1.1 Sensors can Inform Personalized Behavior-Change Interventions

In 2008, the U.S. Department of Health and Human Services issued its Physical Activity Guidelines for Americans report [7] that provides specific science-based guidelines for people of various ages to improve their health through physical activity. It recommends that children and adolescents obtain at least 60 minutes of physical activity per day, adults obtain at least 150 minutes of moderate or 75 minutes of vigorous intensity activity, and older adults try to obtain as much physical activity as younger adults. While these recommendations are based on scientific evidence of health benefits from population studies, on an individual level, a person may find such recommendations meaningless in terms of motivation to increase physical activity if he or she already meets the recommendation or feels that there is no hope of ever meeting the recommendation.

In some cases, such group standards can do more harm than good. Individuals who do not meet healthy guidelines may be ostracized by society [8], and this may lead to negative emotions or ambivalence toward healthy behavior. This suggests that while national population-based guidelines may serve as crude goals for individuals, much greater attention needs to be placed on “personalized” behavioral interventions. Within intervention programs, people need to be thought of as individuals. The ability for one person to be more physically active than another relates to many factors, including their personal motivation and barriers toward exercise. Thus, personalized intervention plans are more likely to be successful compared to intervention programs that are simply based on blindly encouraging people to take action [6]. Indeed, recent “calls to action” within the cardiovascular health community recognize the importance of behavior-change interventions, and specifically the need to combine individual-level with population-based health promotion strategies [9].

Related to the concept of personalized behavioral interventions are “adaptive” interventions. Collins et al. [10] provide a conceptual framework in which interventions are not “fixed” – every subject receiving the same format and dose of intervention – but instead, the characteristics of the intervention are tailored to individuals. Moreover, this allows interventions to change in time for a person based on their individual-level characteristics.

Body sensors can play an important role in collecting measures of physical activity to better tailor interventions to the individual. Specifically, using body sensors over time can help monitor levels of physical activity at baseline pre-intervention, changes in physical activity that occur during an intervention, and the degree to which individuals maintain improvements in physical activity post-intervention. These measures may be useful feedback to the individual, or the people working with the individual, to encourage them to change their behavior. The use of sensors is increasingly being recognized as an important departure from traditional behavioral assessments that are based on only a few, infrequent, unclear concepts – often questionnaires or qualitative interviews – rather than continuous clearly defined objective measures [11]. Indeed, sensors may play an important role in moving away from a one-size-fits-all approach to interventions to a more patient/subject-centric form of adaptive behavioral intervention.

3.1 Critical Power (CP) Model

The CP model describes the capacity of an individual to sustain particular work rates as a function of time (t). In this way, the model represents the relationship between exercise intensity and duration for an individual. The CP is defined as the power that can be sustained without fatigue for a long time. Then we can further define power P=work/time and finally $W\prime$ as the finite amount of energy that is available for work above the critical power:

$W\prime =(P–CP)t$ (1)

(1)

Morton [14] presents four assumptions of the CP model:

This model is useful for describing power duration for maximal exercise lasting from 2 to 30 minutes. As such, the CP model serves as a useful tool for devising pacing and tactical strategies in relatively short athletic competitions. But it can also provide a basis for individualized workout intensities during training, exercise, and rehabilitation procedures. Furthermore, the model is amenable to body sensor measurements. For example, exercise above or below CP results in differences in maximal oxygen consumption.

There are limitations to the CP model, especially when we need to account for intermittent exercises and need to optimize interval workout prescription. Morton and Billat [15] extended the 2-parameter CP model as follows:

$t=n(t_w+t_r)+\{W\prime -n[(P_w-CP)t_w-(CP-P_r)t_r\left]\right\}/(p_w–CP)$ (2)

(2)

where t is the total endurance time, n is the number of intervals, t_w and t_r are the duration of the work and recovery phases in each interval, respectively, and P_w and P_r are power outputs during the work and rest phases, respectively.

3.2 Banister Impulse Response (IR) Model

In contrast to the use of CP for modeling individual exercise sessions or interval workouts, there is a need to model the effects of exercise over time, i.e., training. The IR model relates performance ability at a specific time to the cumulative effects of prior training loads. It describes the individual exercise dose-response relationship and handles the nonlinear time dependence and individuality in a single framework.

