title: Theoretical and empirical efficiency of sampling strategies for estimating upper arm elevation.
abstract: OBJECTIVE
  To investigate the statistical efficiency of strategies for sampling upper arm elevation data, which differed with respect to sample sizes and sample allocations within and across measurement days. The study was also designed to compare standard theoretical predictions of sampling efficiency, which rely on several assumptions about the data structure, with 'true' efficiency as determined by bootstrap simulations.
  
  
  METHODS
  Sixty-five sampling strategies were investigated using a data set containing minute-by-minute values of average right upper arm elevation, percentage of time with an arm elevated <15°, and percentage of time with an arm elevated >90° in a population of 23 house painters, 23 car mechanics, and 26 machinists, all followed for four full working days. Total sample times per subject between 30 and 240 min were subdivided into continuous time blocks between 1 and 240 min long, allocated to 1 or 4 days per subject. Within day(s), blocks were distributed using either a random or a fixed-interval principle. Sampling efficiency was expressed in terms of the variance of estimated mean exposure values of 20 subjects and assessed using standard theoretical models assuming independence between variables and homoscedasticity. Theoretical performance was compared to empirical efficiencies obtained by a nonparametric bootstrapping procedure.
  
  
  RESULTS
  We found the assumptions of independence and homoscedasticity in the theoretical model to be violated, most notably expressed through an autocorrelation between measurement units within working days. The empirical variance of the mean exposure estimates decreased, i.e. sampling efficiency increased, for sampling strategies where measurements were distributed widely across time. Thus, the most efficient allocation strategy was to organize a sample into 1-min block collected at fixed time intervals across 4 days. Theoretical estimates of efficiency generally agreed with empirical variances if the sample was allocated into small blocks, while for larger block sizes, the empirical 'true' variance was considerably larger than predicted by theory. Theory overestimated efficiency in particular for strategies with short total sample times per subject.
  
  
  CONCLUSIONS
  This study demonstrates that when exposure data are autocorrelated within days-which we argue is the major reason why theory overestimates sampling performance-sampling efficiency can be improved by distributing the sample widely across the day or across days, preferably using a fixed-interval strategy. While this guidance is particularly valid when small proportions of working days are assessed, we generally recommend collecting more data than suggested by theory if a certain precision of the resulting exposure estimate is needed. More data per se give a better precision and sampling larger proportion(s) of the working day(s) also alleviate the negative effects of possible autocorrelation in data.
authors.affiliation: Department of Occupational and Public Health Sciences, Centre for Musculoskeletal Research, University of Gävle, Gävle, Sweden.
authors.forename: Per
authors.initials: P
authors.lastname: Liv
authors.forename: Svend Erik
authors.initials: SE
authors.lastname: Mathiassen
authors.forename: Susanne Wulff
authors.initials: SW
authors.lastname: Svendsen
mesh_terms: D000328:Adult; D000368:Aged; D001132:Arm; D001696:Biomechanical Phenomena; D003625:Data Collection / Q000379:methods*; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D016273:Occupational Exposure / Q000032:analysis*; D009790:Occupations / Q000706:statistics & numerical data