Statistical modeling of physical activity based on accelerometer data

Physical activity is generally considered as being bene cial for many health outcomes. Lack of physical activity and increased sedentary behavior are regarded as major risk factors. Therefore physical activity has been in the focus of epidemiological research for a long time. Subjective methods like standardized physical activity questionnaires are frequently used to assess physical activity in epidemiological research. In recent years, objective methods, like pedometers and accelerometers, have become more common. Accelerometers measure the body acceleration along up to three axes. The acceleration is stored as a numerical quantity, the counts for a certain period of the time (epochs). Counts are thought to be proportional to the intensity of the activity. Accelerometer measurements allow to derive the time a person spent in certain intensity ranges, like sedentary, light, moderate and vigorous. After a motivation of the research presented in this thesis and a short outline, the concept of physical activity is introduced in Chapter 2, which particularly focuses on the description of the objective measurement of physical activity using accelerometers and pedometers in contrast to subjective measurements like physical activity questionnaires. Some methodological problems regarding the objective and subjective assessment of physical activity are identi ed and investigated in Chapter 5. Chapter 3 presents more details on accelerometer measured physical activity. The intensity levels are commonly assigned using count thresholds, the socalled cutpoints. The time spent within one activity range without changing into another is called bout. The cutpoint method is a valid way to analyze accelerometer data under the quite unrealistic assumptions that the state of motion at a point in time is independent of the state of motion a person was in just before and that humans switch from sitting to running and back to sitting within a few seconds. It is, however, more realistic to assume that human activity behavior consists of a sequence of non-overlapping distinguishable activities, like walking to work, sit at the desk and playing badminton after work that can be represented by a mean intensity level. The recorded accelerometer counts scatter around this mean level. If this holds true, then the cutpoint method leads to considerable misclassi cation of the bouts into the wrong intensity levels and hence also to an incorrect estimation of the number of bouts. In Chapter 4, two novel approaches to better capture physical activity under these assumptions are developed and implemented. The Hidden Markov models (HMM) are stochastic models that allow tting a Markov chain with a prede ned number of activities to the data. This new method is compared to the standard cutpoint method in a simulation study. HMMs require some a priori information that are not veri able. Therefore, it is desirable to nd a way to model physical activity data that does not need any other a priori information. Thus, a regression model is called for that allows to model accelerometer data as a sort of step function with each jump indicating the start of a new activity and the constant interval being the mean intensity level of that activity. Here, expectile regression utilizing the Whittaker smoother with an L0-penalty is introduced as a second innovative approach, which allows the desired t. The expectile regression is compared to the cutpoint method and the HMMs by means of Monte-Carlo experiments. Both methods, compared to the cutpoint method, reduce the misclassi cation rate of counts and the number of identi ed bouts and therefore present a substantial improvement for modeling accelerometer data to assess physical activity. Chapter 5 presents the results of four studies on physical activity. In the large European IDEFICS study, accelerometer data were collected from several thousands children. These data are used to describe the physical activity behavior in European children using GAMLSS, which is also introduced in this chapter. A second study exploits the collected activity data of the IDEFICS study to investigate the in uence of physical activity and sedentary behavior on high blood pressure in children. The PATREC study is a smaller study in German children and adolescents with a strong methodological focus. Data collected in this study are used to study some problems identi ed in Chapter 2 regarding objectively and subjectively measured physical activity in di erent domains of activity. In the fourth study an energy expenditure equation is derived for one pedometer model. Chapter 6 summarizes and discusses the ndings of the previous chapters and ends with an outlook on future research with respect to the assessment of physical activity data in epidemiological studies. Physical activity, accelerometer data, hidden Markov models, expectile regression, L0-penalty, Whittaker smoother, pattern recognition, physical activity patterns, bout detection, GAMLSS, energy prediction equation