2.1.1 BLSA dataset.

The BLSA was founded in 1958 and contains data on over 3,200 participants. The approximately 1,300 participants still active in the study return every 1–4 years to receive comprehensive health, cognitive, and functional evaluations. A freeze of the BLSA database was accessed August 17, 2021, and the authors performing the analysis had no access to information that could identify individual participants at any time. At the time of this study, the BLSA database consisted of 3,821 gait speed measurements from 1,363 unique subjects. Measurements were performed at intervals depending on subject age, with intervals between visits decreasing with increasing age (<60 = 4 yr intervals, 60–79 = 2 yr intervals, 80+ = 1 yr intervals). The median number of visits per subject was two, with a range of up to 12. This dataset is uniquely suited to our purpose due to the large number of subjects, the high quantity of metrics recorded, the regularity of the testing intervals, and the longitudinal nature of the study.

Gait speed measurements were obtained from timed walks performed according to the Short Physical Performance Battery (SPPB) protocol [59]. The SPPB, including its gait measurement component, is a standardized, widely used tool for measuring physical performance [60]. Participants were timed as they walked unassisted at a normal pace on a 6-meter course. Walking times were converted to gait speed (m/s) and the average of two trials was calculated. These timed walks have high test-retest reliability with ICC values 0.87–0.97 and uncertainty of 0.06–0.11 m/s, depending on the measured population [61–64].

Gait speed outcomes were evaluated using two different cut-points that have been shown to be clinically relevant for normatively aging population represented by the BLSA: (1) 0.8 m/s which has been proposed as a marker for severe mobility disability with a strong correlation to mortality [55–57] and (2) 1.0 m/s, the speed below which the risk of mortality doubles and at which subjects are deemed at high risk for adverse health-related outcomes [4,21,54]. Binary classification was chosen due to its natural clinical interpretation, similar to a host of other clinical outcome measures. In addition, both LR and NN architecture lend themselves naturally to such classification analyses. Indeed, a classification study is a natural design for a NN and allows us to compare the NN to the well-defined, gold standard LR model. In addition, the use of these cut-points provides clinical relevance as they are metrics for health status categorization and treatment guidance.

The number of gait speed measurements in the BLSA database for each cut-point is shown in Table 1. Any of these classifications (columns in the tables) can be used as an output for the DL model. The “Current” timeframe denotes the classification of gait speed at the time of the measurement, where a “Slow” measurement captures any gait speed that is at or below the cut-point value at that time. In the “Future” timeframes, “slow” captures any gait measurement above the cut-point value corresponding to a subject who will develop a slow gait, that is, fall below the cut-point value, within the time frame indicated. Subjects included in the Future timeframes were restricted to only those with at least as many years of follow-up as specified by the timeframe. In this way, subjects who will develop slow gait in the future or who developed this outside of the study were not incorrectly included in the “Normative” class. Other timeframes were also explored but proved to have too few subjects in the “Slow” class to achieve reliable results.

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Table 1. Counts of gait speed measurements and key demographics for each dataset from the BLSA database.

https://doi.org/10.1371/journal.pone.0325172.t001

In order to compare our results to previous models, we selected a subset of 15 markers encompassing demographic, lifestyle, and medical history variables previously identified as potentially correlated to gait speed decline either at current [21,23,26,27,34,38,58] or future [34–37] timepoints. Inclusion decisions were made based on several factors: (1) the amount of missing data for a particular variable across multiple time frames and subjects, (2) the typical availability of the variable in clinical settings, and (3) the interpretability of the variable. We preferred to incorporate fewer, well-selected variables, rather than more of the available variables, in order to increase the overall interpretability of the result and to prevent the difficulties arising from multiple dependencies. We considered age, sex, hypertension, diabetes, stroke, heart attack, osteoarthritis, cognitive impairment, depression, sleep quality, exercise, grip strength, pain, alcohol consumption, and BMI (Table 2). Categorical variables are noted in the table with (y/n) and were input as 0 or 1 to the model (or a scale of 1–5 in the case of sleep quality). Continuous variables (age, cognitive impairment, grip strength, and BMI) were input as exact values, as recorded in the BLSA data. Missing data points were replaced by the median value of that input for all participants, as is common practice in machine learning. Median was chosen in preference to the mean for this imputation to avoid undue sensitivity to outliers. The percentage of missing values was less than 2% for all variables except MMSE, which was missing for 15% of the gait speed measurements.

