The subjects in this study were 524 women and men from the Baltimore, MD/Washington, DC area (Table 1). The data were collected continuously from July 2002 to August 2003. The subjects received an honorarium for completing the study.

The study protocol was approved by the Johns Hopkins University Bloomberg School of Public Health Committee on Human Research. Prior to participation, subjects provided written informed consent and received a medical evaluation by a physician that included measurement of blood pressure and analysis of fasting blood and urine samples to screen for presence of metabolic disease (such as diabetes). Body composition (lean and fat mass) was measured by DEXA (QDR 4500), with lean body mass values adjusted according to Schoeller et al. 25.

The AM (Actigraph 7164; Manufacturing Technology, Inc. Fort Walton Beach, FL) was worn on a snuggly-fitting waist belt (according to the manufacturer's instructions), with the manufacturer's "notch" facing upwards. The AM was set to store the data in 1-min intervals of time (epochs). The technical details of this brand of AM have been described elsewhere 26. Subjects were asked to wear the AM on the right hip, unless they reported being unable to do so. Regardless of the AM placement on the hip (left or right), each individual consistently wore it on the same side and location. The subjects were asked to wear the AM continuously for 13–15 days, depending on study scheduling. In addition to wearing the AM, subjects were asked to maintain an activity log (modified from 27) that detailed when they went to bed, woke up, removed it (and why), and detailed any structured exercise they may have engaged in. The AMs were calibrated according to the manufacturers recommendations prior to each of the measurements.

If a subject takes an AM off and it remains stationary, the AM will record a string of continuous zeroes. However, single zeroes or short strings of zeroes are not indicative of non-wear, because zeroes are a common occurrence when AMs are being worn. To estimate adherence, we utilized the criterion that a 20 min string of continuous zeroes represents an estimate of a non-wear occasion of an AM 1215.

To simulate the effects of removing AMs on a regular basis, we wished to identify a "reference database" of PA in a group of subjects that wore them for prolonged periods of time, then remove data in a manner similar to what would happen if an AM was removed 15. Since AMs are commonly removed by subjects during sleep and periodically during the day (e.g., showering, personal care), it is rare to find subjects that wear an AM 24 hr/day for more than a couple of consecutive days. Therefore, our criterion was to identify subjects that wore an AM for a minimum of 20 hrs/d for seven consecutive days. Of the 524 subjects, 18 women and 17 men fit the criterion (24 HR).

There are two general instances when an AM is removed by a subject: 1) during sleep, and 2) intermittently during waking hours (Figure 1A). Therefore in our simulation study, we wished to differentiate between AM removal during sleeping and waking hours in the 24 HR dataset.

The first step in this simulation study was to estimate when subjects woke up and went to sleep using the data collected from the AM (not using subject self-report). These estimates were necessary because preliminary analyses indicated significant inconsistencies between self-reported waking and sleeping times, and obvious movement in the AM dataset. Also, subjects occasionally failed to report when they woke up or went to sleep. Since there are no sleep detection procedures for the waist-worn Actigraph AM, we developed a computer program using SAS(28(modified from Sadeh et al. 29). The predicted waking and sleeping times from the computer program were compared to those reported by the subjects and by visually inspecting the daily data on a relative scale (positive and negative signs included) and an absolute scale (positive and negative signs ignored). The computer program predicted waking and sleeping times (relative and absolute differences) within -3.6 (30.8) minutes and +34.9 (60.3) minutes, respectively, when compared to those reported by the subjects in their daily activity logs. The computer program predicted waking and sleeping times within -6.0 (16.0) minutes and +34.6 (36.0) minutes, respectively, when compared to visual inspection of the data. The differences between the visual inspection of the data and self-report were -5.4 (32.3) minutes for waking times and +2.1 (41.0) minutes for sleeping times.

