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- Grönkvist, Rode, et al.
(författare)
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Measurement error, minimal detectable change, and minimal clinically important difference of the Short Form-36 Health Survey, Hospital Anxiety and Depression Scale, and Pain Numeric Rating Scale in patients with chronic pain
- 2024
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Ingår i: Journal of Pain. - 1526-5900 .- 1528-8447.
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Tidskriftsartikel (refereegranskat)abstract
- In both pain research and clinical practice, patient-reported outcome measures are used to assess dimensions of health. Interpreting these instruments requires understanding their measurement error and what magnitude of change has subjective importance for patients. This study estimated the standard error of measurement (SEM), one-year minimal detectable change, and one-year minimal clinically important difference (MCID) for the Short Form-36 Health Survey physical component summary (SF-36 PCS) and mental (SF36 MCS), the Hospital Anxiety and Depression Scale anxiety symptoms (HADS-A) and depression symptoms (HADS-D) subscales, and the Numeric Rating Scale (NRS) for past-week average pain intensity. MCIDs for these instruments have not previously been estimated in a large sample of chronic pain patients participating in interdisciplinary pain rehabilitation. Data were drawn from the Swedish Quality Registry for Pain Rehabilitation (n=8854 patients). MCID was estimated as average change and change difference, based on three different anchors. MCID estimates were 2.62-4.69 for SF-36 PCS, 4.46-6.79 for SF-36 MCS, 0.895-1.48 for NRS, 1.17-2.13 for HADS-A, and 1.48-2.54 for HADS-D. The common assumption of an identical SEM for pre- and post-treatment measurements was not always applicable. When estimating MCID, researchers should select an estimation method and anchor aligned with the study's context and objectives.PERSPECTIVE: This article presents estimates of minimal clinically important difference and minimal detectable change for several commonly used patient-reported outcome measures among patients with chronic pain. These estimates can help clinicians and researchers to determine when a measured health improvement is subjectively important to the patient and greater than measurement error.DATA AVAILABILITY: Data Availability Statement: The data utilized in this study are not available due to ethical considerations and the need for appropriate ethical approval.
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| 2. |
- Grönkvist, Rode, et al.
(författare)
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Subalgebras in K[x] of small codimension
- 2022
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Ingår i: Applicable Algebra in Engineering, Communications and Computing. - : Springer Science and Business Media LLC. - 0938-1279 .- 1432-0622. ; 33:6, s. 751-789
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the concept of subalgebra spectrum, Sp(A), for a subalgebra A of finite codimension in K[x]. The spectrum is a finite subset of the underlying field. We also introduce a tool, the characteristic polynomial of A, which has the spectrum as its set of zeroes. The characteristic polynomial can be computed from the generators of A, thus allowing us to find the spectrum of an algebra given by generators. We proceed by using the spectrum to get descriptions of subalgebras of finite codimension. More precisely we show that A can be described by a set of conditions that each is either of the type f(α) = f(β) for α, β in Sp(A) or of the type stating that some linear combination of derivatives of different orders evaluated in elements of Sp(A) equals zero. We use these types of conditions to, by an inductive process, find explicit descriptions of subalgebras of codimension up to three. These descriptions also include SAGBI bases for each family of subalgebras.
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