Development and validation of a prediction model for self-reported mobility decline in community-dwelling older adults

Objectives: The aim of this study is to develop and validate two models to predict 2-year risk of self-reported mobility decline among community-dwelling older adults. Study Design and Setting: We used data from a prospective cohort study of people aged 65 years and over in England. Mobility status was assessed using the EQ-5D-5L mobility question. The models were based on the outcome: Model 1, any mobility decline at 2 years; Model 2, new onset of persistent mobility problems over 2 years. Least absolute shrinkage and selection operator logistic regression was used to select predictors. Model performance was assessed using C-statistics, calibration plot, Brier scores, and decision curve analyses. Models were internally validated using bootstrapping. Results: Over 18% of participants who could walk reported mobility decline at year 2 (Model 1), and 7.1% with no mobility problems at baseline, reported new onset of mobility problems after 2 years (Model 2). Thirteen and 6 out of 31 variables were selected as predictors in Models 1 and 2, respectively. Models 1 and 2 had a C-statistic of 0.740


Introduction
In later life, declining mobility is an early predictor of dependence [1], poor quality of life, increased health care use, and death [2e5]. Generally, mobility limitations increase with age and affect more women than men. Prospective studies identify socioeconomic status, lifestyle habits, physiological and psychological factors, health conditions, social networks and participation, environmental, and organizational/policy factors [6,7] as risk factors for mobility decline.
These factors may be measured using self-reported or objective measures. Objective measures are recommended in the evaluation of an individual's functional status, but are time-consuming and, therefore, difficult to implement in routine primary care. Self-reported measures have low response burden, can capture both current and historical information, and can assess psychological and social factors.
Prediction models estimate absolute risk of a particular outcome for individual people [8,9].
Models to predict mobility decline over a short time period ( 5 years) are scarce [10e12]. Most studies used small sample sizes, were developed using data collected many decades ago, and have methodological limitations, such as the absence of key model performance measures, selection of predictor variables based on univariable analyses, and absence of multivariable analyses [7].
An accurate and user-friendly model to predict mobility decline in older adults could identify higher risk people in the community setting, enabling better targeting of rehabilitation and other interventions in clinical practice. We wanted to examine whether easy to collect self-reported measures of health and mobility could be used for this purpose.
The aim of this study is to develop and internally validate two risk prediction models for predicting the 2-year risk of mobility decline, using a cohort of older adults aged 65e100 years recruited in a community-based study in England.

Materials and methods
We followed the TRIPOD (Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis) guidelines to report the development and validation of the prediction models [13,14].

Study design
We used data from the Oxford Pain, Activity and Lifestyle (OPAL) study which is a prospective cohort study of older people living in England. Full details of the cohort protocol and baseline characteristics are provided elsewhere [15]. Briefly, eligible individuals were identified from electronic record searches of 35 general practice lists across England and randomly selected from two age bands (65e74 and 75 years and over). Exclusion criteria were living in residential care or nursing home, terminal illness with life expectancy !6 months, severe health/social concerns sufficient to preclude approach, or unable to provide informed consent.

Cohort study population
Between October 2016 and March 2018, a sample of up to 400 patients from each participating practice were invited to take part in the cohort study (a total of 12,839 individuals) and 5,409 (42.1%) agreed to participate. After completion of the baseline questionnaire, follow-up data were collected by post annually for 2 years.

Baseline candidate predictors
The list of candidate predictors and how they were defined are described in Table 1 and Appendix 2. We identified 31 candidate predictors based on a recent systematic literature [7] and expert opinion.

Outcomes
We used the mobility question from the EuroQol fivedimensional questionnaire (EQ-5D-5L) [16] to identify participants with mobility decline. Participants rated their mobility status as no problems, slight, moderate, severe problems, and unable to walk. All participants who were able to walk at baseline, regardless of their ability, were included (n 5 5,358/ 5,409; 99%). Mobility decline was calculated by subtracting mobility score at 2 years from baseline scores and classifying participants using a binary outcome [no mobility decline (0) vs. mobility decline (1)].

Key findings
We have derived and internally validated two easyto-use prediction models that quantify absolute risk of mobility decline in community-dwelling older people aged 65 years and over.
Both models demonstrated moderate to good prediction to identify individuals at risk of mobility decline over a 2-year period.
What does this add to what is already known? These models are the first prediction models for self-reported mobility decline in a communitydwelling older adults in England.

