1. 1 Modeling Change in Health Status: Patterns over Time Susan J. Henly, PhD, RN Methods Director Minnesota Center for Health Trajectory Research Seminar: September 24, 2008

2. 2 Pain at bedtime over the 1 st post-op week Busch, S.E. (2002). Sleep patterns following an out-patient surgical procedure. Unpublished MS thesis. University of Minnesota, Minneapolis.

3. Why study change in health status? Within persons, health status varies over time Accurate description of health status over time is essential to understanding health behaviors and illness responses Intervention assumes that health status is malleable-- intra-individual change can be predicted and “controlled” (influenced by nursing actions) Inter-individual differences in intra-individual change can be explained

4. Some ideas about change To be or cause to be different To alter the course of Naturalistic change Experimentally induced change

5. Operationalizing change Increment: difference on 2 occasions Rate: speed, velocity, pace Pattern: form, shape, model

6. Changing ideas about studying change

7. Health as a function of time

8. Purpose Describe mathematical functions that can be used to model change in health status Characterize intra-individual change using personalized functions Recognize that variation in parameters of personalized functions represents inter-individual differences in change Comment on formulation of hypotheses to explain inter- individual differences in change using parameters of personalized functions

9. About functions A function is a rule that maps every point in a defined domain t with one and only one value in its range H Function rules are defined by their parameters Functions can be described using equations Functions can be displayed in tables Functions can be depicted by their graphs

10. The general function Time►Function►Health H i = f i (t) For each person, at each point in time, for any given indicator of health status, there is one and only one value for health status.

11. Time is the primary “predictor” variable Health status is “outcome” Health as a function of time shows patterns of change Each person follows their own pattern: everyone has their own set of parameters H i (t): key features

12. Functions describing change of many kinds FunctionRuleParameters ConstantH (t) = κκ LinearH (t) = π 0 + π 1 tπ 0, π 1 QuadraticH (t) = π 0 + π 1 t + π 2 t 2 π 0, π 1, π 2 Polynomial H (t) = π n t n + π n-1 t n-1 + … + π 1 t + π 0 π 0 to π n ExponentialH (t) = α + (ξ – α) exp (ρt)α, ξ, ρ SineH (t) = α sin (ωt + θ) + δα, ω, θ, δ Piece-wiseH (t) = H 1 (t), t < t t, H (t) = H 2 (t), t ≥ t t, Parameters of H 1 and H 2

13. 13 Change functions

14. Constant functions: H i (t) = κ i iκiκi tH i (t) 1-.5-3-.5 0 4 25-25 05 65 38-48 8 08 For person i, κ i gives the function value at every time t

15. 15 Constant functions H i (t) = κ i

16. 16 Linear functions: H i (t) = π 0i + π 1i t iπ 0i π 1i tH i (t) 11.21.18-50.36 01.21 82.58 21.48.4501.48 11.93 85.13 34.01.27-23.48 14.28 24.55 For person i, π 0i gives the function value at t 0 (intercept) and π 1i gives the rate of change over time (slope). Note that selection of t 0 is critical to scientific interpretation of the parameters.

17. 17 Linear functions H i (t) = π 0i + π 1i t

18. Quadratic and higher order polynomial functions General polynomial form is: H (t) = π n t n + π n-1 t n-1 + … + π 1 t + π 0 Quadratic: H (t) = π 2 t 2 + π 1 t + π 0 Cubic: H (t) = π 3 t 3 + π 2 t 2 + π 1 t + π 0 And so on with higher order functions of time Polynomial Equation Grapher http://www.math.umn.edu/~garrett/qy/Quintic.html

19. Exponential functions

20. Exploring sine functions for periodic change Variations on the Sine Function The website is: http://www.analyzemath.com/trigonometry/sine.htm

21. 21 For person i, κ i gives the baseline value, π 0i gives the function value at the transition point, which is also the intercept in the example and π 1i gives the rate of change over time (slope) after the transition. In this example, the time of transition is known. Sometimes, the transition point is itself a parameter to be estimated. Piece-wise functions (ex) H 1i (t) = κ i, t < 0 H 2i (t) = π 0i + π 1i t, t ≥ 0 iκiκi π 0i π 1i tH i (t) 13.91.303.91 24.52 45.14 25.02.37-25.02 0 56.88 33.54.3103.54 34.47 75.70

22. 22 Piece-wise functions (ex) H 1i (t) = κ i, t < 0 H 2i (t) = π 0i + π 1i t, t ≥ 0

23. Statistical models for individual change Longitudinal data on 3 or more occasions Sensible metric for time Theory about change Graphs of individual cases to identify form of change Personal parameters estimated to produce smoothed curves for each persons change pattern Random coefficients in a mixed effects model

24. 24 Linear change: variation around the least squares fit line for 3 example persons

25. 25 Piece-wise change: variation around the least squares fit line for 3 example persons

26. Theory about change Longitudinal ( ≥ 3 occasions of observation) Measurement sensitive to individual change Statistical models linking intra- and inter-individual change (mixed effects models) Describing and explaining patterns of change

27. 27 Heart soft-touch project

28. Heart soft-touch outcomes: pain/tension mean comparisons PODSCAITtp 1Mean3.52.4-2.52.01 SD2.61.9 2Mean2.11.3-2.10.04 SD2.01.3

29. 29 Heart soft-touch outcomes: ITV vs SC

30. 30 Heart soft-touch outcomes SC vs AITStandard CareIntegrative Therapies

31. 31 Heart soft-touch outcomes ITP vs SC SC ITP

32. Nursing practice: people and change Baby is off to a healthy start. Patient is going downhill fast. She recovered quickly after the nurse lifted her spirits. He had a rocky post-op course. When he exercised regularly, his glucose levels decreased and stabilized. She reacted to her husband’s death with an intense sense of depression, but soon returned to her usual sunny self.

33. 33 Person Environ ment Nursing Health TIME Time for change in the nursing metaparadigm