Abstract
It was great to read constructive feedback on our statistical methodology. Even if we submitted the original manuscript of our study >8 years ago, such attention to detail raises awareness and maintains the rigor of research in orthopaedics and sports medicine, and it should help reduce the frequency of false or invalid conclusions.
The authors of the letter point out that we evaluated improvements in knee laxity and clinical scores at consecutive follow-ups using the Mann-Whitney test and overall trends using the Kruskal-Wallis test…. Since [we] compared the paired samples (knee scores at consecutive follow-ups), it would have been ideal to use the Wilcoxon rank-sum test (2 paired groups) and the Friedman test (>2 groups with paired samples).
It is true that we compared paired samples at consecutive follow-ups, and that we used tests that assume the data collected at each time point to be “independent,” whereas we should have used a test that takes into account the repeated character of the measurements, such as the Wilcoxon rank-sum test for comparisons between 2 paired samples, or the Friedman test for more than 2 groups (or more than 2 time points) with paired samples.
The problem is we had missing data, eg Figure 4 shows the first box plot: preoperative n = 97, 6 months n = 84, 1 year n = 60, and two years n = 79. Using a paired test such as the Wilcoxon rank-sum or Friedman test, only “complete cases” would be included. So, in case of a Friedman, we could only include 60 patients (or maybe even less; as cases should have data available at each of the 4 time points to be included). For 2 groups, the same logic counts.
Alternatively, we could have used a linear mixed model which takes into account that the data belong to certain patients. These models can also deal with missing data and can easily compare between time points without ignoring the “paired” nature of the data.
We are certain that more experienced statisticians could suggest better methods and tests, after verifying certain assumptions and trends, to compare the 2 groups, and we strive to learn and improve from their feedback and advice.
Footnotes
One or more of the authors has declared the following potential conflict of interest or source of funding: P.C. has received royalties from SBM France. AOSSM checks author disclosures against the Open Payments Database (OPD). AOSSM has not conducted an independent investigation on the OPD and disclaims any liability or responsibility relating thereto.