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))
And got
[1] 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?