research-article

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A Human-in-the-Loop Segmented Mixed-Effects Modeling Method for Analyzing Wearables Data

Authors:

Karthik Srinivasan,

Faiz Currim,

Sudha RamAuthors Info & Claims

ACM Transactions on Management Information Systems, Volume 14, Issue 2

Article No.: 18, Pages 1 - 17

https://doi.org/10.1145/3564276

Published: 25 January 2023 Publication History

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Abstract

Wearables are an important source of big data, as they provide real-time high-resolution data logs of health indicators of individuals. Higher-order associations between pairs of variables is common in wearables data. Representing higher-order association curves as piecewise linear segments in a regression model makes them more interpretable. However, existing methods for identifying the change points for segmented modeling either overfit or have low external validity for wearables data containing repeated measures. Therefore, we propose a human-in-the-loop method for segmented modeling of higher-order pairwise associations between variables in wearables data. Our method uses the smooth function estimated by a generalized additive mixed model to allow the analyst to annotate change point estimates for a segmented mixed-effects model, and thereafter employs Brent's constrained optimization procedure to fine-tune the manually provided estimates. We validate our method using three real-world wearables datasets. Our method not only outperforms state-of-the-art modeling methods in terms of prediction performance but also provides more interpretable results. Our study contributes to health data science in terms of developing a new method for interpretable modeling of wearables data. Our analysis uncovers interesting insights on higher-order associations for health researchers.

1 Introduction

Wearables are smart electronic devices that bring the ability to continuously record, monitor, and analyze key health indicators of individuals as they go about their lives. The global market share for wearables is forecasted to be $33 billion by 2025, with an average growth rate of 15% each year [1]. Wearable devices have been instrumental in transforming personalized medicine and individual health monitoring practices. The number of wearables-based research has been steadily increasing each year—a trend that is expected to continue in the future [2]. Wearables are primarily wrist-worn sensors that continuously track elementary wellness indicators such as sleep, heart rate, and activity; however, newer types of wearables, including implantables, chest-worn sensors, head-mounted displays, smart jewelry, and smart clothing, could be capable of capturing a lot more health indicators such as physiological stress, respiration rate, blood alcohol, blood sugar, and other vitals in a noninvasive way.

Many studies employ wearables data for predictive modeling such as fall detection or predicting 30-day readmissions [3–5], yet there is growing interest in conducting natural and quasi-natural experiments to study human health and its relationship with externalities [2, 6, 7]. Health indicators from wearables can be combined with other data sources such as electronic health records and social media to better understand dynamics between human health and society [8–10]. Wearables are capable of continuously monitoring and recording health indicators at fine granularity for multiple participants simultaneously. However, the resulting repeated measures data poses data quality and analytical challenges such as missing values, high dimensionality, lagged effects, and clustered errors [11, 12]. Existing glass-box models such as mixed-effects regression are often insufficient for accurately representing higher-order associations between variables in wearables data [13]. For example, including a second-order term in the mixed-effects regression model can show that a second-order effect of an input is statistically significant, but it is difficult to explain the functional nature of the second-order association from the quadratic expression alone. In other words, it would be interesting to learn the extrema (i.e., maxima/minima) of the second-order effect and how the outcome varies for unit change in the input around such a point. Furthermore, establishing such a functional relationship using visualizations alone can be challenging for wearables data with repeated measures per user and heterogeneity across users. Therefore, there is a need for novel interpretable methods for explaining higher-order associative patterns in wearables data.

Segmented regression, also known as broken-stick or piecewise regression, is an explanatory modeling approach where input variable(s) of interest are partitioned or segmented into intervals followed by fitting straight lines for each interval in the regression model. It is commonly used in design science research applications with a hypothesized curvilinear relationship in simple regression models [14, 15]. The most critical challenge in fitting a segmented model is the determination of input value(s) at which segments need to be separated, a problem also known as breakpoint or change point determination. Studies that use segmented regression with mixed effects [16] determine change points using either ad hoc or black-box procedures [13, 17]. These methods either tend to have low external validity or overfit and are therefore unsuitable for making inferences. To overcome these shortcomings, we propose a new method for determining change points for input segments in a mixed-effects regression. Our method is based on the human-in-the-loop (HITL) paradigm as it uses human inputs during the model training process. Our method repurposes the smooth functions generated by a generalized additive mixed model (GAMM) to allow the analyst to set initial estimates of the change points through visual inspection. Following which, a fast robust root-finding algorithm called Brent's method is used to precisely locate each change point iteratively by maximizing the mixed-effects model's Akaike information criteria [18]. In this way, our method takes advantage of human inputs to fit segmented models that can accurately represent higher-order associations between variables in wearables data. We evaluate our method on three real-world datasets. Our method consistently outperforms existing approaches for all three datasets. The models developed using our method enable clear interpretations of four higher-order associations across the datasets. Inferences from our analysis have multiple managerial implications.

2 Background and Related Work

Sensor-based content is among the key characteristics of third-generation business intelligence and analytics applications [19]. Wearables offer the unique opportunity to observe and physiological changes in individuals through measurement of activity, heart rate, body temperature, and health indicators. Different types of wearables are available for commercial use such as implantables, head-mounted displays, smart jewelry, smartwatches, fitness trackers, and smart clothing. Out of these, the chest-worn and wrist-worn fitness trackers are most widely used in research applications [20–22]. During the early adoption phase of wearable technology, research was primarily directed toward sensor development and architecture [23, 24]. With more and more commercial products being introduced into the market today, the research focus is shifting on wearable data analytics (WDA) and associated design science research applications [25–27].

