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Modeling Change in Health Status: Patterns over Time

Susan J. Henly, PhD, RNMethods DirectorMinnesota Center for Health Trajectory Research

Seminar: September 24, 2008

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Post-Op Day

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Pain at bedtime over the 1st post-op week

Busch, S.E. (2002). Sleep patterns following an out-patient surgical procedure. Unpublished MS thesis. Busch, S.E. (2002). Sleep patterns following an out-patient surgical procedure. Unpublished MS thesis. University of Minnesota, Minneapolis. University of Minnesota, Minneapolis.

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

Some ideas about change

To be or cause to be different

To alter the course of

Naturalistic change

Experimentally induced change

Operationalizing change

Increment: difference on 2 occasions

Rate: speed, velocity, pace

Pattern: form, shape, model

Changing ideas about studying change

Health as a function of time

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

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

The general function

Time ► Function ► Health

Hi = fi (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.

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

Hi (t): key features

Functions describing change of many kinds

Function Rule Parameters

Constant H (t) = κ κ

Linear H (t) = π0 + π1t π0 , π1

Quadratic H (t) = π0 + π1t + π2t2 π0 , π1 , π2

Polynomial H (t) = πntn + πn-1tn-1+ … + π1t + π0 π0 to πn

Exponential H (t) = α + (ξ – α) exp (ρt) α, ξ, ρ

Sine H (t) = α sin (ωt + θ) + δ α, ω , θ, δ

Piece-wise H (t) = H1 (t), t < tt,

H (t) = H2 (t), t ≥ tt,

Parameters of

H1 and H2

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Change functions

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Constant

Linear

Quadratic

Polynomial

Exponential

Sine

Piece-wise

Constant functions: Hi (t) = κi

i κi t Hi (t)

1 -.5 -3 -.5

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For person i, κi gives the function value at every time t

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Constant functions Hi (t) = κi

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Linear functions: Hi (t) = π0i + π1i t

i π0i π1i t Hi (t)

1 1.21 .18 -5 0.36

0 1.21

8 2.58

2 1.48 .45 0 1.48

1 1.93

8 5.13

3 4.01 .27 -2 3.48

1 4.28

2 4.55

For person i, π0i gives the function value at t0 (intercept) and π1i gives the rate of change over time (slope). Note that selection of t0 is critical to scientific interpretation of the parameters.

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Linear functionsHi (t) = π0i + π1it

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Quadratic and higher order polynomial functions

General polynomial form is:

H (t) = πntn + πn-1tn-1+ … + π1t + π0

Quadratic:

H (t) = π2t2 + π1t + π0

Cubic:

H (t) = π3t3 + π2t2+ π1t + π0

And so on with higher order functions of time

Polynomial Equation Grapherhttp://www.math.umn.edu/~garrett/qy/Quintic.html

Exponential functions

Exploring sine functions for periodic change

Variations on the Sine Function

The website is:

http://www.analyzemath.com/trigonometry/sine.htm

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For person i, κi gives the baseline value, π0i gives the function value at the transition point, which is also the intercept in the example and π1i 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)H1i (t) = κi, t < 0H2i (t) = π0i + π1it, t ≥ 0

i κi π0i π1i t Hi (t)

1 3.91 3.91 .30 -1 3.91

2 4.52

4 5.14

2 5.02 5.02 .37 -2 5.02

0 5.02

5 6.88

3 3.54 3.54 .31 0 3.54

3 4.47

7 5.70

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Piece-wise functions (ex)H1i (t) = κi, t < 0H2i (t) = π0i + π1it, t ≥ 0

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Time

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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

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

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

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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

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Heart soft-touch project

Heart soft-touch outcomes: pain/tension mean comparisons

POD SC AIT t p

1 Mean 3.5 2.4 -2.52 .01

SD 2.6 1.9

2 Mean 2.1 1.3 -2.10 .04

SD 2.0 1.3

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Heart soft-touch outcomes: ITV vs SC

Measurement Time

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Condition

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Heart soft-touch outcomes

SC vs AIT Standard Care Integrative Therapies

Measurement Time

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Time of Observation

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Heart soft-touch outcomes

ITP vs SC SC

Measurement Time

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Time of Observation

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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.

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Person

Environment

NursingHealth

TIME

Time for change in the nursing metaparadigm