Dear friends, I'm examining the characteristics of two models that both
fit the sodium concentration in 16 pigs quite well under treatment or
control conditions. The more complicated model is by anova better than
the less complicated model. To take it further I have generated
replicate data using the independent variables and parameter estimates
under the two models. A clinically important criterion is the change in
sodium concentration during the experiment, and as expected due to the
character of the treatment this is larger in all the treated animals
(n=10) as compared to the controls (n=6). This is also the case for 1000
replicated sets under the more complex model while quite a few of
misclassifications (control animal change > treated animal change)
occurs under the less complex model. To understand (a bit at least) what
goes on I have tried to see the observed data under random group
assignment in the hope to be able to compare directly and formally the
results from the replicates under the two models.
Here are the observed changes in the 16 pigs and grp1 is treated and 2
is control.
grp <- as.factor(c(rep(1,10),rep(2,6)))
val <- c(6,12,11,11,11,13,15,13,11,11,2,3,1,1,1,2)
test <- sum(val[grp==1]<max(val[grp==2])) # 0
#Now under random perturbations of group assignments,
#what would occur???
TT <- NULL
for (i in 1:1000){
ind <- sample(c(1:16),16,replace=FALSE)
grp1 <- grp[ind]
TT[i] <- sum(val1[grp1==1]<max(val1[grp1==2]))
}
hist(TT)
table(TT)
TT
0 1 2 3 4 5 6 7 8 9 10
2 5 126 407 408 117 9 1026 3171 879 3850
For the less complex model, the results on 1000 replicates are
"evidently" better than the TT default
table(test11b)
test11b
0 1 2 3 4 5 6 7 8 9 10
279 294 191 114 53 40 17 6 3 2 1
and for the more advanced model I get even more convincing
table(test11d)
test11d
0
1000
Clinically I can say that it is bad to have 1 in 16 misclassified and
therefore judge the complicated model better, but others might disagree.
Also it is not too good that the method here is insensitive to the size
of the changes.
I hope some of you will have remarks on this problem.
Best wishes
Troels
--
Troels Ring - -
Department of nephrology - -
Aalborg Hospital 9100 Aalborg, Denmark - -
+45 99326629 - -
tring at gvdnet.dk