2.1 Wearable Data Analytics

WDA is the discovery, interpretation, and communication of meaningful patterns from large volumes of data generated by wearable devices [12]. WDA applications can be broadly classified into interpretable modeling and predictive modeling applications. Predictive modeling is the process of learning from existing data to effectively predict future unknown outcomes [28]. In the clinical setting, health vital sign parameters such as electrocardiogram, oxygen saturation, heart rate, respiratory rate, and blood pressure are used to provide preemptive care for patients with cardiovascular diseases, renal diseases, neurological disorders, and cerebrovascular disorders [20]. In the nonclinical setting, wearables-enabled predictive modeling has been employed in problem domains including ambient assisted living [5], human activity recognition [29], reality mining [30], and sports medicine [31]. Data mining, machine learning, and deep learning are the most common approaches used in predictive modeling applications of WDA [21, 25].

Interpretable or explanatory modeling is the process of developing a mathematical representation of patterns in the data for explaining a hypothesized phenomenon [32]. Typically, controlled experiment-based and observational studies employing wearables for data collection use interpretable models to explain their phenomena of interest. Wearables-enabled interpretable modeling has been employed in problem domains including lifestyle modeling [27, 33, 34], environment-wellbeing modeling [13, 35, 36], and psycho-physiological stress modeling [37, 38]. Mixed-effects regression is the most common glass-box model used for interpretable modeling in WDA [27, 35, 36]. In mixed-effects regression, fixed effects or the global coefficients represent the overall effects of inputs on outcomes, and the random effects or varying effects represent how these effects differ across individuals [39].

Few studies employing wearables data report linear pairwise associations [34, 37]; however, many studies observe higher-order associations between variables. For example, Föhr et al. [37] identify a linear association between subjective stress and physical stress measured using heart rate monitors among overweight office workers, and Li et al. [34] find a linear association between the number of steps measured using an activity watch and resting heart rate measured using a heart rate monitor for healthy adults. In addition, Pimentel et al. [40] find associations between two different measures of physical stress (pNN50 and SDNN) to be significant only in a limited range for surgeons in a hospital. Cropley et al. [41] address the challenge of modeling the nonlinear association between work-related rumination and heart rate variability (HRV) by dividing the rumination score into low and high categories, whereas Kraus et al. [13] use domain knowledge to set a change point for segmented modeling. [42] measured heat strain using a heat exposure monitor and reported an inverted U-shaped association curve between heat strain and outdoor temperature for workers. Wearables-based studies such as the ones above either hypothesize or empirically observe higher-order associations. Compared to naïve approaches such as discretization of variables [41] which may lead to loss of information or just reporting first-order and second-order effects in regression models [42], characterizing the higher-order association using segmented modeling leads to better interpretable results.

2.2 Segmented Modeling

Higher-order relationships between inputs and outcomes are common in information systems (IS) [14, 15]. Polynomial regression models account for higher-order relationships, but they are not directly interpretable [43]. In other words, first-order effects and second-order effects cannot be used to quantify the unit change in outcome due to a unit increase in input as in the case of a regression model with only first-order effects. Segmented or piecewise regression is a preferred approach for modeling higher-order relationships, as it is easier to interpret. The primary challenge in using a segmented regression approach is the determination of change points linking the input segments. Change point determination has been studied in different problem contexts including detecting structural change in continuous values of parameters [44], interruption of time series [45], and characterizing higher-order functional relationships [46–48]. Common procedures to determine change points include visual inspection of pairwise plots [48], incorporating domain inputs, greedy search [46], and likelihood-based estimation [47]. Fewer procedures exist for change point determination in mixed-effects models as the likelihood function of multilevel models are not directly differentiable, thus making greedy search and likelihood-based estimation more difficult [17, 46]. A maximum-likelihood (ML) estimation of a continuous functional approximation of the piecewise linear function has been proposed as a more robust alternative to subjective/ad hoc assignment of change points based on visualization of pairwise association plots [17]. However, this method estimates multiple change points automatically with no scope for user inputs into the estimation process. For example, manual intervention such as dropping change points at the extremities of an input distribution could avoid overfitting as well as improve interpretability. Moreover, an automated method may fail to execute if there are too many local extrema or due to high sensitivity toward outliers. To summarize, existing procedures for determining change points in studies employing segmented models are either ad hoc or analytically complex, leading to problems such as low external validity, overfitting, or failure in program execution. There is a need for a segmented mixed-effects modeling method that is robust, efficient, and transparent. Such a method can be helpful to better explain higher-order pairwise associations in wearables data.

2.3 HITL Analytics Methods

HITL analytics methods are geared toward enhancing algorithm performance by incorporating human knowledge and inputs into the modeling and program execution process. HITL is an extensive area of research that covers the intersection of computer science, cognitive science, and psychology [49, 50]. HITL can be performed at different stages of an analytics system, from data preprocessing and modeling to system implementation. Human-machine hybrid models have demonstrated superior performance in natural language and computer vision applications [50] and are being actively considered in general analytics applications [49]. For example, one study [51] shows how initial knowledge inputs from domain experts improve downstream performance of automated machine learning systems. Another effort [52] presents an iterative experimentation framework in which users repeatedly make changes to the ML workflow to improve performance. Similarly, HITL also finds applications in model design, training, testing, and model optimization stages and is applicable to health analytics research involving subjective expertise and a higher need for transparency [53, 54]. For instance, one study [55] incorporates physician inputs toward model parameterization for patient-specific IV fluid recommendation in sepsis treatment. An HITL approach is suitable for analyzing wearable data as human expert inputs and observation can spot technical and logical errors in the analysis at an early stage and avoid rework or erroneous conclusions. Although our study does not attempt to specifically contribute to HITL methodology literature, our method is one of the first few attempts to use an HITL approach for accurately determining change points in mixed-effects modeling in the context of wearables data analytics.

3 Our Method

We propose a new method for capturing higher-order associative patterns in wearables data using segmented mixed-effects modeling. Our method uses an HITL approach to determine the change points in the segmented model by combining an algorithmic search process with human inputs for fine-tuning. In other words, our method uses the smooth function estimated by a GAMM to allow the analyst to annotate the change point estimates followed by fine-tuning of the estimates using a constrained optimization procedure. Our method is novel since few studies have used an HITL approach to tune change point parameters for segmented modeling. It also provides a robust mechanism to capture and explain higher-order relationships hypothesized in wearables data. In the rest of this section, we explain our method in detail.

