Estimated Distributions of Usual Physical Activity during Recess NICHOLAS BEYLER1, SUSANNE JAMES-BURDUMY2, MARTHA BLEEKER2, JANE FORTSON3, and MAX BENJAMIN4 1Mathematica Policy Research, Washington, DC; :Mathematica Policy Research, Princeton, NJ; 3Mathematica Policy Research, Oakland, CA; and 4Mathematica Policy Research, Princeton, NJ
ABSTRACT
BEYLER, N., S. JAMES-BURDUMY, M. BLEEKER, J. FORTSON, and M. BENJAMIN. Estimated Distributions of Usual Physical Activity during Recess. Med. Sei. Sports Exerc., Vol. 47, No. 6, pp. 1197-1203, 2015. Purpose: This study aimed to estimate distri butions of usual physical activity during recess in schools in low-income areas using measurement error models and to compare modeladjusted distributions to unadjusted distributions based on a single day of measurement. Methods: A randomized study of the Playworks program was conducted in 29 schools from six U.S. cities. A sample of 365 fourth- and fifth-grade students in 26 of the study schools wore accelerometers during their recess periods on two school days. Estimates for the percentage of time spent in moderate to vigorous physical activity (MVPA) during recess were constructed from the accelerometer data for each school day. Using measurement error models, distributions for the usual amount of time spent in MVPA during recess were estimated for intervention and control groups of males and females. Unadjusted distributions for these same groups were also constructed using data from a single school day. Results: There is considerable intraindividual variability in the students’ physical activity, which accounts for 67%-83% o f the overall variability, depending on the study group. Unadjusted single-day distributions are much wider and have more weight in the tails than model-adjusted distributions owing to this large intraindividual variability in the data. Conclusions: Using measurement error models to analyze physical activity data collected from recess periods will allow for more accurate and reliable inferences on students’ physical activity. Key Words: CHILDREN, MODERATE TO VIGOROUS, MEASUREMENT ERROR MODEL, PLAYWORKS
The use of measurement error models to estimate distri butions of usual dietary intake outcomes has become a staple of nutritional epidemiology. In 1986, the U.S. National Re search Council proposed a simple approach for distin guishing interindividual and intraindividual variability in dietary intake data (21). Subsequently, more advanced sta tistical adjustment procedures for estimating usual intake distributions were developed at Iowa State University (5,23,24), the National Cancer Institute (13,14,37,38,43), and elsewhere (27,32). More recently, similar measurement error modeling procedures have been proposed for estimat ing usual physical activity outcomes (10,22,39), and there is continuing demand for this line of research (4,34). The implications of not accounting and adjusting for errors, biases, and other intraindividual variability in dietary intake and physical activity data have been discussed at length in the literature (14,22,23). Graphics that compare and con trast estimated distribution functions based on measurement error model adjustments to those that do not adjust for mea surement errors are invaluable tools for these discussions because they are easily interpreted by technical and non technical audiences alike. Carriquiry (5) provides a good ex ample in which she graphs distribution functions of vitamin B6 intake. In Figure 1 of her article, the model-adjusted dis tribution of vitamin B6 intake is shifted to the right and has less weight in the tails relative to the unadjusted (single day) distribution. These discrepancies have a real effect on
A
Address for correspondence: Nicholas Beyler, Ph.D., Mathematica Policy Research, 1100 1st Street, NE, W ashington, DC 20002; E-mail: nbeyler@ m athem atica-m pr.com . Submitted for publication March 2014. Accepted for publication September 2014. 0195-9131/15/4706-1197/0 MEDICINE & SCIENCE IN SPORTS & EXERCISE® Copyright © 2014 by the American College of Sports Medicine DOI: 10.1249/MSS.0000000000000535
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ssessment of usual or habitual physical activity is important in studying relationships between physi cal activity and health outcomes (30). An individual’s usual physical activity level is his or her average activity level over a long period, such as a year or more (22). Di rectly obtaining accurate and reliable measurements of usual physical activity is impractical because study participants are typically measured for physical activity only once or twice during a short period and the measurements are often subject to measurement errors and biases (2,16,28,41,42). As an alternative to direct measurement of usual physical activity, model-based approaches, such as measurement er ror modeling (6,11), can be used to estimate distributions of usual physical activity from a sample of study participants by accounting and adjusting for sources of measurement errors, biases, and other forms of intraindividual variations in physical activity data.
inferences about vitamin B6 intake. According to the ad justed distribution, 20% of the study sample is estimated to be below the Estimated Average Requirement (EAR), whereas according to the unadjusted distribution, 37% of the sample is estimated to be below the EAR. High-utility graphics like these are rarely used in studies of physical activity (22) and deserve more attention because they help readers understand the im plications of within-individual variability and errors that may exist in physical activity measurements. The assertion that failure to account and adjust for mea surement errors in physical activity data may result in flawed assessments about physical activity levels in the study populations is based on physical activity data collected from adult populations (10,22,39). To the best of our knowl edge, no study to date has used a measurement error model framework to estimate usual physical activity distributions based on data measured from child populations and partic ularly child populations living in low-income areas where there may be greater risk for obesity (25). In this article, we use a measurement error modeling approach to estimate usual physical activity distributions from accelerometer data collected during recess from a sample of fourth- and fifth-grade students in six U.S. cities who participated in a randomized evaluation of the Playworks program, which places full-time coaches in low-income schools to organize games and activities during recess (26). We compare the distributions from groups based on treatment status (whether students were in an intervention school or a control school) and sex to distributions based on the (unadjusted) physical activity data based on a single day of measurement from each student.
