Jay Tanzman <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > We recently submitted a paper to a journal reporting the results of a diet study > that used a 3-treatment, 3-period crossover design. Subjects consumed all their > meals (which were prepared by study personnel) under tightly controlled > conditions in a metabolic kitchen under the supervision of study personel. > Consequently, there was no variation in diet composition among subjects within a > particular study diet. The data were analyzed using a mixed linear > variance-components model with fixed effects for diet and period and a random > effect for subjects. > > A reviewer has asked us to assess compliance with the diets by comparing the > fatty acid content of subjects' blood on each diet with the fatty acid contents > of the diets "at the individual level using 'correlations'." These variables > can be assumed to be normally distributed, at least after transformation. My > questions are these: > > 1. Is there an appropriate correlation coefficient to do the above, given this > study design? > > 2. Would it be valid to compute the proportion of within-subject variation due > to the diet, like this: > > Var(Diet) / [Var(Period) + Var(Diet) + Var(Residual)]
I will probably be less of help than Donald, but this "proportion of within-subject variation" sounds somewhat like the Eta^2 printout when you do a repeated measures ANOVA. Eta^2 is a measure of "association" within-subjects. Correlation is also sometimes thought of as "magnitude of effect", a form of effect. > > 3. Assuming #2 is OK, can I "partial out" the period effect by leaving > Var(Period) out of the denominator? > > Thanks in advance. > > -Jay Tanzman I am also interested in this, For instance to assess adherence to treatment at the _group_ level, crosstab procedures have several measures of association, all acting very similar to measures of correlation since they are between 0 and 1. For within-subject, Repeated Measures ANOVA, Eta^2 describes the "association", or % change in serum that is due to the change in treatment. Eg., a high Eta would mean that almost all of the change in serum is related to treatment, suggesting adherence. You would conclude: "compliance was good, the serum marker increased dramatically, (Eta^2=0.90, p<0.001) and then show the within-measures ANOVA graph that illustrates compliance" I would also be interested in comments on "reliability" and ICC. One site described ICC as a "misnomer" since it isn't really a correlation: http://www.acponline.org/journals/ecp/janfeb01/primer.htm > 2. Would it be valid to compute the proportion of within-subject variation due > to the diet, like this: > > Var(Diet) / [Var(Period) + Var(Diet) + Var(Residual)] > > 3. Assuming #2 is OK, can I "partial out" the period effect by leaving > Var(Period) out of the denominator? > > Thanks in advance. > > -Jay Tanzman . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
