I am completing a cost analysis using a log transformation I.E. log(cost) = treatment. I am interested in testing for the marginal difference between treatments. I can easily find the marginal log(cost) for each treatment group. Three questions:
- If I exponentiate the marginal log(cost) for each treatment, is that a biased estimator of cost?
- Can I exponentiate the log(cost) for each treatment and find the difference to estimate the difference between treatments?
- If either 1 or 2 is biased, how do I use a smearing estimator?
I have the SAS code below. The top table is the SAS output followed by my work to exponentiate the log(cost) for each treatment and calculating the difference. Appreciate the help.
PROC glm DATA=cost_data;
class Treatment (REF='1');
MODEL log_cost = treatment;
ESTIMATE 'Treatment 1' INTERCEPT 1 treatment 1 0;
ESTIMATE 'Treatment 0' INTERCEPT 1 treatment 0 1;
RUN;QUIT;
| Parameter |
Estimate |
Standard |
t Value |
Pr > |t| |
| |
|
Error |
|
|
| Treatment 1 |
11.315 |
0.01456 |
551.1 |
<.0001 |
| Treatment 0 |
11.05746 |
0.03548 |
442.32 |
<.0001 |
| |
|
|
|
|
| exp(0) |
82043.1 |
|
|
|
| exp(1) |
63415.27 |
|
|
|
| |
|
|
|
|
| Diff |
18627.83 |
|
|
|
