I am working on a paper on smoking and depression in a sample of approximately n=2.000 subjects, and for that, I use longitudinal data (5 waves, 2 years between each wave). For a part of the paper, I want to analyse determinants of smoking in those with depression (both depression and smoking are time-varying variables). The most simple solution would be to do a cross-sectional analysis (for example with the baseline data), but I was wondering whether I could also use all data, and perform a mixed models analysis but without TIME. I feel that the additional value of doing that would be to 1. have more data points (5x2.000=10.000 instead of 2.000); and 2. not only to make a between-person interpretation but also a within-person interpretation. However, I have never read a paper, answering this type of questions (determinants of condition x in disease y) doing a mixed models analysis. Therefore my questions is: am i right and should I do it this way, or do I miss a critical argument not to do so?
1 Answer
You say you want to analyze the determinants of smoking. Can you see why a cross-sectional analysis won't work? Does the smoking cause the depression, or does the depression cause the smoking? Many are attempted to apply heuristic reasoning and ignore sophisticated data analyses, but in many cases this leads to bad science. In the past this led to incorrect inferences such as proximity to alcohol retailers leads to alcoholism, that autism is caused by bad parenting, and that obesity is caused by lack of self control. As per occum's razor, one must go as "simple as possible but no simpler", the truth is that depression and smoking are stochastic variables with complex interrelationships.
Simply averaging repeated measures overtime will "reduce" variability but does not address the design challenges at all.
There's actually quite a lot of literature out there about joint longitudinal modeling, causal inference, etc. I think you might need to do a more comprehensive lit review before tackling this problem and settling on the design. At it's simplest level, you could propose to model a longitudinal model for smoking conditional on baseline smoking and depression levels, that is:
$$ E[\text{Smoke}_{i, t \ge s} | \text{Smoke}_{i, t=s}, \text{CESD}_{i, t=s}] = \beta_0 + \beta_1 \text{Smoke}_{i, t = s} + \beta_2 \text{CESD}_{i, t=s}$$
That is, what is the change from baseline in smoking as a function of baseline depression and smoking status? $\beta_2$ compares the expected smoking status at follow-up for a subject with a given smoking status at baseline as a function of their depression - assuming the CESD scale is used.
There are many variants on this type of ANCOVA design, which should again encourage a wider lit review. But in this case you can use a repeated measures ANOVA (exchangeable correlation matrix) to combine similar observations. (Note: an autoregressive correlation structure will cause a form of bias that may potentially attenuate effects).