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Table 2. Definitions of each input variable from the BLSA database.

https://doi.org/10.1371/journal.pone.0325172.t002

2.1.2 Consideration of dataset bias.

We evaluated several points of potential bias in the BLSA data used for this study. Firstly, highly correlated input variables can pose a problem for logistic regression models, making it harder to interpret coefficients and identify significant independent variables. While this multicollinearity is less of a confounding factor for NNs, it can still slow convergence and affect sensitivity analysis. We checked the correlation of our input variables by calculating the Pearson correlation coefficient between each pair. The resulting coefficients for each pair are shown in S1 Fig in the Supporting Information. Values < −0.5 and >0.5 are generally considered to indicate notable correlations. In our case, we see this only for age and grip strength, with r = 0.54. We conclude that there was minimal multicollinearity in our input data. In fact, we elected to incorporate only the right-hand grip strength in the analysis due to high collinearity with the left-hand grip strength (r = 0.74). The use of dominant hand grip strength was also considered but would have further restricted dataset size since this value was not reported in all participants.

For the use of longitudinal data, the potential for bias due to selective dropout, or non-random loss of participants from a study, must be considered [65]. We compared the age, MMSE score, and gender proportion between the cohort of patients included in each dataset and those dropped due to lack of follow-up (see S1 Table in the Supporting Information). The average of each metric for the included cohort was compared to that of the dropped cohort. Potential bias was evaluated by two-sample t-tests as well as effect size calculations for age and MMSE score and by a two-proportion z-test for the percent males. Any significant differences from the t-test or z-test are denoted by the bold text in the table. The small effect sizes, all less than 0.22, as well as the fact that even statistically significant differences were well within one standard deviation of each other, indicate minimal bias due to selective dropout.

We also considered the possibility of dataset drift, that is, whether the average gait speed of subjects has changed over the many years of BLSA data collection. To evaluate this, we calculated the mean gait speed of subjects grouped by the year in which the measurement was taken. S2 Fig in the Supporting Information shows the lack of a clear trend, indicating absence of substantial drift. We also considered dataset drift with respect to year of birth, as shown in the Supporting Information in S3a Fig; such drift could, for example, result from a secular improvement in overall population health. To separate this from the expected trend with respect to age, we also plotted gait speed versus participant age in S3b Fig. A linear regression analysis resulted in β coefficients of 0.0083 and 0.0082, respectively. Based on the near equality of these coefficients and the shape of the plots, we conclude that the effect of dataset drift on our study due to birth year was also not significant.

Lastly, we considered the possibility of bias from the uneven distribution of participant ages at each timepoint of measurement. We found that there were far more measurements in the middle age range of 60–80 than at the extremes within the dataset. To explore the potential of bias due to this overrepresentation, we examined the pattern of false predictions with respect to age within our current timeframe models. We found that the shape of the age histogram closely matched the shape of the false prediction histogram for both cut-points, suggesting that prediction errors were occurring in proportion to the number of subjects across the dataset, that is, accuracy was relatively independent of age. We conclude that training set size was sufficient across the participant ages and there was consequently minimal bias attributable to sample age distribution.

2.1.3 Ethics approval and consent to participate.

Written informed consent was obtained from all participants and the Institutional Review Board of the Intramural Research Program approved the study protocol.

2.2.1 Neural network methodology.

We implemented feed-forward NNs with the Keras library using TensorFlow as backend, using Python version 3.6. We chose a relatively simple NN architecture in order to incorporate nonlinear relationships without overcomplicating the model. An architecture with a limited number of nodes was chosen to prevent overfitting since the input data (a single column, short length vector) was relatively non-complex compared to many DL tasks. Overfitting was mitigated by careful hyperparameter tuning and 10-fold cross validation as detailed below.