Consider a mixed-effects model commonly used for explaining repeated measures in data from wearables as follows:

\begin{equation} {y}_{ij} = {\beta }_0 + {\gamma }_{0j} + \mathop \sum \limits_{k = 1}^K {\beta }_k{x}_{kij} + \mathop \sum \limits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij} \end{equation}

(1)

Equation (1) is a representation of generalized linear mixed models with a linear link function, but any link function is applicable to our method. ${y}_{ij}$ is value of a given health outcome for the ${i}\hbox{th}$ observation and ${j}\hbox{th}$ individual, ${\beta }_0$ is the fixed intercept, ${\rm{{\rm B}}} = \{ {{\beta }_1, \ldots ,{\rm{\ }}{\beta }_K} \}$ are coefficients for K fixed effects $\{ {{x}_1,{\rm{\ }}{x}_2, \ldots ,{\rm{\ }}{x}_K} \}$, ${{\rm{\Gamma }}}_0 = \{ {{\gamma }_{01},{\gamma }_{02}, \ldots ,{\gamma }_{0j}, \ldots ,{\gamma }_{0J}} \}$ are J random intercepts for each individual, ${\rm{\Gamma \ }} = \{ {{\gamma }_{11}, \ldots ,{\gamma }_{1j}, \ldots ,{\gamma }_{MJ}} \}{\rm{\ }}$ are coefficients for $M{\rm{\ }}x{\rm{\ }}J$ random effects $\{ {{z}_1,{\rm{\ }}{z}_2, \ldots ,{\rm{\ }}{z}_M} \}$, and ${\epsilon }_{ij}$ is the residual error.

Suppose there exists an input ${x}_r$ such that its second-order (or higher-order) effects are significant, then Equation (1) can be represented as follows:

\begin{equation} {y}_{ij} = {\beta }_0 + {\gamma }_{0j} + \mathop \sum \limits_{\substack{k = 1\\ k \ne r}}^K {\beta }_k{x}_{kij} + {\rm{\ }}{\beta }_{{r}_1}{x}_{rij}{\rm{\ }} + \cdots + {\rm{\ }}{\beta }_{{r}_t}x_{rij}^t + \mathop \sum \limits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij} \end{equation}

(2)

In Equation (2), ${x}_{rij}$ denotes the value of input variable ${x}_r$ for the ${i}\hbox{th}$ observation and ${j}\hbox{th}$ individual.

As described earlier, segmented representations of higher-order effects are more interpretable than polynomials. The input variable ${x}_r$ can be represented as the sum of segments as follows:

\begin{equation} {x}_r = {x}_r\cdot I({x}_r < {\eta }_1) + {\rm{\ }}{x}_r\cdot I({\eta }_1 \le {\rm{\ }}{x}_r < {\eta }_2) + \cdots + {\rm{\ }}{x}_r\cdot I({\eta }_P \le {\rm{\ }}{x}_r) \end{equation}

(3)

In Equation (3), ${\rm{{\rm H}}} = \{ {{\eta }_1,{\eta }_2, \ldots ,{\rm{\ }}{\eta }_P} \}{\rm{\ }}$ is a set of P change points defined for the input variable${\rm{\ }}{x}_r$, which is broken into P segments $\{ x_r^{( 1 )} = \ {x}_r\cdot I( {{x}_r < {\eta }_1} ), x_r^{( 2 )} = {x}_r\cdot I( {\eta }_1 \le {\rm{\ }}{x}_r < {\eta }_2 ), \ldots ,{\rm{\ }}x_r^{( P )} = {x}_r\cdot I( {{\eta }_P \le {\rm{\ }}{x}_r} ) \}$. $I( \varphi )$ is an indicator function equal to 1 if condition $\varphi$ is true; otherwise, it is 0. Therefore, the scalar product ${x}_r\cdot I( \varphi )$ has value equal to ${x}_r$ when $\varphi$ is true and is 0 otherwise. The next logical step is to estimate number of change points and their positions.

We propose an HITL method to estimate the change points ${\eta }_{p{\rm{\ }}} \in H,\ P = | H |$ as follows. As the first step, we fit a GAMM [56] with a given input ${x}_r{\rm{\ }}$ as a nonparametric spline as shown next:

\begin{equation} {y}_{ij} = {\beta }_0 + {\gamma }_{0j} + \mathop \sum \limits_{\substack{k = 1\\ k \ne r}}^K {\beta }_k{x}_{kij} + {\rm{\ }}{f}_r{\rm{(}}{x}_{rij}{\rm{)\ }} + \mathop \sum \limits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij} \end{equation}

(4)

Although a nonparametric spline can be included for the corresponding random effect of input ${x}_r$, it is computationally more expensive for fitting the corresponding semiparametric model. We empirically tested on multiple datasets and observed the shape of the component smooth function ${f}_r( {{x}_{rij}} )$ to not be sensitive to random effects as smooth functions. Therefore, we consider the smooth function only in the fixed effects. In the next step, we visualize the plot of the smooth function in Equation (4) approximated as a B-spline [57]. Here, a human input is required to identify the order of the curve by inspecting the number of extrema (i.e., minima and maxima) to set the value of P. The setting of P can be based upon visual inspection as well as prior domain knowledge. For example, in Figure 1, the P values for the different scenarios in (a) through (d) are chosen as 1, 2, 1, and $5,$ respectively. This step also determines whether to opt for a segmented model over a linear model, by inspecting the curvilinear nature of the component smooth function. For instance, although we set P = 1 for scenario illustrated in Figure 1(c), an analyst may also approximate the monotonically increasing curve as a linear function in this case, thus favoring simplicity over slightly better model fit.

Fig. 1.

