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Assessment of Reliable Change: Methods and Assumptions. Michael Basso, Ph.D. Associate Professor and Director of Clinical Training Department of Psychology—University of Tulsa Clinical Associate Professor Department of Psychiatry—University of Oklahoma. Objectives.

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Assessment of reliable change methods and assumptions l.jpg

Assessment of Reliable Change: Methods and Assumptions

Michael Basso, Ph.D.

Associate Professor and Director of Clinical Training

Department of Psychology—University of Tulsa

Clinical Associate Professor

Department of Psychiatry—University of Oklahoma


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Objectives

  • Provide background concerning methods of assessing reliable change

  • Describe assumptions and applications of reliable change scores

  • Illustrate use of reliable change scores


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Assessment of Clinical Change

  • Two Basic Approaches

    • Assessment of Group Differences Across Time

    • Assessment of Individual Differences Across Time


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Assessment of Group Differences Across Time

  • Assessment of statistically reliable change

    • “Does the treatment yield significant benefits for groups of patients?”

      • i.e., do average scores at T1 and T2 come from different distributions

    • This approach describes the average rate of change over groups primarily

    • It is accomplished with repeated measure ANOVA

    • Problem: You could have a statistically significant difference with a very small effect size, but it might not be a clinically meaningful change


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Assessment of Individual Differences Across Time

  • Assessment of Clinically Meaningful Change

    • “Did the patient’s change in performance at T2 exceed base rates of change?”

      • i.e., did the individual show change that exceeded expectations based on measurement error, practice effects, and regression to the mean?

    • This method describes the base rate of change

      • Change that is exceeds the base rate is not normal, and is therefore clinically meaningful

    • Our focus is on the assessment of clinically meaningful change in individuals, but this method can be applied to group data as well


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Assessment of Clinical Change for Individuals

  • How do you establish the base-rate of change?

  • Bear into consideration that:

    • It would be improbable to obtain the exact same score twice

    • There is no perfect test-retest correspondence because of

      • measurement error

      • regression to the mean

      • practice effects


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Two Methods of Assessing Base Rates of Change

  • Reliable change Index scores

    • “Does change exceed what would be expected based on measurement error alone?”

    • This method is based on Reliability of measurement

    • It is used for typical performance tests

      • i.e., attitude, personality, psychopathology, etc.

  • Standardized Regression-Based Change Scores

    • “Does change in scores exceed expectations based on T1 (baseline) scores?”

    • This method is based on a validity coefficient (i.e., what T2 score is predicted by the T1 score)

    • It is used for maximal performance tests

      • i.e., IQ, neuropsychological, etc.


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Reliable Change Index Scores

  • Elaborated by Jacobson and Truax (1991)

    • Based on the standard error of the difference

      • Which in turn is based on the reliability coefficient

    • This reflects the sampling distribution of difference scores

    • it implies the magnitude of differences between two test scores that vary by chance alone

  • Assumptions

    • Error components are mutually independent and independent of true pretest and posttest scores

    • Error is normally distributed with a mean of 0

    • SE of error is equal for all subjects

    • These assumptions are questionable in clinical settings (cf. Maassen, 2004)


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Standard Normal Curve—Distribution of Difference Scores


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Reliable Change Index Scores--Method

  • To use the RCI, you must compute the SE of difference between two scores

  • SEdiff=(2(SD(1-rxx)1/2)2)1/2

  • Then, compute a confidence interval for change scores

  • for 95% confidence, you multiply 1.96 * SEdiff

  • for 90% confidence, you multiply 1.60 * Sediff

  • Does the raw score change between T2 and T1 exceed the confidence interval?

    • If so, it represents change that exceeds the base rate expected based on measurement error

      • Thus, clinically meaningful change has occurred

    • If not, then the change is consistent with the base rate expected based on measurement error

      • Thus, no clinically meaningful change has occurred


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Reliable Change Index Scores—An Example

  • Ferguson, Robinson, & Splaine (2002)

    • SF-36 in 200 patients who had undergone a Coronary Artery Bypass Grafting (CABG) surgery

    • SF-36 contains 8 scales

      • Physical Functioning

      • Role Functioning Physical

      • Bodily Pain

      • General Health

      • Vitality

      • Social Functioning

      • Role Functioning-Emotional

      • Mental Health


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Reliable Change Index Scores—An Example

  • Ferguson, Robinson, & Splaine (2002)

    • Physical Functioning

      • Reliability=.93 (from normative sample of 2474)

