I am interested in how an interaction between a time-varying-predictor and time changes the interpretation of other coefficients in a model.
I am modeling the effect of amphetamine-type substance (ATS) use on opioid use over time. Opioid use and ATS use are reported at the same time, therefore I can model ATS use as a time-varying predictor (see here). Here is the output from the first model. It is a longitudinal mixed effects model with two fixed predictors:
- Time from Start of Treatment, a continuous variable measured in weeks (variable
- Time-varying ATS use, a categorical variable measuring number of days respondents used ATS in the previous 28-day period (variable
atsFactor). The three levels of this variable are
nouse (0 days used ATS in last 28 days),
lowuse (0-12 days used ATS in last 28 days) and 'high' use (13-28 days used ATS in last 28 days). The no use category is the reference level of the categorical predictor.
The outcome variable in this model is opioid use (variable
allOpioids) which measures number of days the respondent used any opioids in the previous 28-day period.
The model is a random slopes model, with
weeksFromStart and participant id (variable
pID) as the random factors.
This is the output from the model, performed using the
lme() function from the
nlme package in R.
# Value Std.Error DF t-value p-value # (Intercept) 3.690054 0.2972079 1493 12.415736 0 # weeksFromStart -0.113363 0.0128773 1493 -8.803276 0 # atsFactorlow 3.376790 0.4386964 1493 7.697328 0 # atsFactorhigh 5.451483 0.9738413 1493 5.597917 0
The way I interpret this output is
- At start of treatment (i.e.
weeksFromStart= 0) respondents in the no use group had used opioids an average of 3.7 days in the previous 28 days.
- Respondents in the no use group reduced their opioids an average of -0.11 days for each extra week they were being treated.
- Averaged across all time points low use of ATS was associated with a 3.4-day increase in number of days of opioid use, compared with no use
- Averaged across all time points, high use of ATS was associated with a 5.5-day increase in number of days of opioid use, compared with no use.
These interpretations seem quite straightforward.
After doing some research I realised I could also measure whether the time-varying effect of ATS use on opioid use also varies over time, but I am confused how to interpret the coefficients once I add the
time-varying ATS Use x time interaction term to the model. Here is the output from the model, identical to the first except for the addition of the 'weeks of treatment x time-varying ATS Use' interaction term (variable
Here is the output
# Value Std.Error DF t-value p-value # (Intercept) 3.384412 0.3060578 1491 11.058080 0.000 # weeksFromStart -0.091329 0.0139118 1491 -6.564843 0.000 # atsFactorlow 4.672925 0.5950429 1491 7.853090 0.000 # atsFactorhigh 9.582114 1.3787037 1491 6.950089 0.000 # weeksFromStart:atsFactorlow -0.100171 0.0322840 1491 -3.102806 0.002 # weeksFromStart:atsFactorhigh -0.322239 0.0770086 1491 -4.184448 0.000
Now my question is what do the
atsFactorhigh coefficients mean, now that the interaction term has been added?
Are these coefficients now the effect of ATS Use (
high) compared to
no use at time = 0. i.e. are they a sort of intercept? They are certainly larger than the same coefficients in the previous model.
Any help much appreciated.