Understanding and validating accelerometry as a measure of physical activity in children with intellectual disabilities

Background Physical activity in children with intellectual disabilities is a neglected area of study, which is most apparent in relation to physical activity measurement research. Although objective measures, specifically accelerometers, are widely used in research involving children with intellectual disabilities, existing research is based on measurement methods and data interpretation techniques generalised from typically developing children. However, due to physiological and biomechanical differences between these populations, questions have been raised in the existing literature on the validity of generalising data interpretation techniques from typically developing children to children with intellectual disabilities. Therefore, there is a need to conduct population-specific measurement research for children with intellectual disabilities and develop valid methods to interpret accelerometer data, which will increase our understanding of physical activity in this population. Methods Study 1: A systematic review was initially conducted to increase the knowledge base on how accelerometers were used within existing physical activity research involving children with intellectual disabilities and to identify important areas for future research. A systematic search strategy was used to identify relevant articles which used accelerometry-based monitors to quantify activity levels in ambulatory children with intellectual disabilities. Based on best practice guidelines, a novel form was developed to extract data based on 17 research components of accelerometer use. Accelerometer use in relation to best practice guidelines was calculated using percentage scores on a study-by-study and component-by-component basis. Study 2: To investigate the effect of data interpretation methods on the estimation of physical activity intensity in children with intellectual disabilities, a secondary data analysis was conducted. Nine existing sets of child-specific ActiGraph intensity cut points were applied to accelerometer data collected from 10 children with intellectual disabilities during an activity session. Four one-way repeated measures ANOVAs were used to examine differences in estimated time spent in sedentary, moderate, vigorous, and moderate to vigorous intensity activity. Post-hoc pairwise comparisons with Bonferroni adjustments were additionally used to identify where significant differences occurred. Study 3: The feasibility on a laboratory-based calibration protocol developed for typically developing children was investigated in children with intellectual disabilities. Specifically, the feasibility of activities, measurements, and recruitment was investigated. Five children with intellectual disabilities and five typically developing children participated in 14 treadmill-based and free-living activities. In addition, resting energy expenditure was measured and a treadmill-based graded exercise test was used to assess cardiorespiratory fitness. Breath-by-breath respiratory gas exchange and accelerometry were continually measured during all activities. Feasibility was assessed using observations, activity completion rates, and respiratory data. Study 4: Thirty-six children with intellectual disabilities participated in a semi-structured school-based physical activity session to calibrate accelerometry for the estimation of physical activity intensity. Participants wore a hip-mounted ActiGraph wGT3X+ accelerometer, with direct observation (SOFIT) used as the criterion measure. Receiver operating characteristic curve analyses were conducted to determine the optimal accelerometer cut points for sedentary, moderate, and vigorous intensity physical activity. Study 5: To cross-validate the calibrated cut points and compare classification accuracy with existing cut points developed in typically developing children, a sub-sample of 14 children with intellectual disabilities who participated in the school-based sessions, as described in Study 4, were included in this study. To examine the validity, classification agreement was investigated between the criterion measure of SOFIT and each set of cut points using sensitivity, specificity, total agreement, and Cohen’s kappa scores. Results Study 1: Ten full text articles were included in this review. The percentage of review criteria met ranged from 12%−47%. Various methods of accelerometer use were reported, with most use decisions not based on population-specific research. A lack of measurement research, specifically the calibration/validation of accelerometers for children with intellectual disabilities, is limiting the ability of researchers to make appropriate and valid accelerometer use decisions. Study 2: The choice of cut points had significant and clinically meaningful effects on the estimation of physical activity intensity and sedentary behaviour. For the 71-minute session, estimations for time spent in each intensity between cut points ranged from: sedentary = 9.50 (± 4.97) to 31.90 (± 6.77) minutes; moderate = 8.10 (± 4.07) to 40.40 (± 5.74) minutes; vigorous = 0.00 (± .00) to 17.40 (± 6.54) minutes; and moderate to vigorous = 8.80 (± 4.64) to 46.50 (± 6.02) minutes. Study 3: All typically developing participants and one participant with intellectual disabilities completed the protocol. No participant met the maximal criteria for the graded exercise test or attained a steady state during the resting measurements. Limitations were identified with the usability of respiratory gas exchange equipment and the validity of measurements. The school-based recruitment strategy was not effective, with a participation rate of 6%. Therefore, a laboratory-based calibration protocol was not feasible for children with intellectual disabilities. Study 4: The optimal vertical axis cut points (cpm) were ≤ 507 (sedentary), 1008−2300 (moderate), and ≥ 2301 (vigorous). Sensitivity scores ranged from 81−88%, specificity 81−85%, and AUC .87−.94. The optimal vector magnitude cut points (cpm) were ≤ 1863 (sedentary), ≥ 2610 (moderate) and ≥ 4215 (vigorous). Sensitivity scores ranged from 80−86%, specificity 77−82%, and AUC .86−.92. Therefore, the vertical axis cut points provide a higher level of accuracy in comparison to the vector magnitude cut points. Study 5: Substantial to excellent classification agreement was found for the calibrated cut points. The calibrated sedentary cut point (ĸ =.66) provided comparable classification agreement with existing cut points (ĸ =.55−.67). However, the existing moderate and vigorous cut points demonstrated low sensitivity (0.33−33.33% and 1.33−53.00%, respectively) and disproportionately high specificity (75.44−.98.12% and 94.61−100.00%, respectively), indicating that cut points developed in typically developing children are too high to accurately classify physical activity intensity in children with intellectual disabilities. Conclusions The studies reported in this thesis are the first to calibrate and validate accelerometry for the estimation of physical activity intensity in children with intellectual disabilities. In comparison with typically developing children, children with intellectual disabilities require lower cut points for the classification of moderate and vigorous intensity activity. Therefore, generalising existing cut points to children with intellectual disabilities will underestimate physical activity and introduce systematic measurement error, which could be a contributing factor to the low levels of physical activity reported for children with intellectual disabilities in previous research.

Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.