Development of a nomogram prediction model for gait speed trajectories in persons with knee osteoarthritis

To examine heterogeneous trajectories of 8-year gait speed among patients with symptomatic knee osteoarthritis (KOA) and to develop a nomogram prediction model. We analyzed data from the Osteoarthritis Initiative (OAI) assessed at baseline and follow-up over 8 years (n = 1289). Gait speed was measured by the 20-m walk test. The gait speed trajectories among patients with KOA were explored by latent class growth analysis. A nomogram prediction model was created based on multivariable logistic regression. Three gait speed trajectories were identified: the fast gait speed group (30.4%), moderate gait speed group (50.5%) and slow gait speed group (19.1%). Age ≥ 60 years, female, non-white, nonmarried, annual income < $50,000, obesity, depressive symptoms, comorbidity and WOMAC pain score ≥ 5 were risk factors for the slow gait trajectory. The area under the ROC curve of the prediction model was 0.775 (95% CI 0.742–0.808). In the external validation cohort, the AUC was 0.773 (95% CI 0.697–0.848). Heterogeneous trajectories existed in the gait speed of patients with KOA and could be predicted by multiple factors. Risk factors should be earlier identified, and targeted intervention should be carried out to improve physical function of KOA patients.

www.nature.com/scientificreports/ such as age, gender and race 9,10 , as well as health-related variables like BMI, comorbidity, pain and depression [9][10][11][12] . To date, it has been demonstrated that there are distinct disease trajectories of function 13 , quality of life 14 , knee pain 15 and structural progression 16 , suggesting that KOA patients have interindividual variability. A previous study has described gait speed trajectories in participants with or at risk of KOA 17 . However, it remains unclear how trajectories of gait speed change over time in KOA patients, nor predicting factors of trajectories. Understanding the heterogeneity in the longitudinal gait speed trajectories is of importance to clarify the natural history.
Recognizing the predicting factors is helpful to find individuals at risk and set specific intervention strategies to improve physical function. Therefore, the purpose of this study was to explore gait speed trajectories of people with KOA, and to develop a nomogram predicting model to identify individuals with low gait speed.

Methods
Study population. Participants included in the study were collected form the Osteoarthritis Initiative (OAI), an ongoing, multicenter, prospective observational, longitudinal cohort of the risk factors and natural history of OA, including 4796 participants between 45 and 79 years. Detailed information of rationale and approach for the OAI can be found at https:// data-archi ve. nimh. nih. gov/ oai/. Data used in this study includes the baseline visit and eight years of follow-up for analyses. An index knee for each participant was set based on the Kellgren-Lawrence (KL) grade at baseline. The knee with higher KL grade was set as the index knee. In case an equal KL grade in both knees, the knee with a higher Western Ontario and McMaster Osteoarthritis Index (WOMAC) pain score was set as the index knee. The index knee was randomly set if knees had the same KL grade and WOMAC pain score. Participants with KOA in at least one knee at baseline were enrolled. KOA was defined as an index knee with KL grade ≥ 2 and having pain, aching, or stiffness in or around the index knee in most days for at least 1 month during the past 12 months. Individuals without 20-m walk gait speed information at baseline or all the follow-up visits were excluded. Supplementary Fig. 1  Gait speed. Gait speed was measured by a 20-m walk test, which was used frequently in KOA studies and had high sensitivity and test-retest reliability 6 . Participants were instructed to walk at a comfortable pace and allowed to use walking aids. The stopwatch was starting when participants began walking and was stopped as soon as participants stepping over the finishing line. Each participant performed 2 20-m walk trials and gait speed was calculated using the average of 2 walking gait speeds. Gait speed at baseline and 1/2/3/4/6/8 year (s) follow-up visits were collected.
Modifiable factors included knee pain, obesity and depressive symptoms. Knee pain was evaluated by the WOMAC pain subscale 28 , which was scored from 0 to 20, and higher scores indicated higher pain severity. Obesity was classified as a BMI ≥ 30 kg/m 2 . Depressive symptoms were defined as the Center for Epidemiological Studies Depression (CES-D) score ≥ 16 29 .
Statistical analyses. Data were analyzed using Mplus version 7.0, STATA version 15.0 and R software 4.2.2. Baseline characteristics of participants were expressed as frequencies or percentages and compared by performing chi-square tests for categorical variables. Restricted cubic spline models were used to describe the possible nonlinear associations between continuous variables and gait speed. Missing data were imputed with the median and the mode in STATA.
Trajectories of gait speed were identified by using latent class growth analysis (LCGA) in Mplus, which is a type of mixture modeling to identify possible distinct subgroups. The optimal number of trajectory groups was determined by considering the smallest Akaike information criterion (AIC), Bayesian information criterion (BIC) and sample size adjusted BIC (aBIC), entropy values closest to 1, bootstrap likelihood ratio test (BLRT) P-value < 0.05 which means the model with n classes is better than the model with n-1 classes, and the number of members per class > 1% of the total cohort. The Guidelines for Reporting on Latent Trajectory Studies (GRoLTS)-Checklist was used for the reporting of the trajectory analysis 30 (Supplementary Table 1). Missing data for gait speed were handled under missing at random and no imputation of gait speed was undertaken.
To make full use of the data, the enrolled participants were randomly allocated to the training cohort (80%, n = 1039) and validation cohort (20%, n = 250). The univariate and least absolute shrinkage and selection operator Ethics approval and consent to participate. The OAI study was approved by the institutional review boards at all OAI clinical centers, the coordinating center (University of California, San Francisco, USA; approval number 10-00532), the NIH, OAI investigators and private funding partners. Informed consent was taken from subjects before the study so no additional approval was needed.