The value of the maxima and minima are used as starting points in a linear search algorithm in the third step. The third step involves iteratively performing search for change points using Brent's method [58], a linear optimization with box constraints. Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method, and the inverse quadratic interpolation that make it robust and highly efficient while incorporating box constraints (i.e., range of permitted values) [59]. For each iteration of the optimizer, a mixed model shown with segmented inputs for ${x}_r$ is fit for a particular change point parameter. The algorithm returns the change point parameter corresponding to the model with minimum Akaike information criteria. Since Brent's method is a single parameter estimator, we identify the change points sequentially by repeating the search algorithm for each subsequent change point after fixing values of previously determined change points. Finally, the segmented mixed-effects model is fit as shown next:

\begin{equation} {y}_{ij} = {\beta }_0 + {\gamma }_{0j} + \mathop \sum \limits_{{\rm{\ }}s{\rm{\ }} \in S} \beta _r^{\left( s \right)}{x}_{rij}\cdot I({x}_{rij} \in s{\rm{\ }}) + \mathop \sum \limits_{k = 1,{\rm{\ }}k{\rm{\ }} \ne r{\rm{\ }}}^K {\beta }_k{x}_{kij} + {\rm{\ }}\mathop \sum \limits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij} \end{equation}

(5)

In Equation (5), $S{\rm{\ }}$ is a set of segments constructed using change points ${\rm{{\rm H}}}$ identified for input ${x}_r$. Significance of the effect of input variable, ${x}_r$, at each segment, s, can be determined by inspecting the corresponding fixed-effects coefficient,${\rm{\ }}\beta _r^{( s )}$, under regular conditions. The algorithm for our method is shown in Table 1.

Table 1.

Input: Mixed-effects model with significant higher-order coefficients for input variable, ${x}_r$
1:	Fit a GAMM with input ${x}_r$ represented as a nonparametric spline (Equation (1)).
2:	Inspect the component smooth function plot ${f}_r( . )$ to identify number of change points $P = \| H \|$, starting points $\eta _p^0$ and box constraints $\{ {\eta _p^{min},\eta _p^{max}} \}$ for corresponding change points ${\eta }_p \in H$.
3:	For $p\ = 1$, compute ${\eta }_1$ as follows: $\mathop {{\rm{argmin}}}\nolimits_{\eta _1^{\min } < {\eta }_1 < \eta _1^{\max }} AIC( {M( {{\eta }_1} )} )$ $M( {{\eta }_1} ):{\rm{\ }}{y}_{ij} = {\beta }_0 + {\gamma }_{0j} + {\rm{\beta }}_{\rm{r}}^{( 1 )}{x}_r\cdot I( {{x}_r < {\eta }_1} ) + {\rm{\beta }}{{\rm{'}}}_{\rm{r}}x{{\rm{'}}}_r\cdot I( {{\eta }_1 \ge {\rm{\ }}{x}_r} ) + \mathop \sum \nolimits_{k = 1,{\rm{\ }}k{\rm{\ }} \ne r{\rm{\ }}}^K {\beta }_k{x}_{kij}$ $+ {\rm{\ }}\mathop \sum \nolimits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij}$
4:	For $1 < p \le P$, fix values of $\{ {{\eta }_1,\ \ldots ,{\eta }_{p - 1}} \}$ in model to compute ${\eta }_p$ as follows: $\mathop {{\rm{argmin}}}\nolimits_{\eta _p^{\min } < {\eta }_p < \eta _p^{\max }} AIC( {M( {{\eta }_p} )} )$ $M( {{\eta }_p} ):\ {y}_{ij} = {\beta }_0 + {\gamma }_{0j} + {\rm{\beta }}_{\rm{r}}^{( 1 )}{x}_r\cdot I( {{x}_r < {\eta }_1} ) + \cdots + {\rm{\ \beta }}_{\rm{r}}^{( p )}{x}_r\cdot I( {{\eta }_{p - 1} \le {\rm{\ }}{x}_r < {\eta }_p} ) + {\rm{\beta }}{{\rm{'}}}_{\rm{r}}x{'}_r\cdot I( {{\eta }_p \ge {\rm{\ }}{x}_r} ) + \mathop \sum \nolimits_{k = 1,{\rm{\ }}k{\rm{\ }} \ne r{\rm{\ }}}^K {\beta }_k{x}_{kij} + {\rm{\ }}\mathop \sum \nolimits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij}$
Output: Segmented model with change points H as shown in Equation (5).

Table 1. HITL Method for Segmented Mixed-Effects Modeling

4 Experimental Setup

To demonstrate the utility and effectiveness of our method, we apply it to model high-order pairwise relationships in four different applications across three real-world wearable datasets: WellbuiltforWellbeing, HospitalMonitoring, and BeerCrawl. We describe each of the datasets in the next section followed by analysis and findings.

4.1 Data

4.1.1 WellbuiltforWellbeing.

The Wellbuilt for Wellbeing (WB2) project [60] was a 16-month multiphase field study funded by the U.S. General Services Administration to better understand the influence of the office environment on human health, comfort, and performance. In the study, self-described healthy adult workers involved in a variety of office-based roles for the U.S. government were recruited across four federal office buildings across the country. Participants wore two sensors for 3 days while carrying out their day-to-day activities, a heart and physical activity monitor, and a personal environment quality sensor-based device. The study also included experience sampling mobile surveys to collect individuals’ perceived psychological responses at periodic intervals of 1 to 2 hours. Post processing, the dataset contained around 3,000 hours of wearables data with a wide range of variables from 231 participants. More details about the field study setup and variables can be found in the work of Lindberg et al. [6].

For our study, we analyze two pairwise associations from this dataset: that of ambient sound level and HRV, and that of instantaneous activity and HRV. HRV is the variability between heart beats and is considered as a proxy measure for the physiological wellbeing of a person—that is, the higher the variability, the higher the physical wellbeing [61]. Among different HRV measures, the mean of standard deviation for all successive R-R intervals (SDNN) measured in milliseconds reflects the overall activity in the autonomous nervous system and is widely used as an indicator of better health and wellbeing [62]. Physical activity levels were assessed in g (i.e., 1 unit of gravitational force) from a triaxial accelerometer sensor and sound levels were measured in dBA (i.e., decibel weighted according to human ear hearing) using separate neck-worn sensors. The raw data from multiple wearables were aggregated at 5-minute intervals to be integrated with the heart rate monitor sensor used for computing SDNN [63]. We consider appropriate covariates in our models including person-level fixed effects (i.e., age, gender, BMI, worktype), time of the day, and day of the week after closely examining all variables collected in the Wellbuilt for Wellbeing project.

