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Prentice New York: Wiley. Course content. General Framework of Statistical Analysis. Statistics of Demographic Rates. Statistical Models as Data-Generating Mechanisms.

Applications of Probability Theory in Demography and Epidemiology. Parametric Statistical Models with Covariates:. Examples Parametric Models for Duration Data:.

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Course prerequisites The course appeals to faculty members, researchers, and students with an interest in demography and related disciplines. Main Readings 1. Course content I. Statistics of Demographic Rates 1. Applications of Probability Theory in Demography and Epidemiology 3.

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Application of Maximum Likelihood Estimation in Demographic Models a age-specific mortality rates and childlessness: the Binomial model b fecundity menstrual cycles to conception : the Geometric model c death counts: the Poisson model 5. Because our models are derived from group eating characteristics vs individual characteristics , and because a wide variety of foods was included, our models are expected to be more generalizable than those from previous studies.

Our work, though carried out under controlled laboratory conditions, holds potential for predicting mass intake and energy intake in free living situations. In our full models, which contained information from both the video observation and the wearable sensor, we found that bites, chews, and within-meal pauses were important for estimation of both mass and energy intake.

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The total number of bites was selected in the mass model and this was expected as initiating a bite is the first physical step of food intake. The hand-to-mouth gestures e. Chewing-related features selected by the full model were variation of chewing duration and number of chews per chewing sequence. Chewing is a reliable indicator of solid food intake and because sucking requires a jaw motion similar to that of chewing, could also potentially be used for liquid intake events that use sucking as the way of consumption e. Chewing duration and chew counts are influenced by the amount of food in the mouth and texture rheological properties of the food consumed and therefore chewing data provides valuable information about the mass, and, potentially, energy density of the food being consumed.

Within meal average pause duration was also found to be significant for predicting mass intake per meal. The study of 40 investigated the effect of within meal pauses among 16 subjects and found that the subjects consumed more when there were within meal pauses compared to no pauses. Our results support the hypothesis that duration of within meal pauses has predictive power for estimation of mass and energy intake. The chewing rate varies between individuals and food properties such as composition, structure, volume, size and shape.

Typically, hard foods e. Chewing rate also contributes to eating rate and therefore is significantly correlated with the total amount of food consumed. A recent study 41 showed that a faster rate of eating increased the mass and energy intake within a single meal. Similarly total chew counts per meal has been shown to have a relationship with total mass consumed in a single meal experiments We note that the method has proportional errors shown in Bland-Altman plots especially in the mass intake models using chew and sensor features. It may relate to the way that how foods were eaten.

For example, people may eat larger piece of food with fewer chews than expected, which may cause underestimation of mass intake for those models based on chews and chewing-related sensor features. However, this is only a hypothesis since eating activity is complex and varies among individuals. Further studies are needed to test the hypothesis and investigate how food characteristics affect chews, bites and swallows features in order to improve our current models. The bite model selected the total number of bites as the best predictor of mass intake.

In the case of the swallow only model, total number of swallows, swallow rate, and instantaneous swallow frequency related features were selected. Since swallowing is necessary to consume food, we expected swallowing to be one of the most significant predictors of total intake. The frequency of swallowing significantly increases during food intake compared with spontaneous swallowing, and therefore, is a reliable indicator of ingestion.

Mass intake and energy intake models were predicted by comparable features in our chew, bite and swallow models. In energy intake full models, more swallow related features were selected and the bite features were not selected, whereas other selected features were similar.

One potential reason could be related to the food items present in the meals comprising of both solid foods and caloric beverages. Swallows play an important role in all food intake related events irrespective of their liquid, semi-solid, or solid state whereas bites are not necessary for liquid ingestion. There is a positive relationship between number of swallows and the energy content of the ingested food.

This relationship is poorly understood and requires further investigation. Compared with our previously reported individual Counts of Chews and Swallows CCS models derived from the same dataset but using individual prediction methods, our current group models participant independent achieved similar accuracy mean absolute percentage error Compared with the individual CCS model by Fontana et al. The models presented in this paper were built on all participants rather than calibrated to each individual participant which increases the generalizability and account for inter-person variability in eating habits.