What is the implication, what should change now?
Our prediction models provide health care professionals with a small set of easy to collect variables that appear to discriminate well in the prediction of mobility decline in older adults living in the community.
After appropriate external validation, these models may be useful in informing clinical decisionmaking about the need for rehabilitation to prevent mobility decline and maintain independence in older age. People with no mobility problems at baseline were eligible (n 5 3,193/5,409; 59%). New onset of persistent mobility problems over 2 years was defined as having any problems in mobility at both 1 and 2 years from baseline.

Sample size
The minimum sample size was based on Riley et al. [17]. The prevalence of mobility decline at 2 years (Model 1) was 18.6%. Based on a conservative Nagelkerke's Rsquared of 0.15 [17] and a prespecified maximum number of predictor parameters of 50, the minimum sample size required to develop the model to minimize overfitting was estimated to be 4,585, with 853 events.

Statistical analysis
Nonlinearity between continuous predictors and the outcome was examined using fractional polynomials before multivariable modeling.
Missing data were imputed using multiple imputation by chained equation technique [18,19] (Appendix 3). Fifty imputed datasets were created. We included all candidate predictors and the outcome variable in the imputation model. To impute for sample attrition (Table 1b/Appendix  1), we included ethnicity, smoking status, place of residence, and cognitive function.
To minimize the risk of overfitting we applied a penalized approach, the least absolute shrinkage and selection operator (LASSO) [20], and forced the inclusion of mobility status at baseline in Model 1. Logistic regression using the LASSO was applied on each imputed dataset separately. The tuning parameter l value for the prediction model was chosen from a grid of 100 l values through 10fold repeated cross-validation [21]. The l that had the average mean-squared error within one standard error from the minimum error was chosen. Predictors selected in 80% of the imputed datasets were retained. Average regression coefficient estimates over all imputed datasets of the variables retained were calculated to obtain the final model.
Model performance was assessed by calculating discrimination, calibration, decision curve analysis (DCA), and overall performance [9,22,23]. Discrimination, assessed by the C-statistic, is the ability of the prediction model to differentiate between those who report mobility decline and do not report decline. Calibrationdhow closely predicted risk corresponds with observed riskdwas assessed visually using calibration plots. DCA determines the clinical validity of the prediction model by measuring the net benefit over a range of different threshold probabilities. As the risk threshold probability increases, the costebenefit ratio increases accordingly [23]. Brier score quantifies how close predictions are to the observed data. Scores range from 0 to 1, with 0 representing perfect concordance between predicted and observed values. The model performance (C-statistic and Brier score) was evaluated on each multiple imputation (MI) dataset and median and range was reported [24]. DCA was assessed using the first MI dataset.
For internal validation 200 bootstrap samples were drawn with replacement from the first MI dataset, with the same size [25]. In each bootstrap sample, we repeated the entire modeling process, estimating the C-statistic in each bootstrap sample and then assessed the performance of each model in the first MI dataset. Optimism was estimated as the mean of the difference between the C-statistic of the bootstrap sample and that of the first MI sample. Optimism-corrected C-statistic was calculated as follows: C-statistic of the model developed in the first MI dataset À optimism.
To allow translation to clinical settings, we designed a simple scoring system based on procedures described by Sullivan et al. [26]. Penalized regression coefficients of the model were used to assign integer points to each level of each predictor. These score points were summed to derive a total risk score for each participant.
All analyses were carried out using STATA 16.1 and R 4.1.2. We used STATA for MI and R for model development, model performance, and internal validation [9].

Missing data among eligible individuals
Of the 5,358 eligible individuals who could walk at baseline (Model 1), 18.7% (n 5 1,001) had one or more missing values for the candidate predictors. For most candidate predictors, the proportion of missing data was !5% (Table 2/Appendix 3).
The absolute change was calculated as the mobility score at year 2 minus the score at baseline (negative values indicate worse change in mobility status and positive values indicate improvement in mobility status). The upper panel represents participants who could walk at baseline and the lower panel represents participants who stratify by mobility status at baseline.

Selection of predictor variables and model fitting.
In addition to mobility status at baseline, 13 variables were identified as predictors of mobility decline at 2 years in !80% of the MI datasets ( Table 2, Model 1).
Older participants and those who perceived their income to be inadequate were more likely to report mobility decline at 2 years (Table 2, Model 1). Participants who reported a slow usual walking pace had difficulty maintaining their balance, had low confidence to walk long distances, rated their walking as worse compared to last year and reported sometimes using a walking aid outside, and were more likely to report a decline in mobility after 2 years. Lower limb pain and the presence of severe general pain or discomfort were also predictors of mobility decline. Other health-related factors associated with decline in mobility at 2 years were having a higher body mass index, greater number of health conditions, problems in daily life due to physical tiredness, and poor general health (Table 2).   (1) Self-reported general health, continuous: range 0 (poor) to 100 (good) Abbreviations: BMI, body mass index; BP, back pain; EQ-5D-5L, EuroQol five-dimensional questionnaire.

