# Is Pre (1 time point) - Post (2 time points) treatment analysis with linear mixed model (lmm) a reasonable technique to answer my research question?

I am facing problem in deciding the right analysis to answer my question.

I have 98 subjects. Each subject was measured 3 times (Baseline Year, Year 1, Year 2) on treatment efficacy marker Albumin and they were nested in site locations. There were two types of treatment or access type- AVF & AVG. Initially, subjects were given an Old treatment "Ot". However, due to some complications from Ot (indicated by a decrease in Albumin. An increase is considered to be an improvement), subjects were assigned to AVF & AVG. This assignment was not randomized.

After collecting the baseline info for each subject, they were given either AVF or AVG. These two treatments were assigned after the baseline year.

87 subjects got AVF and 11 subjects got AVG. There were missing values on the repeated measurements. Missing albumin measurement were more frequent in year 2 (46%) followed by year 1 (13%) and baseline year (6%).

My research question- what is the effect of treatment type on the efficacy marker over time.

I have read that LMM can handle the missing values. Also, it can account for the variation in nesting. So, what is your suggestion about applying LMM technique here.

If I use LMM, I believe that I need to consider time as categorical. Then according to Randel's answer, I need to consider only the random intercept. Not the random slope. But why?

The linear mixed model can work given what you describe here. It can handle missing data in the outcome under the assumption of missing at random as discussed here and elsewhere. Remember that missing on predictor variables is a different problem and if you have that, you will need to consider multiple imputation to recover that data.

In terms of how to treat time, that is very much based on your substantive question and your data. Do you believe (or have evidence) that the outcome changes linearly over the three occasions? Likewise, do you have evidence that individuals vary in how much change they experience? If the answer to both of these is yes, then you would want to treat time as a continuous variable (with a meaningful 0 value) and allow the time slope to vary across individuals. R code for such a model is lmer(y ~ time + trtmt + (time | id)).

If on the other hand you think time effects everyone in the same way and there is no evidence or reason to believe that albumin should change systematically over time, then you would move forward with a model that treats time categorically: lmer(y ~ as.factor(time) + trtmt + (1 | id)).

It may also not be necessary to model time if there is no reason to believe it is important in understanding the effect of treatment on your outcome. There you would simply not include time in the lmer() model. You can of course do model comparison tests using anova() in R to see whether the addition of time (either as a continuous or categorical variable) provides better fit to your data vs. a model without time.

• Thank you for answering here. Don't you think I should be concerned about whether the treatment effects by time point differ qualitatively or quantitatively? Since time 0 happens pre-treatment and times 1 and 2 happen post-treatment, those differ qualitatively, not quantitatively. When I make a predictor continuous, I am really saying that the only effect of that predictor is quantitative. Do you think this reasoning is correct to treat time categorical? I need a proper justification of why time is to be considered as a categorical variable.
– hulk
Dec 23 '19 at 16:17
• One more thing, if we finally consider the time as categorical, the model should include an interaction. lmer(y ~ as.factor(time):trtmt + (1 | id)) rather than lmer(y ~ as.factor(time) + trtmt + (1 | id)). I guess I am confused here!
– hulk
Dec 23 '19 at 16:21
• As I said in my answer, how you treat time is a substantive question as much as a methodological or modeling question. It sounds as if you believe there is some effect that may be different at each time point, in which case you would treat time as categorical. If you further believed this time point specific effect varied depending on which treatment group an individual was in, then you can test the interaction between time and treatment. You can use anova() to test whether the model with the interaction is a better fit to your data than the model without the interaction. Dec 31 '19 at 15:14