linking measurement error to minimal important change oxford... · 2011. 3. 24. · the sdc and the...
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www.kmin-vumc.nl Interpretation of PROMs:
linking measurement error to minimal important change
Caroline Terwee
Knowledgecenter Measurement InstrumentsDepartment of Epidemiology and Biostatistics
VU University Medical Center
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www.kmin-vumc.nl Proposition
detectable change is conceptually different from
important change
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Content
• Measurement error (detectable change) –
difference from reliability
• Important change –
anchor-based MIC distribution
• Linking measurement error to minimal important change in individual patients
• Intermezzo –
why distribution-based methods should not be used to define MIC
• Alternative ways of interpreting change scores•
consider type I error
•
estimate the probability of belonging to the importantly improved group
• Linking measurement error to minimal important change on group level
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Measurement error
Terminology
Minimal Detectable Change
Smallest Detectable Change
Real change
Smallest Real Change
Significant change
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Measurement error
Terminology
Minimal Detectable Change
Smallest Detectable Change SDCReal change
Smallest Real Change
Significant change
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Measurement error
Reliability = The proportion of the total variance in the measurements which is due to ‘true’
differences
between patients
Measurement error = The systematic and random error of a patient’s score that is not attributed to true changes in the construct to be measured
www.cosmin.nl
Reliability
InternalConsistency Reliability
(test-retest,Inter-rater,Intra-rater)
Measurement error
(test-retest,Inter-rater,Intra-rater)
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Measurement error – consistency
errorpatientspatientsICCyReliabilit yconsistenc 22
2
σσσ
+==
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Measurement error – consistency
errorpatientspatientsICCyReliabilit yconsistenc 22
2
σσσ
+==
error)(SEM nt Measuremeof Error Standard yconsistenc2σ=
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Measurement error – consistency
errorpatientspatientsICCyReliabilit yconsistenc 22
2
σσσ
+==
ICCSDSEM yconsistencyconsistenc −= 1*
error)(SEM nt Measuremeof Error Standard yconsistenc2σ=
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Measurement error – consistency
errorpatientspatientsICCyReliabilit yconsistenc 22
2
σσσ
+==
yconsistencyconsistenc SEM2*1.96 (SDC Change Detectable Smallest *) =
ICCSDSEM yconsistencyconsistenc −= 1*
error)(SEM nt Measuremeof Error Standard yconsistenc2σ=
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Measurement error – consistency
errorpatientspatientsICCyReliabilit yconsistenc 22
2
σσσ
+==
error)(SEM nt Measuremeof Error Standard yconsistenc2σ=
agreement of limits SD*1.96 SDC changeyconsistenc ==
yconsistencyconsistenc SEM2*1.96 (SDC Change Detectable Smallest *) =
ICCSDSEM yconsistencyconsistenc −= 1*
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Measurement error – agreement
errortsmeasuremenpatientspatientsICC y Reliabilit agreement 222
2
σσσσ
++==
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Measurement error – agreement
errortsmeasuremen)(SEM nt Measuremeof Error Standard agreement22 σσ +=
errortsmeasuremenpatientspatientsICC y Reliabilit agreement 222
2
σσσσ
++==
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Measurement error – agreement
errortsmeasuremen)(SEM nt Measuremeof Error Standard agreement22 σσ +=
errortsmeasuremenpatientspatientsICC y Reliabilit agreement 222
2
σσσσ
++==
ICCSDSEM agreementagreement −= 1*
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Measurement error – agreement
agreementagreement SEM2*1.96 SDC *=
errortsmeasuremen)(SEM nt Measuremeof Error Standard agreement22 σσ +=
errortsmeasuremenpatientspatientsICC y Reliabilit agreement 222
2
σσσσ
++==
ICCSDSEM agreementagreement −= 1*
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Measurement error – agreement
agreementagreement SEM2*1.96 SDC *=
errortsmeasuremen)(SEM nt Measuremeof Error Standard agreement22 σσ +=
errortsmeasuremenpatientspatientsICC y Reliabilit agreement 222
2
σσσσ
++==
ICCSDSEM agreementagreement −= 1*
agreement of limits SDCagreement ≠
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Measurement error
agreementagreement SEM2*1.96 SDC *=
SDC is the smallest change in score that you CAN detect with the instrument, above measurement error
in individual patients
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Measurement error - example
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Measurement error - example
Scores 0-100
Measurement error of OES Function = 19 points on a scale from 0-100
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Mimimal Important Change (MIC)
MIC is the smallest change in score that you WANT to detect with the instrument
MIC is determined by an anchor-based method
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Mimimal Important Change (MIC)
Example anchor: Global rating of change
1.
Completely recovered
2.
Much improved
3.
Slightly improved
4.
No change
5.
Slightly worse
6.