METHODS
EPIDEMIOLOGY
Study design and intervention. Twenty-nine schools
from low-income areas in six U.S. cities were recruited for the randomized experiment of Playworks. Twenty-five of these schools were recruited from five cities and partici pated in the study during the 2010-2011 school year. Four additional schools from one additional city participated in the study during the 2011-2012 school year. Within cit ies, schools were matched into blocks using data from the U.S. Department of Education’s Common Core of Data (CCD) from 2007 to 2008 (the most recent year the data were available). The CCD variables used for matching schools into blocks included the highest grade in the school; school size (measured as the number of students in the school); the percentage of students who were non-Hispanic black, non-Hispanic white, and Hispanic; and the percent age of students eligible for free or reduced-price lunch. In total, 12 blocks of matched schools were formed: one that included four schools, three that included three schools each, and eight that included two schools each. Within each block, one school was randomly assigned to the control group and the rest (either one, two, or three schools, depending on the size of the block) were randomly assigned to the intervention
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group. Under this design, 17 schools were assigned to the intervention group and 12 were assigned to the control group. More schools were assigned to the intervention group to ac commodate the number of Playworks slots that were available for the study. This study was approved by the Public/Private Ventures Institutional Review Board and the New England Institutional Review Board. All schools in the intervention group implemented Playworks during a full school year (either 2010-2011 or 2011-2012 depending on the city in which the school was located). Playworks is a school-based program that places full-time coaches in low-income schools to provide oppor tunities for organized play during recess and class time (26). The activities organized by coaches are designed to engage students in physical activity, foster better social skills and conflict resolution strategies, decrease behavioral problems, and improve school climate. Schools in the control group were not eligible to implement Playworks during the school year they were in the study (either 2010-2011 or 2011-2012) but were eligible to implement it the subsequent year. In 26 of the 29 study schools (15 intervention schools and 11 control schools), follow-up physical activity data were collected from fourth- and fifth-grade students roughly 7 months after Playworks was first implemented in inter vention schools—starting in late March and ending in early June. The average temperature on the days on which data were collected was comparable for intervention and control schools. Three schools (two intervention schools and one control school) were excluded from these analyses because they did not have any fourth- or fifth-grade students in the analysis sample. To assess the effect of Playworks on students’ physical activity during recess, students in the 26 study schools wore ActiGraph GT3X accelerometers during the school day. Parents were required to sign and return consent forms before their children were allowed to partici pate in the accelerometer data collection. A total of 664 students from the 26 study schools were selected to wear accelerometers for two separate school days. Parental con sent forms were returned for 467 of those students. Analyses were conducted on accelerometer data collected during re cess from 365 of those students (as described below). Data collection and outcome construction. Students wore an elastic belt with an attached accelerometer around their waist during the school day on two separate days. Research staff helped students put on the accelerometers before the start of the school day and take them off after the school day ended. Accelerometer intensity counts measuring vertical movement were recorded during 1-s intervals using the ActiLife 5 soft ware package (1). School-day wear time was defined as the time from the start of a student’s school day to the end, minus periods of nonwear time, which were defined as intervals of >20 min with zero intensity counts. Recess wear time was defined as school-day wear time during students’ scheduled recess periods. Three hundred sixty-five students had recess wear time of >10 min and were included in the analysis sample.
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Estimates for the percentage of time students spent in mod erate to vigorous physical activity (MVPA) during recess were computed for these students. Cut points determined by Edwardson and Gorely (9) were used to determine the amount of wear time spent engaged in moderate or vigorous physical activity during recess. Intensity counts were aggre gated into 5-s intervals (or epochs); intervals with 75 or more intensity counts recorded were considered time spent in MVPA. Intervals with 75 or more intensity counts were accu mulated to get total time spent in MVPA. A measure for the percentage of time spent in MVPA during recess was calcu lated by dividing the amount of time spent in MVPA by the total amount of wear time. Two measurements of the percent age of time spent in MVPA during recess from two distinct school days were obtained for each of the 365 students. Ap proximately 90% of all measurements were collected during outdoor recess periods in both intervention and control schools. P re lim in a ry an a ly s e s . Preliminary analyses examined associations between the outcome measure—percentage of time spent in MVPA during recess—and study design variables and other demographic characteristics. A linear multiple regression model was fit to the data, where the percentage of time spent in MVPA during recess was the response variable and the model predictors were indicators for sex (1 if female, 0 if male), treatment status (1 if the intervention group, 0 if the control group), race/ethnicity (three separate indicator variables for Hispanic, nonHispanic black or African American, and non-Hispanic white), grade (1 if fourth grade, 0 if fifth grade), measure ment day (1 if the measurement was from the student’s first measurement day, 0 if it was from the second measurement day), recess type (1 if outdoor, 0 if indoor), as well as accel erometer wear time during recess (min). The model included a random effect term for school to account for clustering of students within schools during random assignment. M e a s u re m e n t e rro r m o d e lin g . After the preliminary analyses were conducted, measurement error models were fit to data transformed to approximate normality (details about the transfonnation are provided below). The measure ment error model used in all analyses is defined as follows: Xij
Xj
4“
€y,
