s:df 2) noselect powers(1 2 3) cv
The model for the mean of mpg is the best FP1 function of weight, and for the CV, the best degree-1 FP function of weight. The chosen powers will be a subset of {1,2,3}. A graph of the resulting 94% reference interval and new variables are also given.
. xrigls mpg weight, alpha(0.1) fp(m:df 2,s:df 2)
For both the mean and SD, a selection will be made between the best degree-1 FP function, linear and constant fits using a significance level of 10% in the the likelihood-ratio tests.
Stored Results
xrigls is an R-class program and saves in the r() functions:
r(dev) deviance of final model `r(mpow)' powers in final FP model for mean curve `r(spow)' powers in final FP model for SD curve
Authors
Patrick Royston, MRC Clinical Trials Unit, London. pr@ctu.mrc.ac.uk
Eileen Wright, Macclesfield
Also see