A schematic overview of our model is shown in Fig 1. Generally, the model used operational blocks as indicated by the inset of Fig 1; these consisted of a fully connected layer followed by batch normalization, an exponential linear unit (ELU) activation function, and dropout. Batch normalization was used prior to the activation function to standardize inputs and facilitate training. Dropout regularization was implemented to reduce overfitting and improve generalizability. Four such sequential FC blocks were followed by another fully connected layer and then by a final softmax binary output layer. Further details on model optimization through loss function testing and hyperparameter tuning can be found in the Supporting Information.

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Fig 1. Schematic of the NN architecture.

Models for current gait prediction and future gait prediction differ in layer size and activation functions. The final two layers, colored green, do not use the batch normalization and the dropout procedure implemented in previous blocks.

https://doi.org/10.1371/journal.pone.0325172.g001

2.2.2 Logistic regression methodology.

Logistic regression was also implemented using the scikit-learn module in Python for benchmarking our DL results. We compared performance using several solvers: Newton’s method, liblinear, stochastic average gradient (SAG), and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS). We found no significant difference between these, and so selected the default L-BFGS solver with L2-regularization. Inputs to this model were the 15 physiological markers used for the NN method, and the target variable was again a binary slow/normative label assigned based on either the 0.8 or the 1.0 m/s cut-point. Stratified 10-fold cross validation was again used, with results compiled from the average of the 10 folds. Logistic regression was performed both with and without the use of terms representing first order interactions with age.

2.3.1 Random undersampling (RUS).

A manual RUS procedure was used to randomly remove samples from the majority class of the training set until each classifier had an approximately even number of slow and normative samples. Applying RUS individually to each fold rather than to the full training set ensured that normative samples containing potentially important samples were not removed entirely from the experiment.

2.3.2 Synthetic minority oversampling technique (SMOTE).

SMOTE was introduced as a method to increase the sensitivity of predictor’s performance on imbalanced datasets without sacrificing large amounts of data through random undersampling [67]. To implement this, a sample from the minority class is drawn and its k = 3 nearest neighbors, determined by Euclidian distance, are identified. A vector is drawn to one of those neighbors from the selected sample and then multiplied by a number between 0 and 1. The resultant vector is then added to the selected sample to create a new synthetic data point [66]. This procedure is applicable only to numeric data. SMOTE-NC is a variation of this which can be applied to nominal data as well. We implemented SMOTE-NC using the Imbalanced Learning Library in Python to achieve an equal class distribution between slow and normative walkers [68].

2.3.3 Synthetic minority oversampling technique with edited nearest neighbors (SMOTE-ENN).

SMOTE-ENN is a popular class-balancing technique that was developed to combine SMOTE’s ability to generate new minority data with the ENN undersampling algorithm [69]. Following generation of new synthetic data points through SMOTE, ENN is applied. Using the same k-nearest neighbors technique, a sample and its neighborhood is identified. If a sample is found to have a different label than the majority of labels in its neighborhood, then all observations are deleted. Repeating this procedure results in equalized classes as well as less overlap between classes.

3.1.1 Optimized models.

The best performing models of both the NN and the LR were class-balanced with the RUS method. The final dataset sizes after RUS class balancing are listed in Table 3.

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Table 3. Final dataset sizes for each classifier after RUS class balancing.

https://doi.org/10.1371/journal.pone.0325172.t003

The Youden indices of RUS class-balanced models for the NN and LR analyses are shown in Fig 2. These results, along with sensitivity, specificity, precision, and AUPRC values are listed in Table 4. The best performing classifier was for the 10-year prediction using a 0.8 m/s cut-point, where the NN achieved a sensitivity and specificity of 81.2% and 87.9%, respectively. This performance is similar to that of the LR which achieved sensitivity and specificity in this case of 84.5% and 86.3%, respectively.

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Table 4. Performance metrics for the NN and LR models using RUS class balancing.

https://doi.org/10.1371/journal.pone.0325172.t004

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Fig 2. Youden index for NN (blue) and LR (red) models after class balancing using RUS.

RUS class balancing was not implemented for the 10-year prediction due to the balance in the native dataset. Error bars were determined by the standard deviation across all cross-validation folds.

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3.1.2 Comparison of models with unbalanced classes.