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where X y is the estimated percentage of time spent in MVPA during recess for student i on day j (j = 1 or 2). The term x,- is the (unobserved) usual percentage of time spent in MVPA during recess for student i (on a typical school day); x,can be thought of as the average of all Xy for student i taken over an extended period, such as all of student i’s recess pe riods during an entire school year. The term ey is the unobserved error term for student i on day j, which accounts for the difference between what is measured (Xy ) for student i on day j and what is usual or typical (x,) for student i. For the purpose of model fitting, we assume that the x,- terms are independent and normally distributed with a common mean (mx) and common variance (oy2). Similarly, we assume that the ey tenns are independent and normally distributed with a
mean of zero and common variance (a/ ). We also assume, as the measurement error model equation suggests, that the conditional expected value of Ay for student i is x,. That is, we assume that Xy is an unbiased estimate of x,- for student i. The assumption that Xy is an unbiased estimate of x,- is necessary to fit the measurement error model to the study data. This assumption is not without limitation because obtaining accurate and reliable (unbiased) estimates for the usual time spent in MVPA for children is difficult because of the considerable challenges that exist with measuring usual (long-term average) physical activity in children (33) and the lack of a single, standardized method for measuring time spent in MVPA in children (12,20). We believe, however, that the Xy measurements are reasonable estimates of usual physical activity during recess for several reasons. First, the measurements are based on accelerometer data, which pro vide objective measurements of physical activity in children and youth (3). Second, the measurements are based on in tensity cut points that have been validated for measuring MVPA in children (9). Third, the measurements are for MVPA instead of other outcomes like energy expenditure, which are often more difficult to accurately quantify using accelerometer data (41). Before fitting the measurement error model to the data, we transformed the response variable—the percentage of time spent in MVPA during recess—to approximate nor mality. A power transfonnation was used to transform the data to the normal scale, and a Shapiro-Wilk test (29) was conducted to confirm that the transformed data were ap proximately normally distributed. In studies of physical ac tivity measurement error in adults, a log transformation is commonly used to approximate normality before model fitting (10,22), but in this study, a power transformation was more appropriate. Transforming the data to the nonnal scale is necessary because it allows us to back-transform the nonnal-scale data after model fitting to generate distribu tions of usual physical activity in the original (untrans formed) scale. Such an approach is standard for estimating usual distribution functions for physical activity (22) and dietary intake (5,8,23) outcomes. Data in the nonnal scale were divided into four groups based on sex and treatment status: intervention group females, control group females, intervention group males, and control group males. Within each group, we conducted a test for unequal variances (23) to ensure that the model assumption of common error vari ance (cr£,2) was appropriate. The measurement error model was fit to normal-scale data from each group using method of moments estimation (7,23). We used method of moments instead of other esti mation procedures such as maximum likelihood because it was more practical to implement using R statistical software, which we used for all analyses. In a sensitivity analysis, we also fit the models using restricted maximum likelihood (using SAS’s PROC MIXED procedure) and got similar parameter estimates. We estimated the variability due to interindividual and intraindividual variations by dividing
estimates of ax2 and oy2, respectively, by the total variation, represented by the sum of these two estimates. To obtain an estimated distribution of the usual percentage of time spent in MVPA during recess in the original scale, simulated values of usual MVPA were generated from an estimated nonnal distribution (with mean mx and variance ay2) and transform ed to the original scale using the backtransformation procedure for power transformations de scribed in Dodd et al. (8). Estim ating distribution functions. The simulated original-scale data were used to estimate distribution func tions via kernel density estimation (31) using R statistical software. The R function density creates kernel density esti mates for a set of data and the R function plot graphs the density estimates so that the outcome variable (percentage of time spent in MVPA during recess) is plotted along the x-axis and the probability densities are plotted along the y-axis. To generate estimated distribution functions for a single day of data (without any model adjustments), we applied the density and plot functions to the outcome data (percentage of time spent in MVPA during recess) from the first school day. RESULTS
EPIDEMIOLOGY
We present descriptive characteristics of the study sample in Table 1. Approximately half of the students in both the intervention and control groups are female. More students in each group are in fourth grade (approximately 60%) com pared to fifth grade (approximately 40%). Both groups are racially and ethnically diverse—only approximately 20% of students in each group are non-Hispanic white. Average accelerometer wear time during recess was the same in both samples (around 34 min). Results from a preliminary linear regression model fit, which examined associations between percentage of time spent in MVPA during recess and study design and demo graphic characteristics, are presented in Table 2. Sex was significant at the 0.05 level, which indicates that males in the study sample spent more time engaged in MVPA during recess than females. Treatment status, although not signifi cant, has a positive regression coefficient, suggesting that students in the intervention group tended to engage in a higher percentage of MVPA during recess. Neither mea surement day nor wear time was significantly associated with MVPA during recess. Race/ethnicity and grade also did TABLE 1. Descriptive characteristics of the study sample (students who wore acceler ometers for >10 min during recess on two school days).
Intervention Group Control Group (/ j = 187) (n = 1 7 8 )
Characteristic Female (%) Grade (% in fourth grade) Race/ethnicity (%) Non-Hispanic white Non-Hispanic black or African American Hispanic Other or missing Accelerometer wear time during recess, mean ± SD (min)
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48.7 58.8
52.2 56.7
21.4 25.7 38.5 14.4 33.7 ± 12.5
20.2 32.0 40.4 7.3 33.6 ±15.7
College of Sports Medicine
TABLE 2. Estimated coefficients from a linear regression model for response variable, percentage of time spent in MVPA during recess.