4.1.2 HospitalMonitoring.

The HospitalMonitoring dataset contains vital signs data recorded from patients undergoing anesthesia at the Royal Adelaide Hospital [64]. It is publicly accessible from the University of Queensland website.¹ Data was collected for 32 cases using multiple wearables and stationary sensors including the electrocardiograph, pulse oximeter, capnograph, noninvasive arterial blood pressure monitor, airway flow, pressure monitor, Y-piece spirometer, electroencephalogram (EMG) monitor, and arterial blood pressure monitor [64]. The processed data is aggregated at 1-second intervals and has 51 variables out of which we select a meaningful subset for our analysis.

For our study, we analyze the pairwise association between the ST segment index and airway respiratory rate. In electrocardiography, the ST segment connects the QRS complex and the T wave and its depression or elevation is related to acute cardiovascular conditions including myocardial ischemia, infarction, and arrhythmia [65]. The human respiratory rate is measured by counting the number of breaths per minute, with typical values ranging from 12 to 16 for a healthy adult. Respiration rate has been related to abnormalities in oxygen saturation, aging, and cardiovascular diseases and has been widely adopted as part of early warning systems [66]. In our model, we consider heart rate, oxygen saturation, and perfusion index as covariates after examining collinearity and cross correlations among all features and potential confounding effects.

4.1.3 BeerCrawl.

The BeerCrawl dataset contains blood alcohol content and movement information recorded in a field study by Killian et al. [4]. It is publicly accessible from the University of California Irvine (UCI) dataset repository.² Transdermal alcohol content (TAC) was measured using an ankle bracelet wearable and the movement data was captured using raw accelerometer readings from mobile phones for 20 students participating in an annual college bar crawl event. The TAC data was sampled every 30 minutes, whereas accelerator readings were available at a more granular level leading to more than 30M samples across participants. TAC has been shown to be a more reliable indicator of sustained alcohol use as compared to self-reporting [67].

For our study, we analyze the pairwise association between the raw z-axis readings from the tri-axial accelerometer and TAC values in the dataset. Prior studies have proposed several features using accelerometer readings that are related to a person's gait, activities, and wellbeing, with z-axis values contributing significantly to their variability [4, 68]. The units of TAC and accelerometer are g/dL and m/s², respectively. In our model, we consider the x- and y-axis coordinate values as covariates. The accelerometer is mapped to the TAC monitor readings at the minute level.

Table 2 shows a summary of the datasets used in our study. The datasets and respective input-outcome associations were chosen to demonstrate variety of scenarios with higher-order pairwise associations across different problem domains.

Table 2.

Dataset	Size (Rows; Columns)	Accessibility	Outcome	Input	Input Statistics (Mean, SD, Min, Max)
WellbuiltforWellbeing [60]	(31,557; 7)	Not public	SDNN (HRV)	Sound (sound level in dBA)	(50.24, 8.69, 0.00, 87.80)
				Activity (activity level in g)	(0.1738, 0.3187, 0.0000, 3.0000)
HospitalMonitoring [64]	(83,861; 4)	Public	RR (respiration rate)	ST2 (ST segment index)	(0.0635, 0.3969, –1.1000, 1.3000)
BeerCrawl [4]	(8,273; 3)	Public	TAC (blood alcohol level)	z (z-axis of accelerometer)	(0.0503, 0.1840, –0.6705, 0.6676)

Table 2. Summary of Real-World Wearables Datasets Used in Our Study

4.2 Data Preprocessing and Model Assumptions

Training and test samples were partitioned in a 75:25 ratio for performance evaluation. A variance component structure for the covariance matrix of the random effects coefficients is assumed in the mixed-effects regression models. The input variable of interest was included as a fixed effect as well as random effect in the model. We compared models having uncorrelated residual errors with counterparts with autoregressive error residuals and observed that the model fit did not improve significantly after controlling for temporal correlations. We also compared different error distributions and found the normal distribution to be most suitable. Hence, our model is represented as Equation (1) without any special link function or autocorrelation terms.

4.3 Results

We fit mixed-effects models using the three datasets for explaining the following four input-outcome associations: Sound-SDNN, Activity-SDNN, ST2-RR, and z-TAC. The corresponding component smooth functions for the partial effects from GAMM are shown in Figure 1. The smooth functions for Sound-SDNN and Activity-SDNN approximate second-order and third-order polynomial curves, whereas the smooth functions of ST2-RR and z-TAC indicate a higher-order curve.

As part of the HITL step, we made the following model interventions. Figure 1(a) shows a maxima around the 50 to 60 dBA range, whereas Figure 1(b) shows a maximal range between 0.2 and 1 followed by a decrease in the smooth function until it reaches a minima at around 2.5, after which the function again turns upward. The extrema in Figure 1(c) are more subtle with the confidence interval being most conservative around ST2 = 0.0. Figure 1(d) clearly depicts three maxima and two minima within the main range, whereas a minima exists around z = 0.6, which may be ignored due its extreme right position in the input distribution. Based on these observations of the smooth functions, we chose $P\ = \ 1$, $P\ = \ 2$, $P\ = \ 1$, and $P\ = \ 5$ as number of change points for associations Sound-SDNN, Activity-SDNN, ST2-RR, and z-TAC, respectively. Through visual inspection, we set initial change point estimates as well as box constraints for each of the pairwise associations.