      • Mean of normative sample=84.15

      • SD of normative sample=23.28

      • SEdiff=(2(SD(1-rxx)1/2)2)1/2

        • SEdiff=(2(23.28(1-.93)1/2 ) 2))1/2=9.85

        • 95% CI: (SEdiff)*1.96=19.32

        • T1 Mean=40.97

        • T2 Mean=63.39

        • Mean Diff=22.42

        • The mean difference exceeds 19.32

        • Thus, clinically meaningful change has occurred as a result of surgery


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Reliable Change Index Scores—An Example

  • Ferguson, Robinson, & Splaine (2002)

    • Mental Health

      • Reliability=..84 (from normative sample of 2474)

      • Mean of normative sample=75.01

      • SD of normative sample=21.40

      • SEdiff=(2(SD(1-rxx)1/2)2)1/2

        • SEdiff=(2(21.40(1-..84)1/2 ) 2))1/2=10.92

        • 95% CI: (SEdiff)*1.96=21.40

        • T1 Mean=72.08

        • T2 Mean=71.84

        • Mean Diff=-0.24

        • The mean difference fails to exceed 21.40

        • Thus, no clinically meaningful change has occurred as a result of surgery


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Standardized Regression Based Change Scores

  • Elaborated by Charter (1996)

  • Used primarily for maximal performance tests

  • The RCI of Jacobsen and Truax is used for typical performance tests

    • It assumes that errors between test scores at baseline and time 2 are uncorrelated

    • This assumption is untenable in maximal performance tests because of practice effects


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Standardized Regression Based Change Scores

  • Based on the standard error of prediction

    • SEpred=SDY2((1-rY1Y22)1/2)

  • The SE reflects the sampling distribution of predicted scores

  • It implies the range of scores that might be expected at time two that may be expected from the baseline score and prediction error

  • This method requires you to compute the estimated true score

    • Y2True=M+((rY1Y2)(Y1-M))

  • The T2 score is prone to error, and this formula permits an unbiased estimate of the true score

  • The SEpred is used to compute a confidence interval around the estimated true score


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Standard Normal Curve—Distribution of Standard Error of Prediction Around Estimated True Score


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Standardized Regression Based Change Scores--Method

  • To use the SRB, you must compute the estimated true T2 score

  • Compute the confidence interval around this estimated true T2 score

  • For 95% confidence, you multiply 1.96 * SEpred

  • For 90% confidence, you multiply 1.60 * SEpred

  • Does the obtained T2 score fall outside the confidence interval around the estimated true score for T2?

    • If so, it represents change that exceeds the base rate expected based on measurement error, regression to the mean, and practice

      • Thus, clinically meaningful change has occurred

    • If not, then the change is consistent with the base rate expected based on measurement error, practice, and regression to the mean

      • Thus, no clinically meaningful change has occurred


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Standardized Regression Based Change Scores--An Example

  • Basso, Carona, Lowery, & Axelrod (2002)

    • WAIS-III re-tested in a group of control subjects over a 3-6 month interval

    • FSIQ

      • Test-Retest Reliability=.90

      • T1 Mean T1=109.4 (11.6)

      • T2 Mean T2=115.0 (12.1)

      • SEpred=SDY2((1-rY1Y22)1/2)

        • SEpred=(12.1((1-.902) 1/2))=5.29

        • 95% CI: (SEdiff)*1.96=10.36

        • Mean Diff=5.60

          • The mean difference fails to exceed the 95% CI

          • No individual had a score exceeding the 95% CI

        • To apply the SRB, the T2 True Score is estimated

          • If the obtained score falls within the CI around the T2 True score, then no clinically meaningful change has occurred


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Standardized Regression Based Change Scores--An Example

  • Basso, Carona, Lowery, & Axelrod (2002)

    • An example application:

    • T1 obtained score=104

    • T2 obtained score=116

    • Estimated True T2 Score

      • YTrue=M+((rY1Y2)(Y1-M))

      • YTrue=100+(.90)(104-100)=103.6

      • 116 exceeds 10.36 points from 103.6

      • Thus, meaningful change has occurred


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Standardized Regression Based Change Scores--An Example

  • Basso, Carona, Lowery, & Axelrod (2002)

    • An example application:

    • T1 obtained score=103

    • T2 obtained score=106

    • Estimated True T2 Score

      • YTrue=M+((rY1Y2)(Y1-M))

      • YTrue=100+(.90)(106-100)=105.4

      • 105 falls within 10.36 points of 106

      • Thus, no meaningful change has occurred


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Questions?


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