To directly compare the performance of the NN and LR in the unbalanced case, the Youden indices for the NN and LR models without class balancing are presented in Fig 3; these results, along with sensitivity, specificity, precision, and AUPRC values are listed in the Supporting Information, S2 Table. The two distinct model types performed comparably across all cut-points and timeframes, with the NN slightly outperforming the LR in all but one case.

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Fig 3. Youden index values for NN (red) and LR (blue) models without class balancing.

As seen, the NN exhibits overall superior performance. Error bars were determined by the standard deviation across all cross-validation folds.

https://doi.org/10.1371/journal.pone.0325172.g003

3.1.3 Exploration of class balancing.

In addition to RUS, we explored two other class balancing techniques, along with the unbalanced case. Results for each classifier before and after data modification with the class-balancing techniques described above are shown in Fig 4a; these results, along with sensitivity, specificity, precision, and AUPRC values are listed in the Supporting Information, S3 Table. For the 10-year prediction with 0.8 m/s cut-point, classes were approximately equal without balancing, which was therefore not performed.

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Fig 4. Youden index values for all class-balancing techniques beside the unbalanced case (blue bars) for the

(a) NN and (b) LR model. Class-balancing techniques resulted in improved Youden indices. Class balancing performed by RUS, SMOTE, and SMOTE-ENN algorithms are represented with red, green, and purple bars, respectively. Class balancing was not implemented for the 10-year prediction due to the balance in the native dataset.

https://doi.org/10.1371/journal.pone.0325172.g004

Performance of the LR for each dataset after the various class-balancing techniques are shown in Fig 4b. The Youden index, sensitivity, specificity, precision, and AUPRC values are listed in the Supporting Information, S4 Table. Both the NN and LR models were substantially improved through use of class balancing in all but one case (the 10-year prediction with 1.0 m/s cut-point).

4.1.1 Optimized models.

The results for the optimized, class-balanced models (Fig 4 and Table 4) demonstrate that the NN performed as well as or better than the LR. The best performing classifier was for the 10-year prediction using a 0.8 m/s cut-point, where the NN achieved a sensitivity and specificity of 81.2% and 87.9%, respectively. This performance is similar to that of the LR which achieved a sensitivity and specificity of 84.5% and 86.3%, respectively. This is on a par with other complicated clinical analyses, but clearly encourages further work towards improvement.

Of note, all models performed, at best, with only moderate success; the maximum Youden index, for example, was ~ 0.7 (for 10-year prediction of slow gait with respect to the 0.8 m/sec cutoff). This motivates the future use of additional input data and perhaps elimination of those that were found not to provide substantial predictive power. Even with comparable performance, NN methods have an important advantage over LR for future work in that they are adaptable to the incorporation of images into further analysis. In contrast, the LR approach can incorporate image-derived metrics, such as regional volumes, but does not allow for use of images themselves. Similarly, NNs can be expanded to incorporate longitudinal data in a formal way, unlike LR.

We found that all the models performed better for future than for current gait prediction, despite the latter’s greater training set size (Table 3). This may reflect the particular set of input variables we chose or indicate that the chosen markers reflect physiologic status that emerges clinically only after a period of time. This relationship may even be time dependent as we also note that the 10-year classifiers slightly outperformed the 6-year classifiers, again independent of the training set size. Finally, we note that classifiers for the 0.8 m/s cut-point outperformed those using the 1.0 m/s cut-point for the equivalent timeframes, suggesting that the more extreme cut-point was more easily identified as abnormal by this set of input variables.

While the performance difference between the NN and the LR was minimal in the present study, the additional flexibility afforded by the NN and its ability to capture nonlinear relationships may prove to be crucial for future studies of gait and related physical outcomes. In particular, the use of NN allows for the addition of more complex inputs such as images and other non-tabular data.

4.1.2 Comparison of models with unbalanced classes.

Fig 3 shows that when using unbalanced data, across all cut-points and timeframes, the NN slightly outperforms standard LR except in the case of the 10-year prediction using a 0.8 m/s cut-point. However, as in the balanced data case, the model types perform comparably. The relatively weak performance of the current and 6-year predictions for both cut-points is largely attributable to low sensitivities seen in S2 Table in the Supporting Information. Such sensitivity values are not surprising given the extreme class imbalance observed for the corresponding data (Table 1). The NN exhibited substantially greater sensitivity than LR in these cases, suggesting the comparative resiliency of the NN approach to data imbalance. Nevertheless, the sensitivity and Youden index are still poor overall, motivating the exploration of class-balancing techniques to improve sensitivity.