Model performance.
Model 1 revealed a median C-statistic of 0.740 (range: 0.737e0.743) and the median Brier score was 0.136 (range: 0.135e0.137). The model showed good calibration: 95% confidence interval bars and some of the mean values (data points) intersect with the 45 line that indicates perfect agreement between the predicted and observed values of mobility decline at 2 years ( Fig. 1/Appendix 4).
The DCA plot showed (Fig. 3A, Model 1) a clear net benefit gain of the prediction model over the entire range of selected thresholds (0e50%).
The optimism-corrected C-statistic estimate was 0.734 (optimism 5 0.010). The model's performance on internal validation showed only a slight reduction in the C-statistic, indicating low overfitting.
The y-axis shows the net benefit of Model 1 (A) and Model 2 (B). The x-axis of DCA is the threshold of the predicted probability using Model 1 (A) and Model 2 (B) to classify individuals with and without mobility decline. The DCA compares the net benefits of an intervention in three scenarios: intervention for all individuals regardless of prediction (black solid line), intervention for no individuals (black dotted line, horizontal line), and intervention for individuals based on the prediction models (black dashed line); Model 1: 2-year risk of mobility decline; Model 2: 2-year risk of new-onset persistent mobility problems. Models included predictors that selected at least 80% of the imputed datasets.

Point scoring system.
The point scoring system for Model 1 had a score range from 0 to 39 with predicted risks corresponding to each point score ranging from 0.9% (0 points) to 90.1% (39 points) (Tables 1 and 2/Appendix 5). The median C-statistic of this scoring system was 0.734 (range: 0.730e0.735),  Participants with no mobility problems at baseline who were alive at 2 years of follow-up were included (n 5 3,146) (Fig. 1). The mean age (standard deviation) was 73.3 (5.8) years, 51.0% (1,604/3,146) were women, and 7.1% (n 5 201/2,832) had new onset of persistent mobility problems.

Selection of predictor variables and model fitting.
In total, 28 variables (42 parameters) were included in this analysis. Six variables were selected as predictors of new-onset persistent mobility decline (Table 2, Model 2). These were slow usual walking pace, difficulty maintaining balance, low confidence to walk long distances and worse walking ability compared to last year, and two health- related factors (greater number of health conditions and poor general health assessed by EuroQol Visual Analog Scale (EQ-VAS)).

Model performance.
The median C-statistic was 0.765 (range: 0.762e0.768). The median Brier score was 0.069 (range: 0.068e0.070). Model calibration was good, with close agreement between predicted and observed values of new onset of persistent mobility problems (Fig. 2/Appendix 4). Fig. 3B (Model 2) displays the net benefit curves equation. The net benefit clinical decision-making is superior across the range of risk thresholds of roughly 8e40%.
The average optimism of the C-statistic estimate was 0.013.

Point scoring system.
The point scoring systems is given in Tables 3 and 4/ Appendix 5. The final score ranged from 0 to 22 with predicted risks corresponding to each point score ranging from 4.5% (0 points) to 53.8% (22 points). The model showed good predictive validity, with median C-statistic of 0.754 (range: 0.750e0.757).

