Reply to Jüni and colleagues regarding “Converting standardized mean differences to dichotomous outcomes: A comment on the Cochrane review ‘Intra-articular corticosteroid for knee osteoarthritis’”
Creators: name: Mayer, Martin
Publisher: name: figshare
Year: 2019
Subjects: subject: 111502 Clinical Pharmacology and Therapeutics
subject: FOS: Clinical medicine
subject: FOS: Clinical medicine
subject: 111706 Epidemiology
subject: FOS: Health sciences
subject: FOS: Health sciences
subject: Health Care
subject: 10402 Biostatistics
subject: FOS: Mathematics
subject: FOS: Mathematics
subject: 10405 Statistical Theory
subject: 10401 Applied Statistics
subject: Statistics

description: I thank Dr. Jüni and colleagues for their reply[1] to my correspondence[2] about their Cochrane review.[3] Their reply also pertains to my correspondence[4] about another Cochrane review they completed,[5] and they also identify two other Cochrane reviews they completed[6,7] for which my correspondence[2,4] is relevant. However, a considerable portion of their responses[1] are incorrect, so I submit here further correspondence with the hope of reaching resolution. As I noted previously, I submit the following in a spirit of collegial collaboration. They agree with my first point regarding the assumed probability of achieving ≥50% improvement in function in the control group, and they provide a corrected probability in line with my previous correspondence (i.e., they correct the probability from 26% as they used previously[1,3,5–7] to 22% as noted in my previous correspondence[2,4]). Regarding my second point, they state my calculations are for the number needed to treat to benefit (NNTB) to achieve one additional response, which is correct. They also agree the approach I use makes the results easier to interpret, so they commit to adopting the approach I use going forward, and I am glad to hear this. However, they also state their calculations are formally correct, even if somewhat indirect to interpret; they state their NNTB calculations are for preventing one additional non-response. It seems important to note this contradicts the intent stated in each of their four reviews (where they stated the calculations were for NNTBs to “cause one additional treatment response”),[3,5–7] but setting that aside, they are also incorrect that their calculations are formally or technically correct (even for preventing one additional non-response), and they are also incorrect about why the two sets of NNTBs they calculate in their response are different. As I demonstrated previously,[2,4] the conversion factor one should use depends on the specified cutoff, C, and whether one is interested in a patient achieving C or higher or C or lower. Jüni and colleagues specify interest in patients reaching C or lower for both pain and function: For their specified response outcomes of achieving ≥50% improvement in pain and function, they specify control group probabilities of 31% and 22%, respectively (I use 22% here given their acknowledgment that 26% is incorrect), and these probabilities are based on achieving decreases of at least 1.2 standard deviation (SD) units (C = -1.2 SD units or lower) and at least 1.35 SD units (C = -1.35 SD units or lower), respectively.[3,5–7] Because of this, it is incorrect for Jüni and colleagues to use π/√3 (≈ 1.81) for the conversion factor, and I show this in my previous correspondence (the correct conversion factor is –π/√3 ≈ –1.81).[2,4] Consequently, their statement that using π/√3 is technically or formally correct for the outcome of preventing one additional non-response is also incorrect. If Jüni and colleagues are interested in providing calculations for the prevention of non-response, then by definition, they should not be using the probability a patient will respond (the probability a patient will reach the cutoff of C or lower) as the baseline/control group probability. Rather, they should be using the probability a patient will not respond (the probability a patient will reach the cutoff of C or higher) as the baseline/control group probability. These probabilities are complements (probability of response = 1 – probability of non-response). In other words, the baseline/control group probabilities Jüni and colleagues use are for response: 31% for pain and 22% for function (using the corrected value for function). But they use these baseline/control group probabilities with the conversion factor of π/√3 and say this is to perform calculations that offer insight into preventing non-response. This is incorrect. If Jüni and colleagues desire to provide insight into preventing non-response, they should be using baseline/control group probabilities of 69% for pain and 78% for function, because these are the baseline/control group probabilities of non-response (i.e., the probabilities of not achieving ≥50% improvement). Phrased differently and somewhat more technically, the calculations Jüni and colleagues presently perform for the (purported) prevention of one additional non-response conflate left-tail probabilities (i.e., the probability of achieving what they have defined as a response) with a conversion factor intended for right-tail probabilities (i.e., π/√3), yielding inaccurate results. Herein, I elaborate on this and the rest of their response. <br><br>References:<br> 1. Jüni P, Rutjes A, Reichenbach S, et al. Reply to: ‘Converting standardized mean differences to dichotomous outcomes: A comment on the Cochrane review “Intra-articular corticosteroid for knee osteoarthritis”’. May 2019. doi:10.6084/m9.figshare.8111471 2. Mayer M. Converting standardized mean differences to dichotomous outcomes: A comment on the Cochrane review ‘Intra-articular corticosteroid for knee osteoarthritis’. March 2019. doi:10.6084/m9.figshare.7898156 3. Jüni P, Hari R, Rutjes AWS, et al. Intra-articular corticosteroid for knee osteoarthritis. Cochrane Database Syst Rev 2015:CD005328. doi:10.1002/14651858.CD005328.pub3 4. Mayer M. Converting standardized mean differences to dichotomous outcomes: A comment on the Cochrane review ‘Oral or transdermal opioids for osteoarthritis of the knee or hip’. March 2019. doi:10.6084/m9.figshare.7898159 5. da Costa BR, Nüesch E, Kasteler R, et al. Oral or transdermal opioids for osteoarthritis of the knee or hip. Cochrane Database Syst Rev 2014:CD003115. doi:10.1002/14651858.CD003115.pub4 6. Rutjes AW, Nüesch E, Sterchi R, et al. Therapeutic ultrasound for osteoarthritis of the knee or hip. Cochrane Database Syst Rev 2010:CD003132. doi:10.1002/14651858.CD003132.pub2 7. Rutjes AW, Nüesch E, Sterchi R, et al. Transcutaneous electrostimulation for osteoarthritis of the knee. Cochrane Database Syst Rev 2009:CD002823. doi:10.1002/14651858.CD002823.pub2<br>