Issues such as class balancing have come to the fore with the recent explosion of interest in DL and are known to virtually all practitioners. However, such methods have been much less recognized in the context of more traditional analytic methods such as LR. In that sense, the conventional NN approach incorporating class balancing (Fig 2), greatly outperforms the conventional LR approach in which no class balancing is performed (Fig 3). These results highlight therefore the great power of multivariate linear analysis in conjunction with more modern considerations related to dataset structure. This leaves open the question of why the theoretically more limited LR approach exhibited performance on par with the NN after class balancing. Evidently, for the variables selected and over the range of values studied, linear effects capture the dominant biomarkers of gait without the need for nonlinear modeling.

4.1.3 Exploration of class balancing.

As indicated by the Youden index results shown in Fig 4, both the NN and LR models were substantially improved through use of class balancing in all but one case. Increases in Youden index were most evident in models using a 0.8 m/s cut-point, for which class imbalance was more severe, but those with a 1.0 m/s cut-point also saw improvements. Increases in Youden index were driven by large increases in sensitivity as seen in the Supporting Information, S3 and S4 Tables. These increases were most apparent for current timeframe predictions, particularly with LR and for the 0.8 m/s cut-point for which the model was almost entirely unable to identify slow walkers. The current timeframe datasets had the greatest imbalance in the native data (see “% Slow” column in Table 1), and it was in fact for these that class balancing led to the largest increases in performance. These results strongly support the use of class balancing in related studies, particularly since our classifiers were trained on balanced data and tested on natural ratios; this is a more difficult classification task than balancing both training and testing sets.

The one model that did not benefit from class balancing was the NN designed to predict gait speed class in 10 years with the 1.0 m/s cut-point. We attribute this to the fact that this dataset was already well-balanced, actually containing more slow than normative walkers, in contrast to all other datasets used.

The three class balancing methods, RUS, SMOTE, and SMOTE-ENN, exhibited overall similar performance. We therefore selected RUS for class balancing, given its simplicity and the fact that it does not require synthetic data. It is interesting that the simplest approach, RUS, performed as well as the more sophisticated techniques of SMOTE and SMOTE-ENN. In this context, we note characteristics of SMOTE that may have limited its effectiveness in our study. Overlap between classes is particularly problematic for SMOTE, given that it blindly generalizes the region of a minority class without consideration of nearby samples of the majority class [66]. This strategy is particularly problematic in the case of highly skewed class distributions since the minority class tends to be sparse with respect to a majority class, thus resulting in a greater chance of class mixture [73]. SMOTE can also exhibit limited performance in the setting of multiple feature inputs; it becomes much more difficult to generate a representative sample of new data in higher dimensions. High dimensionality also gives rise to the phenomenon of hubness, in which a small number of points are overrepresented in the selection of nearest neighbors [74,75]. Given the efficacy of class balancing in this study, further investigation into the utility of other available methods may be warranted.

4.2.1 Trends across time, cut-point, and model type.

We found that across all the classifiers tested except one, age is the strongest predictor. For the current prediction with 1.0 m/s cut-point, grip strength was a stronger predictor than age. Of note, this was also the lowest-performing classifier. The dominance of age as a predictor was as expected, but we found that its influence was in all cases modulated by other significant predictors.

For the NN, age was less dominant as a predictor for current than for future gait. Consistent with this, there were a greater number of significant variables in these analyses. In fact, for current prediction with a 1.0 m/s cut-point, every input variable was found to be significant. In contrast, for the 10-year prediction with the same cut-point, only three variables were found to be significant: age, depression, and hypertension. This result suggests that a wider array of the chosen variables exhibit a substantial predictive power for current slow gait as compared with future slow gait, which may reflect certain effects becoming dominant over time. In particular, osteoarthritis, diabetes, pain, and sex are significant for current but not for future predictions. One hypothesis for the differences across time is that certain metrics exhibit a more delayed influence on the aging trajectory of a subject. For example, smoking or consistent poor sleep quality presumably correlates to higher morbidity over longer time scales, while poor strength influences gait contemporaneously.

