Thanks for reading. This is my experimental design
1) 5 treatments containing 15 individuals each (75 individuals total)
2) Variable Y is measured over time, however this time-scale is different given treatment conditions.
3a) Treatment 1 measured from time 0 to time 10
3b) Treatment 2 is measured from time 2 to time 10
3c) Treatment 3 is measured from time 4 to time 7
3d) Treatment 4 is measured from time 4 to time 10
3e) Treatment 5 is measured from time 4 to time 10
I've attached quick figure from excel with mock data for visualization of temporal differences. In the figure I plotted mean treatment values for timeY. Could of plotted all points for each treatment/time (given all 15 individuals/treatment/time have Y measured) , but the figure would be difficult to understand.
Hope this makes sense...
Any help would be appreciated! thanks
kind regards,
Damien
The only differences are that the constant (y intercept) differs between your lines i.e. the regression lines are shifted up or down on the y-axis. You can use a hypothesis test to determine whether this vertical shift is statistically significant. See:
http://statisticsbyjim.com/regression/comparing-regression-lines/
I would use HLM regression (http://www.statisticssolutions.com/hierarchical-linear-modeling/). It can estimate the effect of the individual as well as the effect of the different points in time, partializing them out for you. It's perfect for you situation. In general HLM is applicable wherever repeated measures ANOVA is, but not the other way around.
I also just wondered, if it makes sense to look at the absolute time intervals. If the participants in group start earlier but have the same intervals between their measurements as cohorts that start later, then I'm not sure if it really matters that they were measured at different times as long as the intervals are the same. Do you know what I mean? It might make sense to just recode the measurement times relative to the first measurement. Even under these circumstances a HLM regression is probably still better, but less necessary if you're not familiar with it.
You should use a mixed model with the individual (ID) as random factor.
http://bstt513.class.uic.edu/L1LS_SAS_SPSS.pdf
http://lme4.r-forge.r-project.org/book/Ch4.pdf
I'm still not clear on why treatments were undertaken in different time periods. If the treatment was dependent on the time period then time is intrinsic and becomes a factor in the analysis. If it is a factor, it's effect on the design is to be tested.
However, if the time a treatment was undertaken was extrinsic to the condition of the treatment then the time period becomes irrelevant and you are just comparing treatments.
Most of the answers above are useful. As for accounting for time, you may want to bin overlapping time periods if they are not exactly similar. Treating time as a continuous variable or categorical will also make a difference.
The following references may help:
- Applied Longitudinal Data Analysis for Epidemiology (Jos Twisk - Cambridge University Press)
- Some references from this link https://laplacebayes.wordpress.com/2017/06/23/hierarchical-linear-regression-2-level-random-effects-model/
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