We have a rather mathematical/statistical problem and hope to get some help.

We have data from a multicenter randomized clinical trial where we compare single with combined treatments at 4 different time points (baseline, interim visit, final visit, follow up).

We fitted a mixed effect model to predict the outcome by time point, objective (single vs. combined treatment) and the interaction time point with objective as fixed effects and patient ID nested in center as random intercept. Next to the unadjusted model we fitted an adjusted model adding fixed effects such as age and gender. We used the lmer function from the lme4 package in R. Here are the model equations:

lmer(outcome ~ time point*objective + (1 | center / subject))

lmer(outcome ~ time point*objective + age + gender + educational attainment + hearing aid indication + PHQ-9 baseline  + (1 | center / subject))

This is the intention to treat analysis, missing data were imputed with mice before the analysis.

Here is the model output: Model output

For time point (= visit_type) and the interaction with time point, the model output from the unadjusted model is identical to the adjusted model (up to 7 decimals). We are wondering if this is mathematically/statistically possible or if it is more likely that we have a bug in our code?

In the per protocol analysis, where we don't impute missing values, we do not encounter identical results.

  • $\begingroup$ Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. Just to be sure: you reported combined estimates after imputation here (e.g., usingpool()), right? $\endgroup$
    – T.E.G.
    May 9, 2023 at 11:29
  • $\begingroup$ Thank you for the information! Correct, the estimates are pooled. $\endgroup$
    – Milena
    May 9, 2023 at 11:49

1 Answer 1


Without access to your data it is difficult to be sure.

We are wondering if this is mathematically/statistically possible

Yes it is possible. This would be expected if the randomisation process was successful. Randomisation seeks to distribute both known and unknown confounding variables evenly between treatment groups. If the randomisation is successful and the sample size is high enough, we would anticipate factors such as age, gender, and educational achievement to be distributed similarly across treatment arms. As a result, correcting for these factors should not change the estimates of the fixed effects, assuming the groups are balanced.

If the additional covariates are not strongly correlated with the outcome, or if the randomisation effectively balanced these covariates across treatment groups, then including them as fixed effects in the model would not change the estimates or their interaction with the treatment.

or if it is more likely that we have a bug in our code?

This is also possible but without access to the data and related code it is impossible to comment further on that.


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