Model Variable
Estimate (SE)
Intercept Treatment status (1 if intervention, 0 if control) Sex (1 if female, 0 if male) Grade (1 if in fourth grade, 0 if in fifth grade) White (1 if non-Hispanic white, 0 otherwise) Black (1 if non-Hispanic black or African American, 0 otherwise) Hispanic (1 if Hispanic or Latino, 0 otherwise) Measurement day (1 if day 1, 0 if day 2) Accelerometer wear time during recess (min) Recess type (1 if outdoor, 0 if indoor)
36.8 6.9 -4 .6 2.3 2.9 2.4 1.6 0.1 -0 .2 5 12.2
(14.3) (4.6) (1.2) (2.9) (1.7) (1.9) (1.6) (1.2) (0.14) (3.1)
P
0.01 0.15 2 d using two or more different kinds of instruments (e.g., a self-report and a monitoring device). One or more of the modeling equations can also be adapted to account for systematic biases that often exist in self-report instruments (2,16,28). Additional research that uses these and other modeling procedures is as important for advancing the field of physical activity measurement as is research on improving instrumentation for accuracy and reliability. Support for this article was provided by three grants from the Robert Wood Johnson Foundation. The contents of this article are solely the responsibility of the authors and do not necessarily rep resent the official views of the Robert Wood Johnson Foundation or Mathematica Policy Research. The authors would like to thank Ronette Briefel, Kelley Borradaile, and Phil Gleason for their thoughtful com ments on the article. The authors do not have any conflicts of interest. The results of the present study do not constitute endorsement by the American College of Sports Medicine.
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24. Nusser SM, Fuller WA, Guenther PM. Estimating usual dietary in take distributions: adjusting for measurement error and nonnormality in 24-hour food intake data. In: Lyberg L, Biemer P, Collins E, et al., eds. Survey Measurement and Process Quality. New York (NY): Wiley; 1997. pp. 689-709. 25. Ogden CL, Lamb MM, Carroll MD, Flegal KM. Obesity and So cioeconomic Status in Children and Adolescents: United States, 2005-2008, Hyattsville (MD): National Center for Health Statis tics; 2010. p. 8. 26. Playworks Web site [Internet], Oakland (CA): Playworks; [cited 2013 Oct 29]. Available from: http://www.playworks.org. 27. Rosner B, Michels KB, Chen YH, Day NE. Measurement error correction for nutritional exposures with correlated measurement error: use of the method of triads in a longitudinal setting. Stat Med. 2008;27(18):3466-89. 28. Sallis JF, Saelens BE. Assessment of physical activity by selfreport: status, limitations, and future directions. Res Q Exerc Sport. 2000;71(2 Suppl):Sl-14. 29. Shapiro SS, Wilk MB. An analysis o f variance test for normality (complete samples). Biometrics. 1965;52(3/4):591—611. 30. Shephard RJ. Limit to the measurement of habitual physical ac tivity by questionnaires. Br J Sports Med. 2003;37(3): 197-206. 31. Silverman BW. Density Estimation fo r Statistics and Data Analy sis. London (UK): Chapman and Hall; 1986. p. 176. 32. Spiegelman D, Zhao B, Kim J. Correlated errors in biased surro gates: study designs and methods for measurement error correc tion. Stat Med. 2005;24(11):1657-82. 33. Stathi A, Gillison FB, Riddoch CJ. Opportunities and challenges in physical activity research in young people. J Sci Med Sport. 2009; 12(5):515—7. 34. Staudenmayer J, Zhu W, Catellier DJ. Statistical considerations in the analysis of accelerometry-based activity monitor data. Med Sci Sports Exerc. 44(1 Suppl):S61-7. 35. Sugar EA, Wang CY, Prentice RL. Logistic regression with ex posure biomarkers and flexible measurement error. Biometrics. 2007;63(1): 143—51. 36. Tooze JA, Grunwald GK, Jones RH. Analysis of repeated mea sures data with clumping at zero. Stat Methods Med Res. 2002; 11 (4):341—55. 37. Tooze JA, Kipnis V, Buckman DW, et al. A mixed-effects model approach for estimating the distribution of usual intake of nutri ents: the NCI method. Stat Med. 2010;29(27):2857-68. 38. Tooze JA, Midthune D, Dodd KW, et al. A new statistical method for estimating the usual intake of episodically consumed foods with application to their distribution. J Am Diet Assoc. 2006; 106( 10): 1575-87. 39. Tooze JA, Troiano RP, Carroll RJ, Moshfegh AJ, Freedman LS. A measurement error model for physical activity level as measured by questionnaire with application to the 1999-2006 NHANES questionnaire. Am J Epidemiol. 2013; 177( 11): 1199-208. 40. Wickel EE, Welk GJ. Applying generalizability theory to estimate habitual activity levels. Med Sci Sports Exerc. 2010;42(8): 1528-34. 41. Welk GJ. Use o f accelerometry-based activity monitors to assess physical activity. In: Welk GJ, ed. Physical Activity Assessments fo r Health Related Research. Champaign (IL): Human Kinetics; 2002. p. 125^11. 42. Welk GJ, Schaben JA, Morrow JR. Reliability of accelerometrybased activity monitors: a generalizability study. Med Sci Sports Exerc. 2004;36(9): 1637—45. 43. Zhang S, Midthune D, Guenther PM, et al. A new multivariate measurement error model with zero-inflated dietary data, and its application to dietary assessment. Ann Appl Stat. 2011;5(2B): 1456-87.