Discussion
We developed and internally validated two prediction models for self-reported mobility decline in communitydwelling older adults aged 65 years and over, using selfreported measures of health and mobility measures that are easy to collect and could be used in clinical practice. Both models demonstrated moderate to good prediction capacity to identify individuals at 2-year risk of mobility decline. Model calibration showed good agreement between the observed and predicted mobility change. Both models also showed greater net benefit across a range of thresholds compared with not using any model.
Many of the variables identified as important predictors in both our models were associated with mobility decline in a recent systematic literature we conducted to inform this work [7], supporting the plausibility of this model. We found evidence that older age, perceived inadequacy of income, preclinical mobility modifications (ie, use of walking aid, change in walking ability), lower limb pain, comorbidities [with diabetes and arthritis the most important individual conditions in our study (data not shown)], physical tiredness, and self-reported general health are predictors of mobility decline. The evidence for balance difficulties, general pain/discomfort severity, and body mass index was previously limited or unclear, but our findings confirm these as predictors of mobility decline [7].
Self-reported predictors newly identified by this study include confidence to walk half a mile and self-reported speed of usual walking pace. Self-reported slow, or very slow, usual walking pace at baseline was one of the most important predictors of mobility decline in this study, and has previously been validated as a marker of measured walking speed [27].
Unlike some previous studies, we did not find widespread pain to predict mobility decline [28,29]. Discrepancies may be due to the following reasons: differences in the way predictors and outcome were measured; the different sets of predictors/confounders included in the model; and/or those studies that did not consider severity of pain as an independent variable in their models.
Studies developing prediction models for the onset of mobility problems over a short period of time (less than 5 years of follow-up) are scarce [10e12]. Only one of the three previous models was developed and internally validated for onset of mobility difficulty after 18 months of follow-up [11]. This study was based on high physically and cognitively functioning women, aged 70e80 years, in the United States. Both models included self-reported preclinical mobility limitations; however, our model (Model 2) had better performance and is simpler to implement because it is based on self-reported variables only. In a different model, Papachristou et al. included age, slow walking speed, physically inactivity, and exhaustion as predictors. The C-statistic of their model was smaller (C-statistic 5 0.68), and measures of calibration were not assessed. Reynolds and Silverstein constructed a prediction model for onset of walking among community-dwelling adults aged 70 years and older. They reported a C-statistic 5 0.82, for their full model including 42 baseline and timedependent predictors but did not report the statistic for their abbreviated clinical model. None of the previous studies have used rigorous internal validation.
Our prediction models provide health care professionals with a small set of easy to collect variables that discriminate well in the prediction of mobility decline in older men and women living in the community. The number and format of variables in the risk prediction model, mean that it could be used during a routine clinical consultation. Some of these variables are also modifiable and can effectively be targeted through rehabilitation. First, there are several variables that are markers of reduced walking ability and balance. These include slow walking pace, reduced confidence to walk longer distance, and difficulty maintaining balance. We, and others, have demonstrated that walking ability can be improved through a progressive tailored rehabilitation program that targets walking confidence, walking ability (distance and speed), muscle strength, and balance [30,31]. Second, lower limb pain, such as that arising from hip and knee osteoarthritis, is common in older adults and can be effectively managed through rehabilitation incorporating pain self-management, coping strategies, and exercise, as well as surgery [32]. General bodily pain severity was also a predictor suggesting that pain management should be considered more broadly (not just for lower limb pain) as it is often not prioritized against a backdrop of other health conditions by older people themselves [33] or by health professionals [34].

Strengths and limitations
The OPAL cohort study represents a large, representative prospective cohort study with baseline characteristics similar to those in general English population of the same age [15]. This study reports the first prediction model for self-reported mobility decline in a community-dwelling older adults in England. A wide range of predictors were used. The reproducibility of the model was ensured by using MI and penalized regression methods, so that only significant predictors were selected, and anomalous predictors were rejected, reducing the risk of overfitting.
There are several potential limitations to this study. Selfreported mobility variables can be criticized because of subjectivity, but they provide important information about the difficulties people perceive in their everyday environment, can incorporate time-varying estimations such as frequency of balance problems, and are thus clinically highly relevant. Selfreported predictors may be particularly useful in clinical settings face to face or by telephone, or postal follow-up of cohort study participants when more-intense testing is impractical because of time, cost, space, or venue-related concerns. Although the main study mobility outcome was based on EQ-5D-self-report, this is known to have strong validity for measuring mobility performance in older adults [35,36].
We excluded 51 participants who could not walk at baseline, and it is theoretically possible that they could have recovered during follow up. Third, we did not externally validate the models although bootstrap validation takes model over-optimism into account and is considered better than data splitting [37]. Fourth, there were differences between characteristics of participants who remained in the study and those who withdrew, and this may have introduced attrition bias. Although MI was used to reduce the potential biases, this may not overcome all the bias associated with withdrawals. Finally, the small number of participants who died during the first 2 years were excluded from the main analyses.

Conclusion
We have derived and internally validated two easy-touse prediction models that quantify absolute risk of mobility decline in community-dwelling older people. Our models are based on self-reported health and mobility questions that are easy to collect and can inform clinical decision-making regarding the need for rehabilitation aimed at preventing mobility decline and maintaining independence in older age. The models displayed good discrimination.