For the future prediction NN classifiers, more variables were found to be significant for the 0.8 m/s cut-point than the 1.0 m/s cut-point. Grip strength appeared as a significant variable in all but one classifier (10-year prediction with 1.0 m/s cut-point). Sleep quality, BMI, stroke, and hypertension appeared in four classifiers as significant predictors. Interestingly, for the 6-year prediction, age and stroke were the strongest determinants across both cut-points, but stroke did not appear among the predictive variables for the 10-year timeframe.

In this study, we performed direct comparisons of two different model structures, NN and LR. This allowed us to capture model dynamics and consider the key determinants of healthy aging within this dataset without model constraints. We found a similar set of dominant predictors for the LR (Figs 5c, 5d, and S6) as for the NN (Figs 5a, 5b, and S5). In particular, age, grip strength, BMI, and hypertension appeared as significant most frequently across both model types. Further, all four of these were found to be significant in our best performing models (10-year prediction with 0.8 m/s cut-point for both NN and LR). On the other hand, stroke and sleep quality were found to be significant more consistently in the NN than in the LR. This may indicate a stronger non-linearity in the relationship between these variables and gait speed.

Additionally, we found that more variables appeared as significant for the LR model as compared to the NN for the 10-year prediction, but fewer were significant for the LR for current prediction. We also found that the significant predictors in the LR were more consistent across classifiers than in the NN. Age, grip strength, MMSE score, and hypertension appeared as significant in every LR classifier, with age and grip strength among the top three factors in four classifiers and among the top five factors across all LR classifiers. BMI was found to be significant in five of the six LR classifiers, while stroke was found to be significant in four. Interestingly, diabetes and depression only appeared as significant in future prediction classifiers, not those of current timeframe; this may indicate the importance of these variables over time. Pain was the only variable that never appeared as significant in any of the LR classifiers.

While our methodology does not indicate causality versus correlation, the fact that future gait speed can be predicted by models which include modifiable risk factors may prove to be of substantial clinical utility. For example, BMI and grip strength were consistently found to be significant according to Sobol index analysis and can clearly form the basis for therapeutic intervention and guidance.

4.2.2 Consideration of survey data and strongest predictors.

We conducted several additional sensitivity studies with the NN to further define the impact of certain variables. These investigations were confined to the 10-year prediction of the 0.8 m/s classification cut point using balanced data; see S6 Fig.

Our variables included both self-reported survey data and objective, quantifiable data. The limitations of self-reported data have been well-recognized [76]. We therefore investigated the specific contribution of these variables to our models by performing a NN analysis using only sex and the four non-categorical (non-survey) variables of age, BMI, grip strength, and cognitive score as input variable. This resulted in comparable performance with a Youden index of 0.68 as compared to the Youden index of 0.69 for the original dataset of all 15 variables. These results are shown in the Supporting Information, S5 Table. This indicates that the categorical variables do not provide substantial additional predictive power to the model.

Since age was the dominant predictor as indicated by its large Sobol index in all models, we also developed a NN model with age and sex as the only input variables. The resulting Youden index of 0.65 indicated a somewhat degraded performance as compared to the all-variables result of 0.69. The decrease was due to lower sensitivity, 0.764, as compared to the all-variables sensitivity of 0.812. To further investigate the role of dominant variables, we trained a NN model using all variables except age. As expected based on Sobol index analysis, we found a substantial decrease in the Youden index, from 0.69 to 0.49. While performance indeed worsened through omission of age, it is noteworthy that the other variables alone still achieved decent performance for gait classification.

Previous investigators have established a strong correlation between height and gait speed, unsurprisingly, especially when examining current timeframes [77]. However, when we swapped height for BMI in our models, we encountered no discernable difference in the model performance. Thus, we did not include height in our classifiers.

We conclude that the 15 original variables formed a reasonable input set. While performance was essentially maintained when categorical variables were removed, these results support their use in that the self-reported survey data did not negatively impact performance. The results obtained when omitting age provided evidence that multiple input variables are indeed important for gait speed prediction.