Much worse
Importantly improved
Not importantly changed
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Achor-based MIC distribution
+
_
Importantly improved
ANCHORANCHOR
Not importantly changed
O
Cha
nge
on in
stru
men
t
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Anchor-based MIC distribution
+
_
Importantly improved
ANCHORANCHOR
Not importantly changed
O
Cha
nge
on in
stru
men
t
ROC cut-off point
MIC = ROC cut-off point
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Anchor-based MIC distribution - example
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Mimimal Important Change (MIC) - example
Improved = ‘slightly better’, ‘much better’, ‘no problems now’Not improved = ‘no change’, ‘worse’
MIC for OES Function is 5 points
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www.kmin-vumc.nl Proposition
Smallest Detectable Change (SDC)is conceptually different from
Minimal Important Change (MIC)
SDC is the smallest change in score that you CAN detect with the instrument, above measurement error
MIC is the smallest change in score that you WANT to detect with the instrument
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Linking SDC to MIC
In individual patients SDC should be smaller than MIC to distinghuish important change from measurement error
For may PROMs this is not the case
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Linking SDC to MIC - example
For OES Function SDC (19) is larger than MIC (5)For OES Pain SDC (8) is smaller than MIC (12.5)
Thus with the OES pain we can distinguish important change from measurement errobut with the OES Function this is not possible
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Linking SDC to MIC
SDC and MIC are two reference points in the scale that can help interpret change scores
Example 1 -
SDC is smaller than MIC
Change NOT statistically significant and NOT important
Change statistically significant AND important
Change statistically significant, but not important
SDC
MICno change maximum change
OES Pain -
SDC (8) is smaller than MIC (12.5)
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Change NOT statistically significant and NOT important Change statistically significant AND important
Change important, but can NOT be distinguished from measurement error
SDCMICno change maximum change
Linking SDC to MIC
Example 2 -
SDC is larger than MIC
OES Function -
SDC (19) is larger than MIC (5)
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Intermezzo
Why distribution-based methods should not be used to define MIC
Distribution-based methods
e.g. MIC = 1*SEM or MIC = 0.5*SD
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Intermezzo
Why distribution-based methods should not be used to define MIC
Distribution-based methods
e.g. MIC = 1*SEM or MIC = 0.5*SD
If MIC is defined as 1*SEM the SDC will always (by definition) be larger than the MIC, because SDC=1.96*√2*SEM.
This would mean that one can never distinguish important change from measurement error in individual patients
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Taking type I error into account
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Taking type I error into account
agreementagreement SEM2*1.96 SDC *=
If we say that a patient who changed as much as the SDC has been
‘really’ changed (statistically significant change), there is a 5% probability (type I
error) that in fact this patient has not changed.
Patients with change scores smaller than the SDC have a higher probability that they are in fact not changed (larger type 1 error).
Thus if the SDC is larger than the MIC, there is a higher type 1
error if we call patients who changed as much as the MIC importantly improved.
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Change NOT statistically significant and NOT important Type 1 error <5%
Change important, but type 1 error may be substantial
SDCMICno change maximum change
Taking type I error into account
Type I error
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Estimate the probability of belonging to the ‘importantly improved’ group
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Estimate the probability of belonging to the ‘importantly improved’ group
+
_
Importantly improved
ANCHORANCHOR
Not importantly changed
O
Cha
nge
on in
stru
men
t
MIC
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Estimate the probability of belonging to the ‘importantly improved’ group
Logistic regression analysis
Dependent variable = group (0=not importantly changed,1= importantly improved)
Independent variable = change score on the instrument
)(11
Xeyprobabilit predicted βα +−+=
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Example
Hypothetical health questionnaire, score 0-100 (higer score = better health)
Sample n=20.000
Anchor:50% = importantly improved50% = not importantly changed
Prior probability of belonging to the ‘importantly improved’
group = 50%
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B S.E. Wald df Sig. Exp(B)95,0% C.I.for
EXP(B)
Lower Upper
Change score ,050 ,001 4005,047 1 ,000 1,052 1,050 1,053
Constant -,966 ,022 1940,184 1 ,000 ,381
Example
Logistic regression analysis
α=-0.966 and β=0.050
)050.0966.0(11
Xey probabilit predicted +−−+=
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Example
0.28 e
p =+
= +−− )0*050.0966.0(11
Patient 1 –
change score = 0
Patient 3 –
change score = 50 0.82 e
p =+
= +−− )50*050.0966.0(11
Patient 2 –
change score = 25 0.43 e
p =+
= +−− )25*050.0966.0(11
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Example
Predicted probabilities of belonging to the ‘importantly improved’ group for each possible change score on the questionnaire
Change score on instrument
Pred
icted
prob
abilit
y
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Finallylinking SDC to MIC – on group level
In research we use mean change scores of groups
Measurement error is reduced because of repeated measurements
nSDC SDC individual
group =
MIC on group level = smaller ???
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Summary
Smallest Detectable Change (SDC) is conceptually different from Minimal Important Change (MIC)
SDC is the smallest change in score that you CAN detect with the instrument, above measurement error
preferably based on SEMagreement
MIC is the smallest change in score that you WANT to detect with the instrument
Should be based on anchor-based methods
The SDC and the MIC are two important reference points on a scale that can help interpret change scores in individual patients
As an alternative, estimating the probability of belonging to the importantly improved group may be useful
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www.kmin-vumc.nlThank you
Terwee CB, Roorda LD, Knol DL, de Boer MR, de Vet HCW. Linking measurement error to minimal important change of patient-reported outcomes. J Clin Epidemiol 2009;62:1062-1067.
de Vet HCW, Ostelo RWJG, Terwee CB, van der Roer N, Knol DL, Beckerman H, Boers M, Bouter LM. Minimally import ant change determined by a visual method integrating an anchor-
based and a distribution-based approach. Qual Life Res 2007;16:131-142.
de Vet HCW, Terwee CB, Knol DL, Bouter LM. When to use agreement versus reliability measures. J Clin Epidemiol 2006;59:1033-1039.