A convenience sample of 20 patients (10 of preoperative stage, 10 of postoperative stage) diagnosed with hip OA (Gender: 40% female, Age: 63.3 ± 9.2 years, BMI: 23.7 ± 3.8) treated with THA or scheduled for THA at the Department Orthopaedic Surgery and Traumatology, Odense University Hospital (12 males, 8 females), were included.
Inclusion criteria for the preoperative group: Diagnosed primary OA of the hip and scheduled for surgery (THA).
Inclusion criteria for the postoperative group: Diagnosed primary OA of the hip, treated with THA within 6 to 12 months of inclusion.
Exclusion criteria (both groups): Patients with a known history of symptomatic lung or heart disease or known symptoms of claustrophobia or unease using a mask and patients not understanding Danish language were excluded. Patients dependent on walking aid (and therefore unable to comply with the free living protocol) were excluded as well. Finally, for the post surgery group, patients with a scheduled reoperation of the hip or previous dislocation were excluded.
Twenty five were asked, 3 declined to participate and 1 was excluded due to known symptomatic lung disease and 1 due to known symptoms of claustrophobia. All 20 participants were able to complete the free living scenario.
All participants gave informed written consent and the conditions and methods of the study protocol was approved by the Ethical Committee, Region of Copenhagen, Denmark (Identifier; H-2-2010-47) and performed in accordance with the Helsinki Declaration of 1975, as revised in 2000.
The activity monitor:
A small multisensory activity monitor (Sensewear Pro3 armband (SWA)) was positioned over the triceps brachii muscle of the right arm at the midpoint between the acromion and olecranon processes (size; 85.3 mm × 53.4 mm × 19.5 mm). The activity monitor collects physiological data from following sensors; a 2 axial accelerometer, a heat flux sensor, a skin temperature sensor, a near body ambient temperature sensor, and a galvanic skin response sensor. The activity monitor uses an onboard algorithm (InnerView TM Professional software version 5.1.0) fitted with anthropometric data from the participant (gender, age, height, and weight). The output is energy expenditure (kcal/min) calculated by an internal inaccessible algorithm.
Indirect calorimetry: For validation of the SWA armband a portable metabolic monitor (Cosmed model K4b2) was worn during the protocol. The K4b2 weighs 1.5 kg including a battery and is mounted on the chest with a simple harness. The K4b2 has been shown valid in comparison to Douglas bag method . Prior to the study the apparatus had been serviced by the manufacture and validated against Douglas Bag by the authors (Data not shown). Before each test, the monitor was calibrated in accordance with the manufactures instructions. Energy expenditure (kcal/min) was calculated from the breath-by-breath oxygen use and carbon monoxide production.
A two hour protocol of 8 activities of daily living was designed. Activities imitate common activities of daily living expected for the patient/age group. Activities were: I) rest; 53 minutes (which includes all periods of rest in sitting and supine position), II) a simple warm-up program with steps and multi-planar movements; 9 minutes, III) sitting and walking between chairs; 4 minutes, IV) ascending and descending stairs; 4 minutes (4 steps, step height 15 cm), V) walking; normal; 15 minutes (self-paced) and brisk walking; 10 minute, VI) jogging; 5 minutes (or brisk walking), VII) outdoor gardening; 10 minutes (raking), and VIII) indoor cleaning; 10 minutes (sweeping floor).
All activities were supervised and performed in a consecutive order following the protocol without time breaks or discontinuity of measurements. Participants were instructed to perform the activities within the intensities of their daily living. If an activity was impossible to perform due to pain or impairment of hip movements a lower intensity level was selected and the alteration was registered.
Subjects were fasting and refrained from smoking and drinking coffee 1 hour prior to testing to diminish possible influence on the basic energy expenditure. Before each assessment, the activity monitor was initialized and fitted to the patient according to the manufacturer’s instruction. The data was downloaded in 1 minute epochs by software provided by the manufacturer (InnerView Professional Research Software Version 5.1.0).
The K4b2 was calibrated and mounted on the participant. For acclimatization the subjects rested seated 10 minutes prior to the protocol. To identify the time periods of the individual activities during the later data analysis both units (the SWA and the K4b2) and the time scheme of the protocol were synchronized by an electronic clock. The validation procedure including the initial calibration of units was performed by the principal author.
Bias was defined as the difference between the activity monitor and indirect calorimetry outcomes (kcal/min). Activity specific bias was analyzed for each activity separately (the 15 time intervals coded #1-#15). To diminish possible carry over effects between intervals due to VO2 latency, the first minute of each interval (#1-#15) was excluded from the later mean bias analysis of each activity and intervals of 2 minutes and less (interval #3 and #5) were regarded non-conclusive results. Mean bias of all 15 intervals (#1-#15) are presented.
Statistical analysis was carried out using functional data analysis . This approach treats an entire curve of observations as a single datum rather than a collection of separate observations. In the present context each time dependent trajectory of the activity monitor and indirect calorimetry represents an observation. The techniques allow for a flexible characterization of the dynamics with minimal assumptions. In contrast, traditional methods such as linear mixed models that are based on the individual time points impose a parameterization on the functional form of the mean.
Specifically, we are interested in estimating the first two functional moments of the data. The functional mean leads to the definition of a time dependent bias function that varies freely over durations of the activities.
From the second order moments the functional variance processes  and the correlation coefficient were estimated  where the former characterize the internal stability of the activity monitor and indirect calorimetry.
The first step was to project the observed data into function space. We used a cubic b-spline basis with a knot placed at every minute and a data adaptive roughness penalty on the second derivative. The penalty parameter was estimated using the generalized cross-validation criterion .
A two-way functional ANOVA model showed no significant effect of surgical status, thus this factor was removed and the following results are based on pooled data.
The bias function was estimated as the functional mean of the pair-wise differences between the activity monitor and the indirect calorimetry curves with corresponding 95% confidence bands estimated by the method described by Cuevas et al. (2006) using the L2 norm as proximity measure .
The mean and relative biases of each interval (#1-#15) was calculated by a numeric quadrature rule over the corresponding intervals and the confidence intervals were based on a pair-wise re-sampling procedure.
Statistical analysis was carried out using R version 2.15.2 (2012-10-26) “Trick or Treat” Copyright (C) 2012 The R Foundation for Statistical Computing ISBN 3-900051-07-0.