The model is basically a first-order differential equation describing a person’s change in performance as a function of time. The solution of performance p(t) is equal to the initial performance level p(0) plus positive training effect (PTE = “fitness”) minus the negative training effect (NTE = “fatigue”). Both PTE and NTE are expected solutions to first-order differential equation exponentials weighted with some coefficients that are specific to the activity task and the subject. The performance is a nonlinear function of training. Again, body sensors can play a useful role in monitoring changes in performance over time and successive training sessions to provide empirical data to fit such models.

In summary, both CP and IR models can be useful for guiding workout design and long-term planning, respectively. Performance models can serve as an avenue to guide professional reasoning and systematize the trial-and-error adjustments normally featured in exercise protocols. Moreover, these models also can help in identifying what feedback and intervention should be administered (e.g., Is the individual meeting the expectations of CP for a specific workout session? Is the individual training in a way that is most effective?).

Unfortunately, these models assume that individuals are motivated to optimize their exercises. For individuals just embarking on healthy lifestyle changes, or when a healthcare provider is prescribing behavioral intervention, such an assumption cannot be guaranteed. Hence, in the following, we discuss the issue of behavior-change modeling.

4.1 A Framework for Quantitative Modeling of Physical Activity Behavior-Change Interventions

Behavior change is inherently a difficult process due to the opposite of many of the aforementioned core constructs. Individuals may not progress linearly through the stages, but may move forward as well as backward through the stages as they change cognitively and physically. As previously mentioned, forward progression through the stages can be the result of a specific intervention program of some sort aimed at helping individuals change their behavior. In our research, we have been working with health coaches who help individuals change behavior through a process called “motivational interviewing,” which involves exploring a person’s readiness to change through communication and listen strategies, employing empathy, and collaborating to set goals for behavior change [21]. It is a method for achieving personalized adaptive behavioral interventions that we described at the outset of this chapter.

As an example, consider Figure 1, which illustrates a physical activity intervention program in which a health coach interacts with a subject using motivational interviewing techniques over some period of time (e.g., a 6-month period). During this period, there is a feedback cycle in which the health coach provides motivational interviewing to the subject who is conditioned by various inherent characteristics (e.g., gender, age, race, culture, environment, etc.), which in turn affects his exercise (measured by sensors) and cognition (self-efficacy, decisional-balance, and temptation measured by questionnaires). The results of changes in exercise and cognition affect the type of motivational interviewing that the coach performs with the subject. Hence, this sort of feedback enables the adaptive nature of this exercise intervention.

Also consider what data from this adaptive intervention may look like from a study design and a time series perspective (Figure 2). As the subject is recruited into the intervention study, they are given a baseline assessment before any intervention activities begin. The goal of the baseline assessment is to determine their cognitive state toward physical activity (i.e., to figure out where they are in the stages of change). Also, sensors may be worn during this baseline assessment period to determine the individual’s “normal” levels of physical activity and capabilities. It may take a few repeated measurements over a few weeks to obtain reliable baseline estimates. Let’s assume that the health coach finds that the individual has no interest in physical activity or in changing his levels of physical activity. The subject would be in the precontemplative stage. As the intervention begins, the health coach will start to provide feedback to the subject based on observations of body sensor data as well as the results of ongoing cognitive assessments using questionnaires. The use of body sensors to continually evaluate physical activity levels is novel and potentially more accurate compared to the bulk of prior transtheoretical model interventions that have only used self-reported exercise questionnaires (e.g., the 7-day Physical Activity Recall, PARQ) [6].

Based on the stage of change in which the person is at, a health coach may conduct motivational interviewing to help the person identify one or more processes of change that could be used to help the individual transition to the next stage of change. Questionnaires may be used to assess the stage of change to which the individual belongs. Additionally, cognitive assessments may be used to assess changes in the mediators (self-efficacy, pros versus cons, and temptations). Specific questionnaires and assessments are presented later. The interviewing provided by the coach could be tailored to the results of the assessments. Over time, through such personalized and stage-specific intervention, the coach may help the subject establish an exercise plan, which would place the subject in the preparation stage. And when the subject begins to exercise, the various improvements in physical activity would be measureable using the body sensors. Ultimately, the study would assess changes in physical activity during the intervention and at follow-up at the end of the intervention compared to the levels of physical activity at baseline.

