Predicting change in symptoms and function in patients with persistent shoulder pain: a prognostic model development study

Background Persistent shoulder pain causes considerable disruption of the individual’s life and imposes high costs on healthcare and society. Well-informed treatment and referral pathways are crucial as unsuccessful interventions and longer duration of symptoms minimizes the likelihood of success in future interventions. Although physiotherapy is generally recommended as first line treatment, no prognostic model or clinical prediction rules exists to help guide the treatment of patients with persistent shoulder pain undergoing physiotherapy. Thus, the objective of this study was to develop a prognostic model to inform clinical decision making and predict change in symptoms and function in patients with persistent shoulder pain. Methods This was a prospective cohort study of 243 patients with persistent shoulder pain referred to outpatient physiotherapy rehabilitation centres. Data was collected at baseline and six-month follow-up. The outcome was change in shoulder symptoms and function as measured by the shortened version of the Disabilities of the Arm, Shoulder and Hand questionnaire (QuickDASH) from baseline to 6 months follow up. Potential predictors were included in a multivariable linear regression model which was pruned using modified stepwise backwards elimination. Results The final model consisted of seven predictors; baseline QuickDASH score, employment status, educational level, movement impairment classification, self-rated ability to cope with the pain, health-related quality of life and pain catastrophizing. Together these variables explained 33% of the variance in QuickDASH-change scores with a model root mean squared error of 17 points. Conclusion The final prediction model explained 33% of the variance in QuickDASH change-scores at 6 months. The root mean squared error (model SD) was relatively large meaning that the prediction of individual change scores was quite imprecise. Thus, the clinical utility of the prediction model is limited in its current form. Further work needs be done in order to improve the performance and precision of the model before external validity can be examined along with the potential impact of the model in clinical practice. Two of the included predictors were novel and could be examined in future studies; movement impairment classification based on diagnosis and health-related quality of life. Supplementary Information The online version contains supplementary material available at 10.1186/s12891-021-04612-y.

The aim of this appendix is to report all steps in the development process of the prognostic model to clarify how variables were eliminated and on what basis. We wanted a model suitable for clinical practice and believe that it should not be too comprehensive since this will result in too high a time consumption and burden for both the patient and the clinician.
Therefore, a "full model" including all relevant measured variables was pruned using a modified stepwise backwards elimination. The development process is shown below. The full model, from which backwards eliminations was performed, was deemed in line with the assumptions of multiple linear regression and had the following parameter estimates:  (1)). It was checked whether the presumed interrelated variables were correlated using Spearman´s correlation, since high correlations indicate that one of the variables does not add much to the prediction (2). For a variable to be eliminated, it could not lead to a drop in the adjusted coefficient of determination (adjusted R 2 ). This step was chosen before conventional backwards elimination since the candidate predictors were not specifically collected for prognostic modelling.
2. When no more presumptions were present, standardized coefficients, correlations and p-values were used to indicate the next variables to be eliminated(3). Deletion of a variable could not lead to a drop in the adjusted R 2 (drops under 0.5% were however allowed).
The following was presumed: 1. In the EQ5D, the patients are asked questions regarding pain, function and anxiety/depression. Therefore it was presumed that health-related quality of life (EQ5D) could explain changes in QuickDASH for both pain (NRPS) and mental wellbeing (WHO-5) (more pain and lower mental wellbeing leading to lower healthrelated quality of life)(4).
2. Pain catastrophizing is characterized by the tendency to magnify the threat value of pain and to feel helpless in the context of pain and by a relative inability to inhibit pain-related thoughts in anticipation of, during or following pain (5). Therefore, it was presumed that people with higher levels of pain catastrophizing would see their shoulder pain as more likely to become persistent.
3. It was presumed that self-rated ability to cope with the shoulder pain would be contained in or strongly connected to pain catastrophizing (from the characterization of pain catastrophizing: "..to feel helpless in the context of pain..")(5, 6).
4. It was presumed that fear avoidance was connected to pain catastrophizing and selfrated ability to cope with the pain since pain catastrophizing and a feeling of not being able to cope with the pain, could lead to fear avoidance (6).

Steps in the elimination:
Elimination was performed from the previous step (e.g. elimination in step two was performed on the model advancing from step one).
1. Presumption 1: There was a high correlation between health-related quality of life and mental wellbeing (0.62) and a high negative correlation between health-related quality of life and pain (-0.55), supporting the presumption. Firstly, mental wellbeing was eliminated from the model, leading to a higher adjusted R 2 . Then pain was eliminated, leading to a further rise in the adjusted R 2 . A model with both pain and mental wellbeing instead of health-related quality of life was examined to assess whether this would lead to a higher adjusted R 2 than the model with health-related quality of life. However, this led to an adjusted R 2 close to that of the baseline model= 30.8%.

Eliminated in step 1: mental wellbeing and pain (adjusted R 2 = 31.8%)
2. Presumption 2: There was a correlation between the two variables of 0.55, supporting the presumption. Self-rated risk of persistent symptoms was eliminated, resulting in a rise in adjusted R 2 . Eliminating pain catastrophizing instead, would lead to a high drop in adjusted R 2 .
Eliminated in step 2: Self-rated risk of persistent symptoms ( adjusted R 2 = 32.2%) 3. Presumption 3: Self-rated ability to cope with the pain was moderately negatively correlated with pain catastrophizing (-0.43). Self-rated ability to cope with the pain was eliminated, but this led to a drop in adjusted R 2 . Therefore, self-rated ability to cope with the pain was kept in the model. Eliminating pain catastrophizing instead would lead to a higher drop in adjusted R 2 .

Eliminated in step 3: None
4. Presumption 4: Fear avoidance was eliminated, leading to a rise in adjusted R 2 .
Eliminating pain catastrophizing or self-rated ability to cope with the pain instead of fear avoidance led to a drop in adjusted R 2 . Fear avoidance was only correlated with pain catastrophizing by 0.42 and with self-rated ability to cope with the pain by -0.18, which did not support the presumption. However, fear avoidance was correlated with baseline QuickDASH by 0.57 and health-related quality of life by -0.48, which might explain why it could be deleted without loss in the adjusted R 2 . The final model was also deemed to fulfil the assumptions of multiple linear regression. The parameter estimates are shown in Table S3.