Signature
MID_SD = k_SD * SD_0
| Inputs | Definition | Unit |
|---|---|---|
k_SD | 0.5 for the half standard deviation rule, 0.2 for Cohen's small benchmark | standard deviations |
SD_0 | Standard deviation of the instrument's scores in the sample at baseline | instrument units |
MID_SD | Change in score treated as the yardstick | instrument units (for example EQ-5D index points) |
|---|
Function
Distribution-based yardsticks for a minimal important difference in patient-reported and utility scores
Expresses an important or detectable change in a questionnaire or utility score as a multiple of the spread of scores or of the instrument's measurement error: half a baseline standard deviation, a benchmark effect size, one standard error of measurement, the minimally detectable change and the reliable change index for one person. These yardsticks describe precision, not what patients value, and methodological and regulatory guidance ranks them behind anchor-based estimates. Standardised mean differences themselves are HE-FM-CD-001 on the Cohen's d page. Notation follows the Distribution-Based MID article.
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Implementations
Excel
Multiple of the baseline standard deviation from named cells
With BaseSD and SDMult named, the formula returns the distribution-based yardstick, held in MIDSD.
=SDMult*BaseSD
Assumptions
Half a standard deviation summarises earlier published MIDs in chronic disease
The 0.5 multiple comes from a review that re-expressed 62 published MIDs as effect sizes and framed its conclusion for chronic diseases; population-based estimation and brief follow-up gave smaller values and acute conditions larger ones, so the multiple is a summary, not a property of any one instrument.
Baseline standard deviation from the population of interest
SD_0 is the spread at baseline in the sample whose change is being judged; a more heterogeneous sample has a larger SD_0 and so a larger yardstick, although patients' perception of change is the same.
Worked examples
Half a standard deviation of an EQ-5D-5L index with SD 0.20
With a baseline standard deviation of 0.20, half a standard deviation is 0.10 index points, as in the article's illustrative example.
k_SD = 0.5; SD_0 = 0.2; MID_SD = 0.1
Cohen's small benchmark for an EQ-5D-5L index with SD 0.20
An effect size of 0.2 against the same standard deviation is 0.04 index points, as in the article.
k_SD = 0.2; SD_0 = 0.2; MID_SD = 0.04
Half a standard deviation in a more heterogeneous sample
If the baseline standard deviation were 0.30, the half standard deviation yardstick would rise to 0.15 with no change in what patients perceive (computed here for illustration).
k_SD = 0.5; SD_0 = 0.3; MID_SD = 0.15
Common errors
Quoting half a standard deviation as a fixed property of an instrument
Revicki and colleagues note that the MID for a patient-reported outcome instrument is not an immutable characteristic and may vary by population and context; the half standard deviation value moves with every sample's spread.
Treating half a standard deviation as minimally important change
De Vet and colleagues argue that half a standard deviation corresponds more to minimally detectable than to minimally important change; in the article's example it is 0.10, twice the anchor-based estimate of 0.05.
Setting utility gains below the MID to zero in a cost-utility analysis
The NICE manual multiplies the time in each health state by its utility with no importance threshold; in the article a gain of 0.03 for two years at 1,200 pounds is 20,000 pounds per QALY although 0.03 is below every group-level yardstick.
Sources
Half a standard deviation as the typical MID in Norman, Sloan and Wyrwich
Norman GR, Sloan JA, Wyrwich KW. Interpretation of changes in health-related quality of life: the remarkable universality of half a standard deviation. Medical Care. 2003;41(5):582-592. doi:10.1097/01.MLR.0000062554.74615.4C (abstract read). Abstract: 38 studies gave 62 effect sizes; for all but 6 studies the MID estimates were close to one half a standard deviation (mean 0.495, SD 0.155); population-based estimation and brief follow-up were associated with smaller effect sizes and acute conditions with larger ones; for chronic diseases the threshold appears to be about half a standard deviation.
Cohen's small effect size benchmark of 0.2
Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum Associates; 1988 (Routledge digital edition 2013) (full text read). Section 2.2.3: operational definitions of small, medium and large effect sizes, d = 0.2, 0.5 and 0.8.
MID not an immutable characteristic of an instrument
Revicki D, Hays RD, Cella D, Sloan J. Recommended methods for determining responsiveness and minimally important differences for patient-reported outcomes. Journal of Clinical Epidemiology. 2008;61(2):102-109. doi:10.1016/j.jclinepi.2007.03.012 (abstract read). Abstract: MID estimates should be based on multiple approaches and triangulation, with anchor-based methods primary and distribution-based methods in support or where anchor-based estimates are unavailable; the MID for a patient-reported outcome instrument is not an immutable characteristic but may vary by population and context.
Half a standard deviation and the SEM as detectable rather than important change
de Vet HC, Terwee CB, Ostelo RW, Beckerman H, Knol DL, Bouter LM. Minimal changes in health status questionnaires: distinction between minimally detectable change and minimally important change. Health and Quality of Life Outcomes. 2006;4:54. doi:10.1186/1477-7525-4-54 (full text read). Section on the distinction between minimally detectable and minimally important changes: the 0.5 SD criterion may be considered a threshold of detection and corresponds more to minimally detectable change than to minimally important change. Introduction: the major disadvantage of all distribution-based methods is that they do not, in themselves, give a good indication of the importance of the observed change.
NICE reference case QALYs multiply time in each state by its utility
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated 31 March 2026 (full text of chapter 4 read). Section 4.3.2: each health state experienced within the time horizon of the model is given a utility, and the time spent in each health state is multiplied by the utility.
Canonical Identity
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