Repeated measures ANOVA; missing data and multiple measures at each time point

#1
Hi TalkStats

I have data from a project. The data is the blood pressure for each participant at day of "baseline" visit, and 3 time points after baseline visit. Index these baseline and post-baseline time points j=0,1,2,3.

For the \(i\)th participant, at time point \(j\), we have measurement \(x_{ij}\) of blood pressure. In fact, we may have 1, 2 or 3 (or no!) measures of blood pressure at some time points \(j\). So at time point \(j\), participant \(i\) may have blood pressure \(x_{ij1},x_{ij2}\) etc. See the table below

\(
\begin{tabular}{|l|cccc|}
\hline
Participant & Baseline & 3 Months & 6 Months & 12 Months \\
\hline
\#1 & 220,180 & 170,160 & 110,120 & 80,65 \\
\#2 & 130 & 180,80 & Missing & 70 \\
\#3 & 120,145 & 108 & 100,50 & 40,30 \\
\hline
\end{tabular}
\)

As you can see, at some time points, there is one value, at some 2, and at some the data is missing. Now we want to see what happens to blood pressure compare to the baseline visit.

There are approximately 20 participants, but at some time points we have more than 20 data points due to the multiple readings taken at that time point, for some participants. We want to compare the recordings to baseline data, using a repeated measures ANOVA. But we have either 1, multiple or no measures at some time points!! Which measure do we take?!

  • For each participant, do we mean the recordings at each time point, then compare the means? E.g. do we work out mean baseline recording for each participant (either 1 or 2 recordings), and compare the mean response at each visit to this baseline mean, using a repeated measures ANOVA?
  • If we do this we cannot use a non-parametric ANOVA in GraphPad Prism, as the data is entered as Mean +/- SEM!?
  • How do we treat missing values with a repeated measures ANOVA? A number of people have said that for such a small n we can try listwise deletion or mean replacement. What would you guys recommend?
 

Karabiner

TS Contributor
#2
[*] For each participant, do we mean the recordings at each time point, then compare the means?
You did not say what this study is actually about and why there are
instances of 2 or 3 measurements instead on just one. The values
from the same person at the same point of time vary considerably
in your example.
[*] How do we treat missing values with a repeated measures ANOVA? A number of people have said that for such a small n we can try listwise deletion or mean replacement. What would you guys recommend?
Never do mean replacement. Listwise deletion will waste information
and probably leave you with a very samll sample. You could
perhaps leave out the global ANOVA and just perform 3 comparisons
between baseline and the respective time points (Wilcoxon signed
rank tests, with Bonferroni-corrected significance level alpha/3).

With kind regards

K.
 

hlsmith

Not a robit
#3
Options, not overly experienced in but fitting:

Use multiple imputation to fill in data, or

I know multi-level models can still function with all observations (no listwise deletion) when dataset has missing data points.