I am testing whether self-reported days' use of illicit cannabis in the previous 28-day period predicts levels of a cannabis metabolite measured in participants' urine. There are four 4-week periods, with urine and reported days' use recorded at the end of each period. As I am not really interested in trend over time I used
lmList() in the
nlme package to perform a regression at each measurement period in isolation.
This is the
lmList output for the slopes of each regression - with estimates representing how much the raw level of the cannabinoid metabolite is predicted to change with an increase of one days' increase in self-reported use. The left-most column represents how many weeks into the trial measurements were made, 0 for baseline then 4 weeks, 8 weeks, and 12 weeks.
Estimate Std. Error t value Pr(>|t|) 0 165.2543 78.90671 2.094300 3.773392e-02 4 125.8289 31.13957 4.040802 8.092335e-05 8 104.4929 33.17259 3.149977 1.933232e-03 12 139.5357 38.49324 3.624940 3.828149e-04
The outcome data was extremely non-normal and had a massive range, so I log-transformed it, and found, to my pleasant surprise, that the outcome was now distributed normally and much easier to graph against the predictor. Here are the results after the log-transformation. Once again these are slopes only for regressions of the metabolite of self-reported days' use at each of four time points.
Estimate Std. Error t value Pr(>|t|) 0 0.07753396 0.03461041 2.240192 2.638964e-02 4 0.07375009 0.01365858 5.399545 2.249782e-07 8 0.07836017 0.01455030 5.385466 2.405177e-07 12 0.10416654 0.01688407 6.169515 4.951663e-09
So far so good, right? Well...unfortunately the estimates from a regression involving a log-transformed outcome are not very intuitively comprehensible for readers. So I anti-logged the slope estimates in order to be able to express the regression coefficients in the original scale of the metabolite
exp(c(0.07753396, 0.07375009, 0.07836017, 0.10416654))
 1.080582 1.076538 1.081512 1.109785
Huh?!! This is a very long way from the estimates obtained from the regressions on the raw scale. Are the anti-logged estimates kosher? What am I missing?