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1. Actigraph Website [Internet], Pensacola (FL): ActiGraph Corporation; [cited 2013 Oct 29], Available from: http://www.actigraphcorp.com/ support. 2. Adams SA, Matthews CE, Ebbeling CB, et al. The effect o f social desirability and social approval on self-reports of physical activity. Am J Epidemiol. 2005; 161 (4):389-98. 3. Ainsworth BE. How do I measure physical activity in my patients? Questionnaires and objective methods. B r J Sports Med. 2009;43:6-9. 4. Ainsworth BE, Caspersen CJ, Matthews CE, Masse LC, Baranowski T, Zhu W. Recommendations to improve the accuracy of estimates of physical activity derived from self report. J Phys Act Health. 2012;9(1):S76. 5. Carriquiry AL. Estimation of usual intake distributions of nutrients and foods. J Nutr. 2003; 133(2):601 S—8. 6. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM. Measure ment Error in Nonlinear Models: A Modern Perspective. 2nd ed. New York (NY): CRC; 2006. p. 455. 7. Casella G, Berger RL. Statistical Inference. 2nd ed. Pacific Grove (CA): Duxbury; 2002. p. 660. 8. Dodd KW, Guenther PM, Freedman LS, et al. Statistical methods for estimating usual intake o f nutrients and foods: a review of the theory. J Am Diet Assoc. 2006; 106(10): 1640-50. 9. Edwardson CL, Gorely T. Epoch length and its effect on physical activity intensity. Med Sci Sports Exerc. 2010;42(5):928-34. 10. Ferrari P, Friedenreich C, Matthews CE. The role of measurement error in estimating levels of physical activity. Am J Epidemiol. 2007;166(7):832-40. 11. Fuller WA. Measurement Error Models. New York (NY): Wiley: 1987. p. 440. 12. Kim Y, Beets MW, Welk GJ. Everything you wanted to know about selecting the “right” ActiGraph accelerometer cut-points for youth, but...: a systematic review. J Sci Med Sport. 2012;15(4):311—21. 13. Kipnis V, Midthune D, Buckman DW, et al. Modeling data with excess zeros and measurement error: application to evaluating re lationships between episodically consumed foods and health out comes. Biometrics. 2009;65(4):1003-10. 14. Kipnis V, Subar AF, Midthune D, et al. Structure of dietary mea surement error: results o f the OPEN biomarker study. Am J Epidemiol. 2003; 158(1): 14-21. 15. Levin S, Jacobs DR, Ainsworth BE, Richardson MT, Leon AS. Intra-individual variation and estimates o f usual physical activity. Ann Epidemiol. 1999;9(8):481—8. 16. Matthews CE. Use of self-report instruments to assess physical activity. In: Welk GJ, ed. Physical Activity Assessments for Health Re lated Research. Champaign (IL): Human Kinetics; 2002. pp. 107-23. 17. Matthews CE, Ainsworth BE, Thompson RW, Bassett DR. Sources of variance in daily physical activity levels as measured by an accelerometer. Med Sci Sports Exerc. 2002;34(8): 1376-81. 18. Mattocks C, Leary SAM, Ness A, et al. Intraindividual variation of objectively measured physical activity in children. Med Sci Sports Exerc. 2007;39(4):622-9. 19. McClain J, Abraham T, Brusseau T, Tudor-Locke C. Epoch length and accelerometer outputs in children: comparison to direct ob servation. Med Sci Sports Exerc. 2008;40(12):2080-7. 20. McClain J, Tudor-Locke C. Objective monitoring of physical ac tivity in children: considerations for instrument selection. J Sci Med Sport. 2009;12(5):526-33. 21. National Research Council. Nutrient Adequacy. Washington (DC): National Academies Press; 1986. p. 146. 22. Nusser SM, BeylerNK, Welk GJ, Carriquiry AL, Fuller WA, King BM. Modeling errors in physical activity recall data. J Phys Act Health. 2012;9(l):S56-67. 23. Nusser SM, Carriquiry AL, Dodd KW, Fuller WA. A semiparametric transformation approach to estimating usual daily in take distributions. J Am Stat Assoc. 1996;91(436):1440-9.