One of our motivations is to use wearable sensors that carry lesser burden compared to other methods, including multimedia image diaries. Significant information may be obtained from sensors for features that describe eating behavior such as eating rate that are not available from images 24 , 25 , There are several other studies which have proposed use of sensor data for estimation of mass and energy intake. For example, the combination of audio and motion sensors with video annotation and ground truth food type achieved a mean absolute percentage error of Another relevant work used acoustic signals for bite weight estimation for only 3 food items where the prediction error varied from However, in 18 , both the number of food items and the number of participants 8 participants, single visit were small.

The innovation of this study was exploration of features describing bites, chews and swallows during the meal in the context of their predictive ability to estimate mass and energy intake. Such analysis is potentially useful in considerations of sensor choices. In the present study, we tested the models on a wide range of foods with a variety of physical characteristics while in other studies the food variety is limited 12 , Another difference between this work and our previous work 34 is that mass and energy intake estimation is on the meal level compared to the food item level.

A meal usually consists of multiple foods and people often mix them during eating Although meal level estimation is more difficult than item level estimation because of the greater variability of the food present in mass and energy content , our models results are comparable to previously reported results We further presented energy intake estimation models directly trained on the features extracted from the video and sensor signals without the need of first estimating mass.

This approach is different from our previous study where mass and energy density of food known food type were used to compute energy intake The average percentage error in estimation of energy intake is close to the error for mass intake The estimates of ingested mass are potentially useful in combination with computer vision methods, which most frequently attempt to estimate volume portion size from a single pose image, which is an ill-posed problem unless special actions are taken by the user, such as placing a fiducial marker into the view of the camera.

The wearable sensor may provide independent estimates of food portion size or refine image-based estimates. Similarly, the sensor-based estimates of energy intake may be used as points of comparison in field experiments where the ground truth for ingested energy is not available.

However, because our study was laboratory-based, the results cannot be directly extended to community-dwelling conditions. Therefore, future experiments will involve the testing of the models on data collected during multi-meal experiments collected in free living situations.

Although video observation and annotation as used in this manuscript is highly accurate in counting chews, bites and swallows, we do not suggest it as a method to measure energy intake in practical situations, rather our approach is to use wearable sensors to detect and characterize bites, chews and swallows, potentially in combination with an egocentric wearable camera that could capture the foods being eaten. Also, the nature of the sensor piezoelectric strain sensor we used for monitoring chewing presented a limitation.

The sensor was required to be attached to the skin via medical adhesive, which limited the long term use of the sensor. Since the sensor used can detect only chewing, sensor information was not available for liquids consumed by themselves i.

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However, as the sensor technology develops, we are improving the sensors. For example, since the study was conducted, we have reported on user-friendly sensors not needing an adhesive attachment that can provide the same chewing information as the piezoelectric strain sensor used in this study Future studies will involve the evaluation of the proposed models in multi-day and multi-meal free-living experiments, where models will be trained to estimate mass and energy intake over several meal types including breakfast, lunch, dinner and snacks within and among participants.

This approach will ensure the practical usability of the developed models for application to real life eating events. Methods need to be developed to determine food type and improve estimation accuracy. The accuracy of food type recognition can be substantially improved by employing imaging techniques such as wearable cameras. Potential directions include combining emerging computer vision methods to provide recognition of food type and energy density with sensor methods that provide independent estimates of mass and energy intake.

Chapter 5 Fitting models to data | Statistical Thinking for the 21st Century

The food intake recognition from analysis of the sensor signals may also be used to trigger a wearable camera during food consumption and thus provide a completely passive method for energy intake measurement. Our future work will add image recognition and sensor-based models. Thompson, F. Nutrition in the prevention and treatment of disease. Beasley, J. Accuracy of a PDA-based dietary assessment program. Nutrition 21 , — Whybrow, S.

Interpreting Data with Statistical Models

Plausible self-reported dietary intakes in a residential facility are not necessarily reliable. Goris, A. Use of a triaxial accelerometer to validate reported food intakes. Underreporting of habitual food intake is explained by undereating in highly motivated lean women. Van Horn, L.

Dietary assessment in children using electronic methods: telephones and tape recorders. Martin, C. Measuring food intake with digital photography. McClung, H. Monitoring energy intake: a hand-held personal digital assistant provides accuracy comparable to written records. Lambert, N. Using smart card technology to monitor the eating habits of children in a school cafeteria: 1. Developing and validating the methodology. Yon, B. The use of a personal digital assistant for dietary self-monitoring does not improve the validity of self-reports of energy intake.

Sazonov, E. The energetics of obesity: A review: Monitoring energy intake and energy expenditure in humans. IEEE Eng.