4.2 Assessing Stages of Change

In order to monitor a person’s progression through the stages of change we need some way to assess his stage. Various algorithms have been developed for exercise-related stages of change, including Marcus and Simkin [22], who created the Stage of Exercise Behavior Change (SEBC) questionnaire to assign people into stages. A related approach called the Stage of Exercise Scale (SOES) developed by Cardinal et al. [23–25] asks individuals to place themselves on a 5-rung ladder, which determines their stage. The validity of these questionnaires has typically been evaluated if exercise increases as individuals progress through their assigned stages. This correlation between physical activity and stage change over time is consistent with the framework we have described in Figure 2.

Aside from assessment of stage of change, other questionnaire-based assessments of mediating factors have been developed. For instance, assessments have been developed for decisional balance [17], self-efficacy [26], and temptations [27]. These questionnaires may be used to estimate the probability of transitioning between stages based on each of these factors, respectively.

In all cases, results of such questionnaires, as is common in psychological studies, are variables that are either binary or ordinal ratings. Moreover, despite having undergone various validation studies, when applied at the individual person level, they should be viewed as only indicators, subject to error, rather than absolute assessments [28].

As a concrete example, consider the following questionnaire adapted from Marcus, Rossi et al. [17] aimed at assessing stages of change:

Note that the questions lead to ordinal, scored responses. Asked over large numbers of people, we would generally find the scored responses to each question fit normal distributions. Thresholds may be specified such that those scoring low in questions 1 and 2 would indicate subjects in the precontemplation stage. Those scoring low in question 1 and high in question 2 would indicate subjects in contemplation. Those scoring high in question 1 and low in question 3 would indicate subjects in preparation. Those scoring high in questions 1 and 3, but low in question 4 would indicate subjects in the action stage. And those scoring high in question 4 would indicate those in maintenance.

Although these assessments have traditionally been conducted fairly infrequently over the course of an intervention, new technologies may play an emerging role in more frequent (e.g., daily) assessments. Approaches like Ecological Momentary Assessment [29], in which subjects are asked in-the-moment during random or fixed-interval times about their feelings and attitudes, can be conducted on more pervasive technologies, such as personal computers, phones, and tablets.

4.3 Opportunities to Use Behavior-Change Models to Guide Intervention Programs

Over the last several years, progress has been made toward applying engineering control theory approaches to the challenges of understanding behavior-change interventions. As we have alluded to in Figure 2, data from behavioral interventions can be viewed as time series. Moreover, particularly for adaptive interventions, in which intervention characteristics change over time, more formal modeling of the feedback process (Figure 1) can benefit from more generic studies of feedback for control systems. Notable literature includes the work of Rivera et al. [30], who applied ordinary differential equations to an adaptive behavioral intervention, and Böckenholt [28], who examined the use of a Markov model in cases where there are stages (i.e., states) associated with the behavior-change process.

Because the stages of change are essentially states, they are amenable to implementation via a Markov model, whereby a person belongs to a given state at any given point in time, transitions between states are governed by probabilistic processes, and future state depends only on current state. Böckenholt [28] combines two main components to end up with a continuous-time latent Markov (CT-LM) model for behavior change. The first component considers that binary or ordinal responses to typical behavioral surveys depend upon a latent (not directly observable) state to which a person belongs. Second, changes in responses over time are modeled by a stochastic process that governs transitions between states. Detailed derivations of the model are presented in Böckenholt [28], which are discussed briefly below.

Based on prior work by Samejima [31,32], Böckenholt describes the probabilistic nature of binary or ordinal responses to questionnaires as being a function of the latent state in which a person resides:

$\mathit{Pr}(y=j|s)=\Phi \left(\frac{{\tau }_{j+1}-{\mu }_s}{{\sigma }_s}\right)-\Phi \left(\frac{{\tau }_j-{\mu }_s}{{\sigma }_s}\right)$ (3)

(3)

where the probability that a variable $y$ (i.e., a question in a questionnaire) takes on a response $j$ is conditional on the characteristics of the latent state $s$, and is related to the difference of two normal cumulative distribution functions $\mathrm{\Phi }$ defined by the mean ${\mu }_s$ and standard deviation ${\sigma }_s$, for a set of lower and upper thresholds ${\tau }_j$ and ${\tau }_{j+1}$, respectively.

Due to the challenges of collecting and processing body sensor data that we described earlier, physical activity data are also subject to error. Thus, they may also be amenable to such a probabilistic treatment as questionnaire response data, in which physical activity levels determined from sensor measurements are ranked into ordinal levels.