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ABSTRACT
BEYLER, N., S. JAMES-BURDUMY, M. BLEEKER, J. FORTSON, and M. BENJAMIN. Estimated Distributions of Usual Physical Activity during Recess. Med. Sei. Sports Exerc., Vol. 47, No. 6, pp. 1197-1203, 2015. Purpose: This study aimed to estimate distri butions of usual physical activity during recess in schools in low-income areas using measurement error models and to compare modeladjusted distributions to unadjusted distributions based on a single day of measurement. Methods: A randomized study of the Playworks program was conducted in 29 schools from six U.S. cities. A sample of 365 fourth- and fifth-grade students in 26 of the study schools wore accelerometers during their recess periods on two school days. Estimates for the percentage of time spent in moderate to vigorous physical activity (MVPA) during recess were constructed from the accelerometer data for each school day. Using measurement error models, distributions for the usual amount of time spent in MVPA during recess were estimated for intervention and control groups of males and females. Unadjusted distributions for these same groups were also constructed using data from a single school day. Results: There is considerable intraindividual variability in the students’ physical activity, which accounts for 67%-83% o f the overall variability, depending on the study group. Unadjusted single-day distributions are much wider and have more weight in the tails than model-adjusted distributions owing to this large intraindividual variability in the data. Conclusions: Using measurement error models to analyze physical activity data collected from recess periods will allow for more accurate and reliable inferences on students’ physical activity. Key Words: CHILDREN, MODERATE TO VIGOROUS, MEASUREMENT ERROR MODEL, PLAYWORKS
The use of measurement error models to estimate distri butions of usual dietary intake outcomes has become a staple of nutritional epidemiology. In 1986, the U.S. National Re search Council proposed a simple approach for distin guishing interindividual and intraindividual variability in dietary intake data (21). Subsequently, more advanced sta tistical adjustment procedures for estimating usual intake distributions were developed at Iowa State University (5,23,24), the National Cancer Institute (13,14,37,38,43), and elsewhere (27,32). More recently, similar measurement error modeling procedures have been proposed for estimat ing usual physical activity outcomes (10,22,39), and there is continuing demand for this line of research (4,34). The implications of not accounting and adjusting for errors, biases, and other intraindividual variability in dietary intake and physical activity data have been discussed at length in the literature (14,22,23). Graphics that compare and con trast estimated distribution functions based on measurement error model adjustments to those that do not adjust for mea surement errors are invaluable tools for these discussions because they are easily interpreted by technical and non technical audiences alike. Carriquiry (5) provides a good ex ample in which she graphs distribution functions of vitamin B6 intake. In Figure 1 of her article, the model-adjusted dis tribution of vitamin B6 intake is shifted to the right and has less weight in the tails relative to the unadjusted (single day) distribution. These discrepancies have a real effect on
A
Address for correspondence: Nicholas Beyler, Ph.D., Mathematica Policy Research, 1100 1st Street, NE, W ashington, DC 20002; E-mail: nbeyler@ m athem atica-m pr.com . Submitted for publication March 2014. Accepted for publication September 2014. 0195-9131/15/4706-1197/0 MEDICINE & SCIENCE IN SPORTS & EXERCISE® Copyright © 2014 by the American College of Sports Medicine DOI: 10.1249/MSS.0000000000000535
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EPIDEMIOLOGY
ssessment of usual or habitual physical activity is important in studying relationships between physi cal activity and health outcomes (30). An individual’s usual physical activity level is his or her average activity level over a long period, such as a year or more (22). Di rectly obtaining accurate and reliable measurements of usual physical activity is impractical because study participants are typically measured for physical activity only once or twice during a short period and the measurements are often subject to measurement errors and biases (2,16,28,41,42). As an alternative to direct measurement of usual physical activity, model-based approaches, such as measurement er ror modeling (6,11), can be used to estimate distributions of usual physical activity from a sample of study participants by accounting and adjusting for sources of measurement errors, biases, and other forms of intraindividual variations in physical activity data.
inferences about vitamin B6 intake. According to the ad justed distribution, 20% of the study sample is estimated to be below the Estimated Average Requirement (EAR), whereas according to the unadjusted distribution, 37% of the sample is estimated to be below the EAR. High-utility graphics like these are rarely used in studies of physical activity (22) and deserve more attention because they help readers understand the im plications of within-individual variability and errors that may exist in physical activity measurements. The assertion that failure to account and adjust for mea surement errors in physical activity data may result in flawed assessments about physical activity levels in the study populations is based on physical activity data collected from adult populations (10,22,39). To the best of our knowl edge, no study to date has used a measurement error model framework to estimate usual physical activity distributions based on data measured from child populations and partic ularly child populations living in low-income areas where there may be greater risk for obesity (25). In this article, we use a measurement error modeling approach to estimate usual physical activity distributions from accelerometer data collected during recess from a sample of fourth- and fifth-grade students in six U.S. cities who participated in a randomized evaluation of the Playworks program, which places full-time coaches in low-income schools to organize games and activities during recess (26). We compare the distributions from groups based on treatment status (whether students were in an intervention school or a control school) and sex to distributions based on the (unadjusted) physical activity data based on a single day of measurement from each student.