We compared the prediction performance of mixed-effects models fitted using our method with the following benchmarks: (i) model with inputs as first-order effects (i.e., linear), (ii) model with inputs as first-order and second-order effects (i.e., curvilinear), (iii) segmented inputs using change points identified by the ML method [17], and (iv) segmented inputs using visually identified change points (i.e., visual). The fixed-effects model was used as a baseline, representing the case when only fixed effects are considered in the mixed-effects regression. The model with linear inputs (i.e., first-order effects only) is a benchmark that emphasizes simplicity over better model fit through capture of higher-order associations. The curvilinear model is more commonly used in prior literature as it improves model fit when compared to the linear effects only model, but at the cost of lower interpretability of its higher-order coefficients. The segmented models with change points determined visually or using the fully automated ML approach can be considered as the state-of-the-art approaches for segmented mixed-effects modeling for capturing higher-order associations. Other methods in machine learning or statistical modeling such as multivariate adaptive regression splines or nonparametric analysis are not considered as their objective of capturing higher-order patterns is not primarily toward explanatory modeling but toward making predictions.

We performed repeated fourfold cross validation with 10 iterations (i.e., 40 runs in total) for evaluating the performance of our method against the benchmarks across the three datasets. Table 3 shows the mean and standard deviation (in parentheses) of performance metrics (R-squared, root mean squared error (RMSE), and mean absolute prediction error (MAPE)) of our method and benchmarks across the three datasets and four higher-order association scenarios. A higher value of R-squared and lower values of RMSE and MAPE are preferred. Statistical significance of better performance of our method over each benchmark was tested using the Tukey-Kramer pairwise comparison test on ANOVA fit over the performance metrics of our method and benchmarks. The R-squared values and error estimates for the best-performing models are highlighted. Our method has a statistically significant improvement in the prediction performance over existing higher-order mixed-effects modeling benchmarks for the WellbuiltforWellbeing and HospitalMonitoring datasets. For the BeerCrawl dataset, our method is better than other benchmarks except the visual method, but the performance difference between the visual method and our method is not statistically significant. Although the ML approach is popular for GLMMs with the R package segmented [69], it is not very compatible for wearables data in terms of setting the number of change points and convergence. And although the visual method performs well for the BeerCrawl dataset, the complete dependence on human inputs and rationalization renders it less robust as is evident from its significant lower performance in the other two datasets.

Table 3.

Model	WellbuiltforWellbeing: HRV (Sound)			WellbuiltforWellbeing: HRV (Activity)			HospitalMonitoring: RR			BeerCrawl: TAC
	R-sq.	RMSE (ms)	MAPE (%)	R-sq.	RMSE	MAPE	R-sq.	RMSE (br/min)	MAPE (%)	R-sq.	RMSE	MAPE
	R-sq.	RMSE (ms)	MAPE (%)	R-sq.	(ms)	(%)	R-sq.	RMSE (br/min)	MAPE (%)	R-sq.	(g/dL)	(%)
Fixed effects	0.5168 (0.01)***	17.78 (0.03)***	25.81 (0.05)***	0.5557 (0.01)***	17.54 (0.02)***	26.12 (0.07)***	0.7335 (0.00)***	2.58 (0.00)***	5.47 (0.00)***	0.6007 (0.01)***	0.04 (0.00)***	70.38 (0.72)***
Linear	0.5237 (0.01)***	17.65 (0.03)***	25.47 (0.05)***	0.6128 (0.01)***	16.65 (0.08)***	24.44 (0.10)***	0.8781 (0.00)***	2.36 (0.00)***	4.92 (0.00)***	0.6003 (0.01)***	0.0377 (0.00)***	66.54 (0.73)***
Curvilinear	0.5876 (0.00)**	16.83 (0.04)**	23.78 (0.06)***	0.6630 (0.01)***	15.64 (0.05)***	23.12 (0.06)***	0.8875 (0.00)***	2.36 (0.00)***	4.92 (0.00)***	0.5995 (0.01)***	0.0377 (0.00)***	66.56 (0.72)***
Visual	0.5891 (0.00)	16.81 (0.04)	23.74 (0.06)	0.6719 (0.01)***	15.70 (0.06)***	23.01 (0.07)***	0.8856 (0.00)***	2.35 (0.00)***	4.85 (0.00)***	0.6419 (0.01)	0.0369 (0.00)*	63.09 (0.72)
ML	0.5860 (0.00)***	16.82 (0.04)**	23.80 (0.06)***	0.6734 (0.01)***	15.69 (0.06)***	23.01 (0.07)***	0.8810 (0.00)***	2.35 (0.00)***	4.84 (0.00)***	0.6011 (0.01)***	0.0380 (0.00)***	66.57 (0.72)***
Our method	0.5900 (0.00)	16.80 (0.04)	23.72 (0.06)	0.7628 (0.01)	14.93 (0.09)	21.99 (0.10)	0.9201 (0.00)	2.33 (0.00)	4.82 (0.00)	0.6412 (0.01)	0.0373 (0.00)	63.17 (0.70)

Table 3. Model Fit and Predictive Performance Comparison of Segmented Multilevel Models

Statistical significance of the Tukey Kramer test for comparison of performance metrics of benchmark with HITL.

