Follow up medical study with missing data

I am analyzing some patient data for a medical study that has a duration of several years.

Once a year, the patients are expected to visit the doctor, where they get four treatments, say A, B, C, D. Afterwards, to get an indication for the effect of each treatment the patient is scored on a numerical scale (same scale for each treatment).

For various reasons I have a lot of missing data because a patient may:
1. Miss the appointment, and I end up with missing data on specific years.
2. Not get all four treatments due to reasons related to the health of the patient or other technical reasons.

I am interested in both:
1. Finding whether there are differences in the mean score for each treatment separately over time.
2. Finding whether at specific point in time, there are differences in the mean score between the treatments.

Since the data for each year are not independent, the right tests to use to check whether there are differences in the mean scores for each treatment for different years is e.g., paired t-test or repeated measures ANOVA.

To have complete sets of data over the years, I must have different samples, i.e., I can find X patients that had treatment A for n years and then Y different patients that had treatment B for n years. For each group I would then perform e.g., paired t-test and then draw conclusions from it.

Is this methodology sound? Or are there other factors that I need to take into account for having a correct comparison between different groups?

• So a patient will visit a doctor at least 4 times in a year and get all 4 treatments in random order where the duration is also random? How are the visits arranged? Are they fixed? Are they based on the outcome of his previous treatment? What happens if a patient does not get all 4 treatments in a year? Do these treatments have long lasting effects? Also if you indeed decide to perform t-tests you would need to adjust the p-values for multiple testing. Commented Oct 16, 2018 at 9:09
• A patient has fixed appointments once a year for 4 years without being based on the previous treatment. If the patient does not come for the treatments in one year or comes and receives not all of them, they will still have an appointment for the next year. The treatments are done in random order and they have long lasting effects yes. Commented Oct 16, 2018 at 9:36
• A paired t-test based on the treatments would work, however that long lasting effect of the previous treatment may also have an effect, although if the treatments are randomly assigned these effects should cancel out. And the p-value adjustment. Commented Oct 16, 2018 at 10:26
• Please say what you mean by "scores for each treatment." E.g., are these indicators of the extent of treatment, perhaps the dose? Also, what is the outcome and how is it measured? E.g., on a numerical scale, as in 0-100, or binary, as in disease/no disease? Commented Oct 16, 2018 at 12:00
• @rolando2 The scores are indicators for the effect of the treatment and they are on a numerical scale (UPDRS scale). Commented Oct 16, 2018 at 13:06

A better option compared to paired t-test and repeated measurements ANOVA (also with regard to the missing data you have), is to use a (linear) mixed-effects model. In this model, you should appropriately specify the time effect for the score variable (i.e., is it linear/nonlinear), and its interaction with treatment indicator (i.e., a factor with levels A-D). You will also need to appropriately model the correlation structure, using, for example, random intercepts and (potentially nonlinear) random slopes. Also because at each visit you have up to four score values per patient, it may also be required to consider a nested random effect for the visit.

This type of models provided that the mean and correlation structures are appropriately specified will provide you with correct inferences under the missing at random assumption (i.e., the reasons why patient miss visits may depend on their previously observed score values).

If you're interested in learning more about these models, you can have a look in my Repeated Measurements course notes.