How to test for dose effect in non-linear model

Question

I would like to examine whether there is an effect of dose in a data set that looks at repeated measurements over time. I expect the dependent variable to decrease exponentially over time. My experiment has 9 animals total, 3 per treatment group testing placebo, low dose, and high dose. Each animal is observed weekly for 4 weeks. The hypothesis is that the higher the dose, the greater the reduction in the parameter under observation (say for discussion purposes it's hemoglobin). My data are in a similar format to below, although these data are example. Can you please advise me how to test my hypothesis (preferably using SAS)?

    data test;
 input animal time dose hemoglobin @@;
 datalines;
 1  0   0   500
 1  1   0   450
 1  2   0   400
 1  3   0   600
 1  4   0   550
 2  0   0   700
 2  1   0   750
 2  2   0   550
 2  3   0   500
 2  4   0   650
 3  0   0   950
 3  1   0   950
 3  2   0   1000
 3  3   0   800
 3  4   0   900
 4  0   100 600
 4  1   100 350
 4  2   100 400
 4  3   100 300
 4  4   100 350
 5  0   100 700
 5  1   100 750
 5  2   100 550
 5  3   100 500
 5  4   100 450
 6  0   100 950
 6  1   100 950
 6  2   100 1000
 6  3   100 700
 6  4   100 600
 7  0   200 800
 7  1   200 780
 7  2   200 600
 7  3   200 400
 7  4   200 580
 8  0   200 700
 8  1   200 600
 8  2   200 480
 8  3   200 500
 8  4   200 540
 9  0   200 980
 9  1   200 1200
 9  2   200 800
 9  3   200 700
 9  4   200 400
 ;
 run;

Also, I've tried to use proc nlin as below to develop a model for each dose level over time, but the model failed to converge I think due to sparse data.

proc nlin data = tg;
by dose;
parms top = 3000 bottom = 20 EC50 = 1 hill = 1;
model value = bottom + ((top-bottom) / (1 + (time / EC50)**hill));
run;

I think I may need to use proc NLMIXED, and have come across references to Pinheiro and Bates (1995) but I am just not getting it.

Answer 1

Not sure about using SAS or what standard practice is for this test, but I would use log-linear regression to analyze the trend of the parameter.

To regress on the exponential trendline, I would take the natural log transformation of the dependent variable (the parameter) so your equation to regress would look like:

ln(Parameter) = B0 + B1*(Week)

where you are looking for the coefficients B0 and B1

Then run 3 different regressions (one for each group), and compare the B1 coefficients from the regression. If the range of the coefficients overlap then there is not a significant difference. If they do not overlap then there is a significant effect.