4.3.1 Data considerations.

Our chosen variables are based on those identified in other studies, and most closely following the important work of Verghese et. al [34]. Other investigators have included similar sets of modifiable risk factors and medical conditions, [34–36] with some also incorporating or focusing on cognition [37,38]. In addition, inflammatory markers, [39] body composition, [2] and brain volumes [35] have all been incorporated into gait studies. While lower extremity strength would seem an influential factor in the analysis of gait determinants, few studies have incorporated it [2,23,25]. This may be due to its presumed high correlation with the gait outcome itself, or with the relative difficulty and lower reproducibility in measuring it as compared to hand grip strength. Of note, previous work has shown that grip strength contributed more than lower-extremity strength to variance in walking speed [78].

In spite of this literature, there remains a knowledge gap regarding the relationship between gait speed decline and a range of potentially determinative factors. Although in the present case LR performed on par with the more flexible NN model, we conjecture that these more flexible DL architectures will prove to be better able to capture the influence of complex datasets, including evaluation of longitudinal variables and raw imaging data. An important part of our effort was to develop a DL model and to establish its performance on well-studied variables, so that with further developments, we will be able to more deeply exploit the full potential of the extensive, longitudinal BLSA database.

A further advance in the present work is the evaluation of two clinically relevant gait speeds, defined as the point of severe mobility disability (0.8 m/s) and the speed below which the risk of mortality doubles (1.0 m/s). In contrast, a number of previous studies employ very low cut-points which capture only the most severely impaired subjects [27,34].

4.3.2 Model considerations.

Previous work on future gait speed prediction has implemented only linear statistical models, including mixed-effects models, [2,37,38] hierarchical regressions, [35]. Poisson regressions, [34] and cross-sectional analysis [39]. Similarly, current gait speed prediction models have also mainly employed linear regressions [23–26,58] and cross-sectional analyses, [22] along with logistic regressions, [21,27] although support vector regression [79] and decision tree analysis [48] have also been explored. We sought to introduce the NN approach to this important problem, given the complexity of human biochemistry and physiology. With numerous contributing and overlapping factors to consider, AI techniques, such as NNs, offer a potentially superior tool for the study of gait speed decline and aging trajectories. Deep learning models allow for the simultaneous consideration of multiple patient factors, and thus tend to be more suitable than classical statistical methods for problems involving large numbers of predictors by accounting for their combined influence and accommodating the inclusion of complex data such as images, clinical data, and other biomarkers and health [80,81]. Thus, our work represents a promising new application of NNs and, in addition to our biomedical results, serves as a pilot study towards exploration of more complex input variables including images and longitudinal data.

4.3.3 Sensitivity analysis.

Previous studies have used a variety of performance metrics, making direct comparisons difficult. Several of these, like ours, have found BMI, [34,35] grip strength, [34,35] and cognitive impairment [34,37] to be significant predictors of gait. However, other studies found these variables not to be significant [2,38]. Verghese et. al also found exercise and pain to be significant [34]. While Pinter et. al identified age as a strong determinant [35], we note that most modeling studies use age as a covariate or for stratification, instead of investigating its influence directly as we did. Though there is not a strong, clear consensus, there is overall support in the literature for our findings that age, grip strength, and BMI are among the strongest determinants of future gait speed. Sleep quality also emerged as an important predictor in some of our models, as did cognitive impairment and exercise. As compared to previous studies, we evaluated model performance over a longer timeframe (six and ten years, rather than three-to-four years), allowing us to capture longer-term effects. This is especially important for the BLSA dataset, which is derived from a relatively healthy cohort in which slow gait may develop over longer time scales.

Previous investigators have identified additional significant predictors of future gait speed decline include vision loss, [34] balance metrics, [34,36] brain volume and white matter hyperintensity change, [35] baseline gait speed, [36] difficulty with activities of daily living, [36] frailty, [36] reaction time, [36] thigh intermuscular fat area, [2] and inflammatory markers [39] Beavers et. al even found the longitudinal change in thigh fat and thigh muscle to be a strong predictor [2]. These findings further motivate the NN approach with application to a richer set of input variables.