Cognitive Decline Slope
Fit longitudinal cognitive score change after caller-supplied visit-specific practice offsets; score direction and diagnostic interpretation are not assumed.
Description
Repeated cognitive scores can be adjusted for expected practice effects before estimating a longitudinal trend.
Repeated cognitive scores can be adjusted for expected practice effects before estimating a longitudinal trend. The slope retains the units of score change per year.
The tool returns adjustedScores (adjusted scores); changePerYear (change per year); interceptScore (intercept score); fitRSquared (fit r squared). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Cognitive Decline Slope
Use Cognitive Decline Slope when you already have elapsedYears, scores, expectedPracticeOffsets and want adjustedScores, changePerYear, interceptScore, fitRSquared. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Cognitive Decline Slope and understand its results
- Enter elapsedYears, scores, expectedPracticeOffsets using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read adjustedScores, changePerYear, interceptScore, fitRSquared. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| elapsedYears | Elapsed years | list of number | Required |
| scores | Scores | list of number | Required |
| expectedPracticeOffsets | Expected practice offsets | list of number | Required |
Use strictly increasing elapsed years and aligned score and practice-offset lists. Fit ordinary least squares with an intercept and return R².
adjustedScore = score−practiceOffset; adjustedScore ≈ intercept+slope×years The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"elapsedYears": [
0,
1,
2
],
"scores": [
20,
18,
16
],
"expectedPracticeOffsets": [
0,
1,
1
]
},
"output": {
"adjustedScores": [
20,
17,
15
],
"changePerYear": -2.5,
"interceptScore": 19.833333333333332,
"fitRSquared": 0.9868421052631579
}
}Limitations and assumptions
The practice offsets are supplied, not inferred. Score direction determines whether a positive or negative slope indicates worsening.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Reliable Change Index: Compute a practice-adjusted Jacobson–Truax reliable-change index from caller norms and criterion; not a diagnosis or a universal improvement cutoff. Ebbinghaus Forgetting Curve: Evaluate a caller-calibrated exponential forgetting approximation with a nonzero floor; elapsed times and tau share one unit, and this is not a universal Ebbinghaus law.
Methodological background: Least squares estimation.1
References
-
Least squares estimation — NIST/SEMATECH
Similar or alternative tools
- Reliable Change Index
Compute a practice-adjusted Jacobson–Truax reliable-change index from caller norms and criterion; not a diagnosis or a universal improvement cutoff.
- Ebbinghaus Forgetting Curve
Evaluate a caller-calibrated exponential forgetting approximation with a nonzero floor; elapsed times and tau share one unit, and this is not a universal Ebbinghaus law.