METHODS
EPIDEMIOLOGY
Study design and intervention. Twenty-nine schools
from low-income areas in six U.S. cities were recruited for the randomized experiment of Playworks. Twenty-five of these schools were recruited from five cities and partici pated in the study during the 2010-2011 school year. Four additional schools from one additional city participated in the study during the 2011-2012 school year. Within cit ies, schools were matched into blocks using data from the U.S. Department of Education’s Common Core of Data (CCD) from 2007 to 2008 (the most recent year the data were available). The CCD variables used for matching schools into blocks included the highest grade in the school; school size (measured as the number of students in the school); the percentage of students who were non-Hispanic black, non-Hispanic white, and Hispanic; and the percent age of students eligible for free or reduced-price lunch. In total, 12 blocks of matched schools were formed: one that included four schools, three that included three schools each, and eight that included two schools each. Within each block, one school was randomly assigned to the control group and the rest (either one, two, or three schools, depending on the size of the block) were randomly assigned to the intervention
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group. Under this design, 17 schools were assigned to the intervention group and 12 were assigned to the control group. More schools were assigned to the intervention group to ac commodate the number of Playworks slots that were available for the study. This study was approved by the Public/Private Ventures Institutional Review Board and the New England Institutional Review Board. All schools in the intervention group implemented Playworks during a full school year (either 2010-2011 or 2011-2012 depending on the city in which the school was located). Playworks is a school-based program that places full-time coaches in low-income schools to provide oppor tunities for organized play during recess and class time (26). The activities organized by coaches are designed to engage students in physical activity, foster better social skills and conflict resolution strategies, decrease behavioral problems, and improve school climate. Schools in the control group were not eligible to implement Playworks during the school year they were in the study (either 2010-2011 or 2011-2012) but were eligible to implement it the subsequent year. In 26 of the 29 study schools (15 intervention schools and 11 control schools), follow-up physical activity data were collected from fourth- and fifth-grade students roughly 7 months after Playworks was first implemented in inter vention schools—starting in late March and ending in early June. The average temperature on the days on which data were collected was comparable for intervention and control schools. Three schools (two intervention schools and one control school) were excluded from these analyses because they did not have any fourth- or fifth-grade students in the analysis sample. To assess the effect of Playworks on students’ physical activity during recess, students in the 26 study schools wore ActiGraph GT3X accelerometers during the school day. Parents were required to sign and return consent forms before their children were allowed to partici pate in the accelerometer data collection. A total of 664 students from the 26 study schools were selected to wear accelerometers for two separate school days. Parental con sent forms were returned for 467 of those students. Analyses were conducted on accelerometer data collected during re cess from 365 of those students (as described below). Data collection and outcome construction. Students wore an elastic belt with an attached accelerometer around their waist during the school day on two separate days. Research staff helped students put on the accelerometers before the start of the school day and take them off after the school day ended. Accelerometer intensity counts measuring vertical movement were recorded during 1-s intervals using the ActiLife 5 soft ware package (1). School-day wear time was defined as the time from the start of a student’s school day to the end, minus periods of nonwear time, which were defined as intervals of >20 min with zero intensity counts. Recess wear time was defined as school-day wear time during students’ scheduled recess periods. Three hundred sixty-five students had recess wear time of >10 min and were included in the analysis sample.
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Estimates for the percentage of time students spent in mod erate to vigorous physical activity (MVPA) during recess were computed for these students. Cut points determined by Edwardson and Gorely (9) were used to determine the amount of wear time spent engaged in moderate or vigorous physical activity during recess. Intensity counts were aggre gated into 5-s intervals (or epochs); intervals with 75 or more intensity counts recorded were considered time spent in MVPA. Intervals with 75 or more intensity counts were accu mulated to get total time spent in MVPA. A measure for the percentage of time spent in MVPA during recess was calcu lated by dividing the amount of time spent in MVPA by the total amount of wear time. Two measurements of the percent age of time spent in MVPA during recess from two distinct school days were obtained for each of the 365 students. Ap proximately 90% of all measurements were collected during outdoor recess periods in both intervention and control schools. P re lim in a ry an a ly s e s . Preliminary analyses examined associations between the outcome measure—percentage of time spent in MVPA during recess—and study design variables and other demographic characteristics. A linear multiple regression model was fit to the data, where the percentage of time spent in MVPA during recess was the response variable and the model predictors were indicators for sex (1 if female, 0 if male), treatment status (1 if the intervention group, 0 if the control group), race/ethnicity (three separate indicator variables for Hispanic, nonHispanic black or African American, and non-Hispanic white), grade (1 if fourth grade, 0 if fifth grade), measure ment day (1 if the measurement was from the student’s first measurement day, 0 if it was from the second measurement day), recess type (1 if outdoor, 0 if indoor), as well as accel erometer wear time during recess (min). The model included a random effect term for school to account for clustering of students within schools during random assignment. M e a s u re m e n t e rro r m o d e lin g . After the preliminary analyses were conducted, measurement error models were fit to data transformed to approximate normality (details about the transfonnation are provided below). The measure ment error model used in all analyses is defined as follows: Xij
Xj
4“
€y,
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where X y is the estimated percentage of time spent in MVPA during recess for student i on day j (j = 1 or 2). The term x,- is the (unobserved) usual percentage of time spent in MVPA during recess for student i (on a typical school day); x,can be thought of as the average of all Xy for student i taken over an extended period, such as all of student i’s recess pe riods during an entire school year. The term ey is the unobserved error term for student i on day j, which accounts for the difference between what is measured (Xy ) for student i on day j and what is usual or typical (x,) for student i. For the purpose of model fitting, we assume that the x,- terms are independent and normally distributed with a common mean (mx) and common variance (oy2). Similarly, we assume that the ey tenns are independent and normally distributed with a
