Signature
c_95 = d_S + 1.645 * s_S
| Inputs | Definition | Unit |
|---|---|---|
d_S | Unit: score points | — |
s_S | Unit: score points | — |
c_95 | Unit: score points | — |
|---|
Function
Anchor-based thresholds for a minimal clinically important difference and their use for responder shares and trial size
Maps a meaningful step on an external anchor, usually a patient's global rating of change, onto the score scale of an outcome measure. The between-group estimate subtracts the mean change of patients reporting no change from that of patients reporting a small change; the ROC cut-off chooses the change score that best separates anchor-improved patients from the rest; the 95 per cent limit cut-off sits above almost all unchanged patients. A threshold then gives the share of patients reaching it in each arm, and a between-group difference sets the target difference of a sample size calculation. Distribution-based yardsticks are HE-FM-DMID-001 to HE-FM-DMID-003 on the Distribution-Based MID page. Notation follows the Minimal Clinically Important Difference article.
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Implementations
Excel
Ninety-five per cent limit cut-off from named cells
With MeanChgSame and SDChgSame named, the formula returns the cut-off, held in LimitC95.
=MeanChgSame+1.645*SDChgSame
Assumptions
Approximately normal change among patients not importantly changed
The 1.645 multiplier assumes the change scores of the not importantly changed group are close to normal, so that about 5 per cent of them exceed the cut-off; in the article's example that group is the 70 patients rating themselves about the same.
Worked examples
Unchanged group with mean change 2.0 and standard deviation 5.0
The cut-off is 2.0 + 1.645 x 5.0 = 10.225, shown as 10.2 points in the article, against 6 for the ROC cut-off and 8.0 for the mean change method.
d_S = 2; s_S = 5; c_95 = 10.2
Same mean with a standard deviation of 4.0
Less spread among unchanged patients lowers the cut-off to 2.0 + 1.645 x 4.0 = 8.58 points (computed here for illustration).
d_S = 2; s_S = 4; c_95 = 8.58
Common errors
Choosing the stricter limit without saying so
The same data support thresholds of 6.0, 8.0 and 10.2 points; a model that gives responders and non-responders different utilities changes its responder shares, and so its QALYs, when the 10.2-point limit replaces the 6-point ROC threshold.
Using the whole reference group of the ROC analysis for the 95 per cent limit
The limit is built on the patients the anchor classes as not importantly changed; in the article's example that is the 70 rating themselves about the same, not all 110 patients outside the improved group, which include patients who got worse.
Sources
De Vet and colleagues on the 95 per cent limit cut-off
de Vet HC, Ostelo RW, Terwee CB, van der Roer N, Knol DL, Beckerman H, Boers M, Bouter LM. Minimally important change determined by a visual method integrating an anchor-based and a distribution-based approach. Quality of Life Research. 2007;16(1):131-142. doi:10.1007/s11136-006-9109-9 (full text read). Methods: the MIC for improvement is defined as the 95% upper limit of the distribution of the persons who are not importantly changed according to the anchor, mean change + 1.645 SD change; the 95% limit cut-off point corresponds with 95% specificity on the ROC curve.
Canonical Identity
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