Results
Baseline characteristics. A total of 1289 patients were included in the study, including 709 patients aged 60 years or older at baseline. There were 562 males and 727 females; 908 were white and 381 were black/yellow/ other races; 824 were married and 465 were single/divorced/widowed. The baseline characteristics of the training cohort and validation cohort are listed in Table 1, and there was no significant difference in variables between the two cohorts (P > 0.05).
Trajectories. The  Univariate analysis of trajectories. The fast and moderate gait speed group were combined into the good gait speed group. Univariate analysis showed that there existed significant differences in age, gender, race, marital status, education level, annual income, drinking history, obesity, depressive symptoms, comorbidity and pain between the good gait speed group and the slow gait speed group (P < 0.05) (Supplementary Table 2).
Nomogram construction. The baseline variables were screened by the LASSO regression model, and the best value of parameter λ was screened through cross-validation. The selected predictors were 9 when the overall deviation of the model was the minimum. Age, gender, race, marital status, annual income, obesity, comorbidity, depressive status, and pain were independent predictors of slow gait speed trajectory (Fig. 2). The above 9 factors were used to construct the nomogram prediction model using logistic regression, with the walking speed trajectory (0 = good gait speed trajectory, 1 = slow gait speed trajectory) as the dependent variable (Fig. 3). The results of parameter estimation and regression are shown in Table 3.
Nomogram validation. The AUC of the nomogram was 0.775 (95% CI 0.742-0.808) in the training cohort and 0.773 (95% CI 0.697-0.848) in the validation cohort, indicating high accuracy in predicting the risk of the slow gait speed trajectory (Fig. 2).
Calibration curves were employed to evaluate the calibration (Fig. 2), demonstrating the high degree of agreement between the predicted and observed probabilities. The Hosmer-Lemeshow goodness-of-fit test indicated that the nomogram had a good fit for the data ( χ 2 = 10.64, P = 0.223).

