Mixed effects repeated measures model - not all variables measured at each time point.

[James Lebowski]

Hi everyone, hope you're all well.

First post - so please let me know if I have missed anything from the posting FAQ,

I've got a question regarding the use of mixed effects ordinal logistic regression for repeated measures analysis where I have repeated measures of both the dependent variable at 5 time points (e.g. days 0, 28, 90, 180, 365) as well as multiple independent variables - where the independent variables may be measured at some/all of those time points e.g. only at Day 180 and Day 365. My dependent variable is a scale with categories from 0 - 6.

I am interested in utilising all of the repeated measures in my model, as well as being able to predict the outcome variable at different time points. However, if I include all repeated measures independent variables that are not measured at every time point, I've realised that naturally my model will omit the time variable (due to empty observations). It also has the curious effect of removing one of the cutoff points (e.g. should be 6 for a 7 point scale).

I was wondering if there was any way to utliise all the repeated measures variables and time variable? My first thought was imputation/some linear back extrapolation over time but I don't know if that would be particularly rigorous.

I have attached a sample of my code and corresponding output - my apologies if unclear. To simplify the code, I have included my repeated measures dependent variable (POS), the time variable (i.days) and 2 repeated measures independent variables: PHQ (measured at all 5 time points) and SF36 (measured only at 2 time points)

I've attempted to understand this by looking through the documentation and forum but to no avail. Hope you made it through the long post and I would be very grateful for any suggestions.

Code:

reshape long POS PHQ EQ5D5L, i(regono) j(days)
xtset regono days
meologit POS i.days PHQ
meologit POS i.days EQ5D5L
meologit POS i.days PHQ EQ5D5L

Output with independent variable measured at all 5 time points (PHQ):

 POS |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        days |
         28  |  -1.149115   .0740449   -15.52   0.000    -1.294241    -1.00399
         90  |  -1.836681   .0763513   -24.06   0.000    -1.986327   -1.687035
        180  |  -2.288859   .0789507   -28.99   0.000    -2.443599   -2.134118
        365  |  -2.433143   .0835774   -29.11   0.000    -2.596952   -2.269335
             |
         PHQ |    .105064   .0063705    16.49   0.000      .092578      .11755
-------------+----------------------------------------------------------------
       /cut1 |  -4.185908   .0825713                     -4.347745   -4.024071
       /cut2 |  -1.772225   .0666063                     -1.902771   -1.641679
       /cut3 |  -.8859034    .064558                     -1.012435   -.7593722
       /cut4 |   .3948111   .0623225                      .2726613    .5169609
       /cut5 |    2.54402   .0806856                      2.385879    2.702161
       /cut6 |   4.327243   .1559541                      4.021578    4.632907

Output with independent variable measured at only 2 time points (EQ5D5L):

        POS |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        days |
          0  |          0  (empty)
         28  |          0  (empty)
         90  |          0  (empty)
        180  |  -8.499786   .3015914   -28.18   0.000    -9.090894   -7.908677
        365  |          0  (omitted)
             |
      EQ5D5L |  -8.175158   .2752685   -29.70   0.000    -8.714675   -7.635642
-------------+----------------------------------------------------------------
       /cut1 |  -9.343137   .2739839                     -9.880135   -8.806138
       /cut2 |  -6.464956    .243897                     -6.942985   -5.986927
       /cut3 |  -5.132735   .2294906                     -5.582528   -4.682942
       /cut4 |  -2.003746   .1904413                     -2.377004   -1.630488
       /cut5 |   2.974826   .3917165                      2.207076    3.742576
------------------------------------------------------------------------------

Output with independent variable measured at only 2 time points (EQ5D5L) and at 5 time points (PHQ):

 POS |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        days |
          0  |          0  (empty)
         28  |          0  (empty)
         90  |          0  (empty)
        180  |  -8.465161   .3186536   -26.57   0.000    -9.089711   -7.840612
        365  |          0  (omitted)
             |
         PHQ |   .0048066   .0144241     0.33   0.739     -.023464    .0330773
      EQ5D5L |  -8.141514   .2928335   -27.80   0.000    -8.715457   -7.567571
-------------+----------------------------------------------------------------
       /cut1 |  -9.302017   .3001149                     -9.890231   -8.713803
       /cut2 |  -6.422326   .2750666                     -6.961447   -5.883206
       /cut3 |  -5.089812   .2628265                     -5.604942   -4.574681
       /cut4 |  -1.966184    .221139                     -2.399608   -1.532759
       /cut5 |   3.007101   .4038256                      2.215617    3.798584

[Clyde Schechter]

I suspect the reason you are losing a cutpoint when you throw in the SF36 is that after Stata drops all observations with missing values of the SF-36, which reduces you to just two timepoints, one of the original values of your outcome variable just doesn't happen to occur in the remaining data.

The fact of the matter is that you really only have a 2 timepoint study for any analysis that relies on including the SF36. One possible way to get around this is, instead of having the SF36 as one of your time-varying predictors, you could create new variables, SF36_1 and SF36_2 that contain the early and late scores on the SF36 and have those by time-invariant covariates in your modeling. It is not ideal by any means, but is probably the best you can do with what you have.

By the way, although it is of no importance, it seems odd to name your SF36 variable EQ5D5L. The name is much more suggestive of the somewhat related EuroQol scale.

[James Lebowski]

Thanks Clyde - appreciate the suggestion! I suppose I will have to consider which time variables are essential. My apologies - I misnamed the variable I mixed the two up.

[Joseph Coveney]

I suppose I will have to consider which time variables are essential.

I'm not sure just what your intervention is, or even if there is any explicit intervention other than the start of the longitudinal survey. But why not consider the observations on the two or three health questionnaires (PHQ-9, SF-36 or EQ-5D-5L) that are administered after the start of the time course as additional outcome variables (a.k.a., dependent variables, response variables) that are parallel to the palliative-care outcome measure? That is, model the data in the same manner as in an ANCOVA. You don't normally put a variable in again as a predictor after the intervention.

They are responses of mixed type (i.e., both continuous and ordered categorical scores), but you can model them together in an generalized structural equation model (SEM) using an official Stata command, such as gsem for example in a latent growth model-like set up or in user-written command, such as gllamm available from SSC as well as its own website.

And if you insist on putting in little arrows in order to indicate that responses on the interim health survey questionnaires are somehow mediating or otherwise predicting responses on later POS results, then you can do so when setting up the SEM.