Next, because the responses are dependent upon the state $s$ to which an individual belongs, we need to define switching probabilities between states. A person can belong to only one state at any time. In the CT-LM model, states are discrete, defined by the above parameters ${\mu }_s$ and ${\sigma }_s$. Switching between states follows a Markov process and depends upon time within a given state:

$\alpha (d)=\theta [1-\mathrm{e}\mathrm{x}\mathrm{p}(-\eta \mathit{d})]$ (4)

(4)

where (0<$\mathrm{\theta }$<1) and ($\eta$>0), such that the probability of switching $\alpha (d)$ is small if the duration $d$ of the time interval spent in a state has been short. These are called transition probabilities.

If the average time that a person spends in a state $s_l$ is $1/{\omega }_{s_l}$, then ${\omega }_{s_l}$ is the termination rate of the state per unit of time, with transition rates between specific states $l$ and $h$ denoted as ${\omega }_{s_l{s}_h}:$

${\omega }_{s_l}=\sum _{h,h\ne l}{\omega }_{s_l{s}_h}$ (5)

(5)

And state-switching generally following these probabilities:

${\tau }_{s_i{s}_h}={\omega }_{s_l{s}_h}/{\omega }_{s_l}$ (6)

(6)

Assuming that responses and physical activity are tracked over time longitudinally for a number of subjects, data are available to parameterize the CT-LM model. Böckenholt combines the above relationships into the CT-LM model of the probability of observing a particular response pattern over time from the $i$-th subject at times $t=t_0^i,t_1^i,\dots ,t_T^i:$

$Pr(y_{t_0^i},y_{t_1^i},\dots ,y_{t_T^i})=\sum _{s_u=1}^S\sum _{s_v=1}^S\dots \sum _{s_r=1}^S\sum _{s_w=1}^S{\pi }_{s_u}(t_0^i)P_{y_{t_0^i}|s_u}{\pi }_{s_u{s}_v}(t_0^i,t_1^i)P_{y_{t_1^i}|s_v}\dots {\pi }_{s_r{s}_w}(t_{T-1}^i,t_T^i)P_{y_{t_T^i}|s_w}$ (7)

(7)

where ${\pi }_{s_u{s}_v}(t_0^i,t_1^i)$ is the probability of switching from state $s_u$ to $s_v$ between times $t_0^i$ and $t_1^i$, ${\pi }_{s_u}(t_0^i)$ is the probability of being in state $s_u$ at time $t_0^i$, and $P_{y_{t^i}|s}$ is the probability of observing the response at time $t$ given that the $i$-th person is in state $s$.

This leads to a log-likelihood formulation from which parameters of interest ($u,\sigma ,\tau ,\pi$) may be estimated using maximum likelihood estimation techniques given sufficient data observations from subjects’ responses tracked over time as they transition between states.

Within this framework, there are two remaining challenges. The first is how individual-level factors are considered. In the absence of individual-level covariates in the maximum likelihood estimation, population average parameters based on the provided data will be estimated. These can be useful if the data provided are already for a specific population group. However, for larger and more general population data, if individual-level covariates are provided, e.g., related to the transition probabilities or duration of time within a state, parameters related to these individual-level covariates may also be estimated.

The second question is how feedback with the health coach is implemented. We may assume that the health coach has no state. Consistent with the concept of motivational interviewing, the coach responds simply to the state of the subject. Hence, the motivational feedback $K$ that a health coach provides to their subject – the processes of change that they prescribe to the subject – is modeled as a function $f$:

$K(t^i)=f[E(s(t^i))]$ (8)

(8)

where $K$ depends upon the expectation of the subject’s state $s$, and results in a vector of binary (yes/no) outcomes as to whether the subject should or should not work on each of the 10 processes of change as a specific intervention strategy to encourage movement to subsequent stages of change. Evidence from the successes of stage-matched intervention studies in which individuals are matched to specific processes of change based on the stage they belong to may help define function $f$. Moreover, if this function is parameterized, it may be included into the transition probabilities above and subject to maximum likelihood estimation.

While the calibration of such models to real-world body sensor data has not been fully realized, the conceptual and methodological underpinnings as described by these studies will soon allow for more widespread application of numerical modeling to sensor-enabled behavioral intervention studies. For instance, assuming behavioral intervention studies lead to data from which parameters of such models can be estimated, it would be possible to estimate the expected state to which an individual belongs with greater certainty, thereby informing greater personalization of health coaching.