Discussion
In this study, we used LCGA to identify distinct trajectories of gait speed over 8 years and developed and internally validated a nomogram prediction model to identify patients with KOA following the slow gait speed trajectory. We found that the gait speed remained slowly decreased in all three trajectories, and there existed a minority with low-level gait speed that had not reached 1.0 m/s at baseline and all follow-up visits. Due to our concern about the worst gait speed trajectory, we combined the high-level and medium-level trajectories into one trajectory named good gait speed trajectory. The nomogram prediction model included nine easily obtained risk factors, including age, gender, race, marital status, annual income, obesity, comorbidity, depressive status, and pain. To our knowledge, this is the first study to use gait speed detected by the 20-m walk test to identify distinct trajectories in patients with KOA. Additionally, we used baseline characteristics to characterize patients in different trajectories and develop a nomogram model to predict the progression of gait speed, which was suggested by the results to be used to aid the early intervention of KOA.
In another study, Daniel et al. found 5 distinct trajectories in patients with or at the risk of KOA over 4 years using group-based trajectory modeling, one of them (5%) with a relatively rapid decrease in gait speed 17   Few studies have previously taken concern of prediction model development for slow gait speed in patients at high risk of KOA 9 and gait speed change after education and exercise therapy in patients with KOA 35 . In contrast to the above studies, we first identified distinct trajectories of progression with similar gait speed changes and developed a prediction model to recognize patients belonging to the slow gait speed trajectory, providing new insights into understanding gait speed.
A variety of unmodifiable risk factors for gait speed have been discussed, which is similar to findings in this study, including old age 19,21,25 , female 10 , non-white 24 , low income 10 and comorbidity 20 . Race-related differences in gait speed trajectories are possible ascribed to accumulated exposure of unmeasured factors, such as residential conditions, intergenerational wealth transferring, or adverse health events 36 , which can lead to more opportunities relevant to maintaining gait speed for whites, including accessibility and receipt of medical services 37 , and safe walking environments. Since income is inextricably associated with race in the United States, participants with higher income are also more likely to get access to potential chances of maintenance in gait speed. Although there is no clear evidence, we found that married patients with KOA had faster gait speed, which might be related to more connubial care, less perceived fatigability 38 , and motivated physical activities form spouse 39 . In general, a higher KL grade indicates worse physical function, whereas no significant correlation was found in this study between the KL grade and the slow gait speed trajectory, which might be because the disease symptoms rather than the structural progression itself were the main factor affecting gait speed in symptomatic KOA patients.
As for modifiable variables, obesity is related to low gait speed with causing cartilage decomposition and leading to degenerative changes of the knee joint and reducing physical activity function in patients with KOA 40,41 . Previous studies identified that individuals with obesity had slow gait speed 25 and especially muscle-reducing obesity was associated with slow gait speed in KOA patients 42 . Consequently, tackling obesity in patients with KOA is of great significance to maintain or improve gait speed, and effective strategies incorporate bariatric surgeries, weight reduction diets, exercise regimens and cognitive behavioral strategies 43,44 , which can generate greater weight loss when combined together 45 . Morone et al. found that with the increase in pain level, the gait speed of KOA patients decreased significantly 23 , which was consistent with findings in this study. As the most troublesome symptom in patients with KOA, knee pain can result in limitation of activities, nevertheless, with www.nature.com/scientificreports/ the absence of treatments to eliminate pain. It's common for individuals to take analgesics or receive total knee replacement surgeries on account of knee pain 46 , and there exists some conservative treatments relieving pain, including the low-calorie diet, exercise intervention and physical therapy 43 . A relationship between slow gait speed and depressive symptoms has been found in a recent study 18 , while anxiety-related pain response, rather than anxiety and depression, has been suggested as an important factor related to slow gait speed in patients with lower limb osteoarthritis 22 , indicating that the causal relationship between depressive symptoms and gait speed needs further study. Common in patients with KOA 47 , depressive symptoms are generally attenuated with participation in exercise programs 48 , drug therapy, and psychotherapy, more safer as well as acceptable, mainly including cognitive behavioral therapy and mindfulness-based interventions.
There are several important limitations in this study. First, due to the observational nature of the OAI, treatment interventions including medications and injections continued to be received and might have an impact www.nature.com/scientificreports/ on trajectory patterns, while our analysis did not take these factors into account. In addition, although variables included in the prediction model were significantly associated with the slow gait speed trajectory, the mechanisms of these associations need advanced research. Finally, we did not conduct external validation of the model, which is necessary before its use in clinical studies to select patients.

Conclusion
In conclusion, this study revealed 3 distinct trajectory patterns in patients with KOA over 8 years. While a majority of patients had high-level or medium-level gait speed, those in the slow gait speed trajectory were more likely to undergo worse clinical outcomes, indicating physical function deterioration. A nomogram prediction model was developed and validated, which manifested that presence of age ≥ 60 years, female, White, married, annual income < 50,000 dollars, obesity, comorbidity, depressive symptoms, and WOMAC pain score ≥ 5 can precisely predict the slow gait speed trajectory. Our prediction model may contribute to identifying individuals at risk of the slow gait speed trajectory within 8 years in the early stage, allowing education and targeted intervention of modifiable risk factors for improving the physical function of patients with KOA.