*** = p < .01, ** = p < 0.05, * = p < 0.1.

In addition to better model fit and prediction performance, our method is able to generate better interpretable models. The fixed effects of segmented inputs across all three datasets are shown in Table 4. In the WellbuiltforWellbeing dataset, HRV increases by 0.19 ms/dBA for sound levels less than 51 dBA, indicating that physical wellbeing improves with every unit increase in sound in quiet environments. Higher activity levels such as brisk walking (i.e., activity ≥ 0.9) decreases SDNN by 15.21 ms/g, whereas moderate walking speed (0.9 > Activity ≥ 0.21) is related to a steep increase of 90.49 ms/g in SDNN. Assuming that brisk walking is confounded by an intention to reach meetings on time and therefore is related to higher stress, the steep gradient in the moderate walking range underscores the value of intermittent low-level activity on physiological wellbeing in office spaces. In the HospitalMonitoring dataset, we observe that a unit increase in the ST segment index beyond –0.18 is related to an increase in the respiration rate by 2.28 breaths/minute. This finding underscores the importance of looking for elevated values of the ST segment as reported in the medical literature [65]. It also hints at a possible association between acute cardiovascular events and elevation in the respiration rate in bedridden patients. In the BeerCrawl dataset, the z-axis indicates acceleration perpendicular to the phone screen by participants. Although experimental research is required to understand the precise interpretations of the coefficients identified in our study, our study does uncover significant associative patterns between z-axis values and blood alcohol levels across different z-axis range segments. Higher inebriety is associated with an increase in acceleration at the upper range of z (i.e., 0.41 > z ≥ –0.01) and also associated with a decrease in the lower range of z (i.e., –0.01 > z ≥ –0.15). Table 4 also shows that the preceding interpretable pairwise associative patterns are not evident from linear and curvilinear inputs in the mixed-effects models.

Table 4.

Dataset/Outcomes	Input	Coefficient (SE)
		Segmented	Linear	Curvilinear
WellbuiltforWellbeing/ SDNN	Sound		0.07 (0.02)***	0.09 (0.02)***
	Sound²			–0.01 (0.00)***
	Sound < 51	0.19 (0.04)***
	Sound ≥ 51	–0.01 (0.03)
	Activity		18.19 (1.27)***	46.09 (1.68)***
	Activity²			–43.39 (1.64)***
	Activity < 0.21	9.00 (1.41)***
	0.9 > Activity ≥ 0.21	90.49 (3.87)***
	Activity ≥ 0.9	–15.21 (1.46)***
HospitalMonitoring/RR	ST2		1.63 (0.85)	1.75 (0.85)**
	ST2²			–0.44 (–4.09)***
	ST2 < –0.18	1.51 (1.92)
	ST2 ≥ –0.18	2.28 (0.95)**
BeerCrawl/TAC	z		–0.0073 (0.0104)	–0.0061 (0.0098)
	z²			–0.026 (0.0102)**
	z < –0.44	–0.0246 (0.0205)
	–0.2 > z ≥ –0.44	–0.0318 (0.0167)
	–0.15 > z ≥ –0.2	–0.0340 (0.0390)
	–0.01 > z ≥ –0.15	–0.2014 (0.0734)***
	0.41 > z ≥ –0.01	0.0857 (0.0279)***
	z ≥ 0.41	0.0030 (0.0182)

Table 4. Fixed Effects of Segmented, Linear, and Curvilinear Models Across All Three Datasets

*** = p < .01, ** = p < .05.

Figure 2 shows a visual representation of the segmented model coefficients compared to coefficients from linear and curvilinear models. Coincidentally, the shapes of the piecewise relationships for each of the pairwise association resemble the corresponding smooth functions shown in Figure 1, reinstating the importance of our HITL approach to train robust interpretable segmented inputs in the mixed-effects models.

Fig. 2.

5 Discussion and Conclusion

In this study, we presented the problem of developing an interpretable model that captures piecewise pairwise associations between different modalities captured by wearables. Since existing methods for segmented modeling for mixed-effect regression are insufficient to determine robust and verifiable change point, our method is timely with increasing research applications utilizing wearables in a natural experimental setup. Our method involves the inspection of smooth functions of pairwise associations captured using GAMM, followed by using Brent's method to sequentially position change points optimizing model fit. Our method not only uses analytical tools to determine change points but also utilizes user discretion to control the number of change points and its localization. For example, it is often desirable to avoid change points at extremities as data corresponding to these segments may be very sparse, rendering inference unreliable. We apply our method to three different wearables datasets and show that not only is it effective in terms of improving model fit and prediction performance but also significantly enhances model interpretability and ability to derive meaningful inferences.

5.1 Managerial Implications

Our method and analysis have several managerial implications. Our study provides a novel tool to analyze wearables data, thus boosting the value for storing and processing of large amounts of big data generated by wearables. Our HITL-based segmented modeling method can be used in a wide range of wearables applications such as patient monitoring systems, military fitness management programs, smart diet applications, and COVID-19 contact tracing. Our analysis over the three wearables datasets presents interesting pairwise associations. The positive relationship between sound level and physical wellbeing measure below the range of 51 dBA informs workplace design practices on the need for further examination of sound level effects on employee health for different sound level ranges. A higher gradient of an activity-wellbeing relationship in the lower range of activity provides additional empirical evidence on the value of low-intensity/intermittent activities on elevating instantaneous stress and improving wellbeing. The significant association between cardiovascular wellness measure and respiration rate after a certain threshold of the ST segment index solicits clinical researchers to further examine inter-relationships between pulmonary and cardiovascular wellness indices to improve on existing hospital monitoring and early warning systems. Finally, the association between a dimension of raw accelerometer data and extrinsic phenomena such as alcohol consumption stresses the value of looking at raw data in addition to expert-engineered features such as gait variability and the number of continuous steps.

5.2 Contribution to IS Research

Predictive modeling and statistical modeling in analytics go side-by-side as one predicts the future using existing data, focusing on informing us on the question “What will be,” whereas the other explicates hidden patterns and tells us about “What is” with respect to a phenomenon. Both of them are important and require attention to optimize the utility of the generated data. As the number of wearable technology-based applications increases in the future, the quantum of available data to analyze will exponentially increase and warrant more and more advancements in explainable modeling for meaningful interpretations of patterns. In this study, we introduce a new method to address the design challenge of representing nonlinear associative patterns in wearables data. Our contribution is timely in IS research, as the discipline is widening its scope in design science as well as explanatory modeling applications by using novel data sources such as wearables [70]. WDA is a promising area in IS [5, 19], opening a wide range of research applications owing to the following two reasons: the ubiquitous nature of wearables in today's lifestyle, and the promise of wearables to generate rich, personalized, temporal, and highly grained information content. We therefore posit that our contributions through a novel interpretable modeling method for addressing challenges in WDA lays the foundation for promising research in IS using data generated from wearables.