mean of zero and common variance (a/ ). We also assume, as the measurement error model equation suggests, that the conditional expected value of Ay for student i is x,. That is, we assume that Xy is an unbiased estimate of x,- for student i. The assumption that Xy is an unbiased estimate of x,- is necessary to fit the measurement error model to the study data. This assumption is not without limitation because obtaining accurate and reliable (unbiased) estimates for the usual time spent in MVPA for children is difficult because of the considerable challenges that exist with measuring usual (long-term average) physical activity in children (33) and the lack of a single, standardized method for measuring time spent in MVPA in children (12,20). We believe, however, that the Xy measurements are reasonable estimates of usual physical activity during recess for several reasons. First, the measurements are based on accelerometer data, which pro vide objective measurements of physical activity in children and youth (3). Second, the measurements are based on in tensity cut points that have been validated for measuring MVPA in children (9). Third, the measurements are for MVPA instead of other outcomes like energy expenditure, which are often more difficult to accurately quantify using accelerometer data (41). Before fitting the measurement error model to the data, we transformed the response variable—the percentage of time spent in MVPA during recess—to approximate nor mality. A power transfonnation was used to transform the data to the normal scale, and a Shapiro-Wilk test (29) was conducted to confirm that the transformed data were ap proximately normally distributed. In studies of physical ac tivity measurement error in adults, a log transformation is commonly used to approximate normality before model fitting (10,22), but in this study, a power transformation was more appropriate. Transforming the data to the nonnal scale is necessary because it allows us to back-transform the nonnal-scale data after model fitting to generate distribu tions of usual physical activity in the original (untrans formed) scale. Such an approach is standard for estimating usual distribution functions for physical activity (22) and dietary intake (5,8,23) outcomes. Data in the nonnal scale were divided into four groups based on sex and treatment status: intervention group females, control group females, intervention group males, and control group males. Within each group, we conducted a test for unequal variances (23) to ensure that the model assumption of common error vari ance (cr£,2) was appropriate. The measurement error model was fit to normal-scale data from each group using method of moments estimation (7,23). We used method of moments instead of other esti mation procedures such as maximum likelihood because it was more practical to implement using R statistical software, which we used for all analyses. In a sensitivity analysis, we also fit the models using restricted maximum likelihood (using SAS’s PROC MIXED procedure) and got similar parameter estimates. We estimated the variability due to interindividual and intraindividual variations by dividing
estimates of ax2 and oy2, respectively, by the total variation, represented by the sum of these two estimates. To obtain an estimated distribution of the usual percentage of time spent in MVPA during recess in the original scale, simulated values of usual MVPA were generated from an estimated nonnal distribution (with mean mx and variance ay2) and transform ed to the original scale using the backtransformation procedure for power transformations de scribed in Dodd et al. (8). Estim ating distribution functions. The simulated original-scale data were used to estimate distribution func tions via kernel density estimation (31) using R statistical software. The R function density creates kernel density esti mates for a set of data and the R function plot graphs the density estimates so that the outcome variable (percentage of time spent in MVPA during recess) is plotted along the x-axis and the probability densities are plotted along the y-axis. To generate estimated distribution functions for a single day of data (without any model adjustments), we applied the density and plot functions to the outcome data (percentage of time spent in MVPA during recess) from the first school day. RESULTS
EPIDEMIOLOGY
We present descriptive characteristics of the study sample in Table 1. Approximately half of the students in both the intervention and control groups are female. More students in each group are in fourth grade (approximately 60%) com pared to fifth grade (approximately 40%). Both groups are racially and ethnically diverse—only approximately 20% of students in each group are non-Hispanic white. Average accelerometer wear time during recess was the same in both samples (around 34 min). Results from a preliminary linear regression model fit, which examined associations between percentage of time spent in MVPA during recess and study design and demo graphic characteristics, are presented in Table 2. Sex was significant at the 0.05 level, which indicates that males in the study sample spent more time engaged in MVPA during recess than females. Treatment status, although not signifi cant, has a positive regression coefficient, suggesting that students in the intervention group tended to engage in a higher percentage of MVPA during recess. Neither mea surement day nor wear time was significantly associated with MVPA during recess. Race/ethnicity and grade also did TABLE 1. Descriptive characteristics of the study sample (students who wore acceler ometers for >10 min during recess on two school days).
Intervention Group Control Group (/ j = 187) (n = 1 7 8 )
Characteristic Female (%) Grade (% in fourth grade) Race/ethnicity (%) Non-Hispanic white Non-Hispanic black or African American Hispanic Other or missing Accelerometer wear time during recess, mean ± SD (min)
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48.7 58.8
52.2 56.7
21.4 25.7 38.5 14.4 33.7 ± 12.5
20.2 32.0 40.4 7.3 33.6 ±15.7
College of Sports Medicine
TABLE 2. Estimated coefficients from a linear regression model for response variable, percentage of time spent in MVPA during recess.
Model Variable
Estimate (SE)
Intercept Treatment status (1 if intervention, 0 if control) Sex (1 if female, 0 if male) Grade (1 if in fourth grade, 0 if in fifth grade) White (1 if non-Hispanic white, 0 otherwise) Black (1 if non-Hispanic black or African American, 0 otherwise) Hispanic (1 if Hispanic or Latino, 0 otherwise) Measurement day (1 if day 1, 0 if day 2) Accelerometer wear time during recess (min) Recess type (1 if outdoor, 0 if indoor)
36.8 6.9 -4 .6 2.3 2.9 2.4 1.6 0.1 -0 .2 5 12.2
(14.3) (4.6) (1.2) (2.9) (1.7) (1.9) (1.6) (1.2) (0.14) (3.1)
P
0.01 0.15 2 d using two or more different kinds of instruments (e.g., a self-report and a monitoring device). One or more of the modeling equations can also be adapted to account for systematic biases that often exist in self-report instruments (2,16,28). Additional research that uses these and other modeling procedures is as important for advancing the field of physical activity measurement as is research on improving instrumentation for accuracy and reliability. Support for this article was provided by three grants from the Robert Wood Johnson Foundation. The contents of this article are solely the responsibility of the authors and do not necessarily rep resent the official views of the Robert Wood Johnson Foundation or Mathematica Policy Research. The authors would like to thank Ronette Briefel, Kelley Borradaile, and Phil Gleason for their thoughtful com ments on the article. The authors do not have any conflicts of interest. The results of the present study do not constitute endorsement by the American College of Sports Medicine.
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