I have a measurement with a detection threshold. I can see that one group has more succesfull measurements (larger number) and also have more higher measurements (longer tail). Comparing the mean shows no difference, intuitively I think that is because of the detection threshold.
Because I see more measurements and higher measurements in one group, I think that the mean in that group is really higher. But the real mean is probably below my threshold. Also, the closer a measurement is to the detection threshold, the larger the probability that it is a false positive.
Incidentally, my data is also hierarchical, but this might not be essential to the question. In each of my two groups I have about 20 subjects and for each subject I have a number of measurements N (between 20 and 100). Between subjects, I assume measurements are independent. Within subjects, I assume measurements are dependent. I use
R for my analysis.
If I take the top n measurements for each subject, there is a significant difference between groups (tested with
contrast). I took n to be the smallest number of measurements I had in one subject. So for the subject with the least number of measurements I included all measurements, but for the subject with the largest number of measurements I included only the top n which was about 20%.
dat = loadsomestuff('from here') fit = lme(measurement ~ group, random = ~1|subject, data = dat) ctrst = contrast( lsmeans(fit, pairwise ~ group, adjust="tukey"), "trt.vs.ctrl", ref=1) ctrst contrast estimate SE df t.ratio p.value B - A -0.08378559 0.06237481 24 -1.343 0.1918 dat.top20 = dat %>% group_by(subject) %>% top_n(n = 20, wt = measurement) fit.top20 = lme(measurement ~ group, random = ~1|subject, data = dat.top20) ctrst.top20 = contrast( lsmeans(fit.top20, pairwise ~ group, adjust="tukey"), "trt.vs.ctrl", ref=1) ctrst.top20 contrast estimate SE df t.ratio p.value B - A -0.3088250 0.10896501 34 -2.834 0.0148
I pretty sure this approach is not valid, since if sampling the same distribution twice and taking more samples the second time, the mean of the top n samples would be higher for the second time. I also suspect just testing the difference between the values straight away is not the best approach, as by inspecting the data manually its very suggestive that one group has higher values.
What are ways to compare the values found in these groups? (I assume my approach is invalid)
I found one similar question that has had a response to it. I dont completely understand it, because I have no experience with survival data and that question posts values like
<5 while I have definite values like