5.3 Limitations

There are some caveats and limitations to our study. We have focused on the design science problem of developing an interpretable modeling method but do not delve into the subject of determining the significance of input variables themselves. In addition, our method by itself does not imply causation, although it can be applied to any explanatory modeling scenario including causal or quasi-causal experimental settings. If curvilinear effects are absent, the segmented modeling approach should be avoided to prevent overfitting. The modeling approach described in this study is useful when higher-order association is predetermined between pairs of repeated measures and there is a need to better explain these associations for making inferences. For high-dimensional large datasets, GAMM can take longer time to fit, and the change point optimization can be tedious for the analyst. A few ways to avoid this problem are to apply feature selection, variable transformation, and outlier detection procedures before examining pairwise associations using our method. Next, our HITL approach involves human inputs and therefore may still be susceptible to human errors and biases, despite the fine-tuning step using the optimization procedure. One way of reducing such potential errors is to consult domain experts post determination of change point from the optimization procedure. Finally, it is worth noting that our method caters to the problem of improving interpretability of glass-box models, at the cost of increased bias and limited predictive power when compared to black-box data mining models [28].

5.4 Conclusion

With the increasing availability of wearables, we can measure and understand different health phenomena at a highly granular level. We propose an HITL method for accurate estimation of change points in segmented mixed-effects regression facilitating the interpretations of pairwise associations of variables in wearables data. Our method is robust and efficient, and the resultant segmented models provide better prediction accuracy than state-of-the-art alternatives for a given problem. Our proposed method is empirically validated, more reliable due to human verification, and provides better interpretable results. Our approach can be generalized to other areas of IS where nonlinear pairwise associations are anticipated.

Footnotes

HospitalMonitoring dataset URL: https://outbox.eait.uq.edu.au/uqdliu3/uqvitalsignsdataset/index.html.

BeerCrawl dataset URL: https://archive.ics.uci.edu/ml/datasets/Bar+Crawl%3A+Detecting+Heavy+Drinking.

References

[1]

GlobalNewsWire. 2022. Smart Wearables Market and Wearable Apps Market Global Share Insights 2021. Retrieved January 11, 2022 from https://www.globenewswire.com/news-release/2021/12/15/2352316/0/en/Smart-Wearables-Market-and-Wearable-Apps-Market-Global-Share-Insights-2021-Top-Countries-Data-Future-Growth-Developments-Impact-of-Covid-19-on-Industry-Size-Production-Cost-Value-V.html.

Input: Mixed-effects model with significant higher-order coefficients for input variable, \({x}_r\)
1:	Fit a GAMM with input \({x}_r\) represented as a nonparametric spline (Equation (1)).
2:	Inspect the component smooth function plot \({f}_r( . )\) to identify number of change points \(P = \| H \|\), starting points \(\eta _p^0\) and box constraints \(\{ {\eta _p^{min},\eta _p^{max}} \}\) for corresponding change points \({\eta }_p \in H\).
3:	For \(p\ = 1\), compute \({\eta }_1\) as follows: \(\mathop {{\rm{argmin}}}\nolimits_{\eta _1^{\min } < {\eta }_1 < \eta _1^{\max }} AIC( {M( {{\eta }_1} )} )\) \(M( {{\eta }_1} ):{\rm{\ }}{y}_{ij} = {\beta }_0 + {\gamma }_{0j} + {\rm{\beta }}_{\rm{r}}^{( 1 )}{x}_r\cdot I( {{x}_r < {\eta }_1} ) + {\rm{\beta }}{{\rm{'}}}_{\rm{r}}x{{\rm{'}}}_r\cdot I( {{\eta }_1 \ge {\rm{\ }}{x}_r} ) + \mathop \sum \nolimits_{k = 1,{\rm{\ }}k{\rm{\ }} \ne r{\rm{\ }}}^K {\beta }_k{x}_{kij}\) \(+ {\rm{\ }}\mathop \sum \nolimits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij}\)
4:	For \(1 < p \le P\), fix values of \(\{ {{\eta }_1,\ \ldots ,{\eta }_{p - 1}} \}\) in model to compute \({\eta }_p\) as follows: \(\mathop {{\rm{argmin}}}\nolimits_{\eta _p^{\min } < {\eta }_p < \eta _p^{\max }} AIC( {M( {{\eta }_p} )} )\) \(M( {{\eta }_p} ):\ {y}_{ij} = {\beta }_0 + {\gamma }_{0j} + {\rm{\beta }}_{\rm{r}}^{( 1 )}{x}_r\cdot I( {{x}_r < {\eta }_1} ) + \cdots + {\rm{\ \beta }}_{\rm{r}}^{( p )}{x}_r\cdot I( {{\eta }_{p - 1} \le {\rm{\ }}{x}_r < {\eta }_p} ) + {\rm{\beta }}{{\rm{'}}}_{\rm{r}}x{'}_r\cdot I( {{\eta }_p \ge {\rm{\ }}{x}_r} ) + \mathop \sum \nolimits_{k = 1,{\rm{\ }}k{\rm{\ }} \ne r{\rm{\ }}}^K {\beta }_k{x}_{kij} + {\rm{\ }}\mathop \sum \nolimits_{m = 1}^M {\gamma }_{mj}{z}_{mij} + {\epsilon }_{ij}\)
Output: Segmented model with change points H as shown in Equation (5).

Abstract

1 Introduction

2 Background and Related Work

2.1 Wearable Data Analytics

2.2 Segmented Modeling

2.3 HITL Analytics Methods

3 Our Method

4 Experimental Setup

4.1 Data

4.1.1 WellbuiltforWellbeing.

4.1.2 HospitalMonitoring.

4.1.3 BeerCrawl.

4.2 Data Preprocessing and Model Assumptions

4.3 Results

5 Discussion and Conclusion

5.1 Managerial Implications

5.2 Contribution to IS Research

5.3 Limitations

5.4 Conclusion

Footnotes

References

Cited By

Index Terms

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