The second step was to simulate the effect of data loss due to AM removal during sleep. There are two general ways investigators treat the zeroes produced during sleep when AMs are removed: (1) include the zeroes in all estimates of PA 182430, or (2) measure PA during waking hours only by removing the data observed during sleep 163132. Therefore, to simulate the effect of AM removal, we replaced the minute-by-minute data recorded during sleep from the 24 HR database with zeroes (Simulation A1), or deleted the sleeping hours from the database all together (Simulation B1).

The third step was to simulate AM removal during waking hours by putting zeroes in hourly blocks of time in the place of the raw data. These one hour blocks of time (10 per day for each of the seven days of data) were spread throughout the waking hours of the day, and randomly distributed between each of the seven days. Simulations were generated for single hourly blocks of time, and for multiple hours of time up to ten hours.

In Simulation A2, we replaced the raw data observed during sleep and the hourly blocks of time during waking hours with zeroes. In Simulation B2, raw data recorded during sleep were deleted altogether (like Simulation B1) and zeroes replaced the missing hourly blocks of time during waking hours. Figure 2 demonstrates what a single day of minute by minute raw data from a random subject looks like (24 HR), and 10 hours of simulated AM removal during waking hours for the same subject and day.

Last, we compared the estimates of PA (counts/min) from the different simulations and total energy expenditure (MJ/day) measured by the doubly labeled water technique (see below) to the 24 HR database.

If missing data create biased estimates of PA, then substituting some reasonable value by imputation should improve the estimates of PA 15. To estimate an imputation value for AM removal during sleep, we took the mean value for PA observed during sleep from the 24 HR database (23.1 counts/min), then imputed this value into the 24 HR database (Simulation C1). We also imputed this value for sleep and compared the sleep imputations to Simulations A2 and B2, where hourly blocks of time were removed from waking hours (Simulation C2).

To estimate the effect of correcting for AM removal during waking hours, we generated imputation estimates using a robust geostatistical technique, kriging 33. Kriging, which has well established statistical properties, such as minimizing mean squared error under fairly general conditions, is used in spatial data for making predictions at locations for which data were not collected, based on the covariance structure of the observed locations. This prediction method is available in the SAS proc mixed software 28. One must choose a covariance structure to use kriging. We selected an exponential decay model, so that the autocorrelation between neighboring one-hour AM averages decreased exponentially with increasing time separating the observations. This approach is analogous to the autoregressive (1) time series model for unequally spaced observations (missing data could occur at any waking time point). Predictions were generated using only data from that day of the subject's record. These imputations were used to substitute for the missing data, and were combined with imputation for sleeping hours (Simulation D). While many other models are available, in practice, for the small (one day) data sets actually used as support for the imputed data, different models would produce statistically indistinguishable results and, as described above, the exponential decay model is a reasonable choice.

Resting energy expenditure (REE) was measured by respiratory gas analysis using a ventilated hood for 30 minutes in the early morning after a 12 hour overnight fast and 15 min of sitting quietly 34. Energy expenditure was calculated by using the calculations of Weir 35.

Another way to assess the effect of missing data on the prediction of PA is to examine its effect on the calculation of TEE for a two week period, where TEE was estimated using doubly labeled water (DLW) 36. Subjects reported to the laboratory on the first day of the study between 6:30 and 9:00 a.m., at which time they received an oral dose of H₂¹⁸O (0.08 g/kg body weight) and ²H₂O (0.10 g/kg body weight). Urine samples were collected in the laboratory immediately before the dose and on four different mornings (second void) during the observation period. Two additional urine samples were collected away from the laboratory on days different from those collected in the lab. Thus, six urine samples were available for the analysis. Enrichments of ²H and ¹⁸O in urine samples were measured by isotope ratio mass spectrometry (Europa Scientific Hydra)37. TEE was calculated using the equation described by Weber et al. 38, which is based on the multipoint method described by Schoeller 3940, dilution space adjustment described by Racette et al. 41, and the energy equivalent of carbon dioxide (5.6535)42 based on an assumed respiratory quotient of 0.86.

To estimate TEE from PA data, linear regression equations were generated from the 24 HR database (proc mixed procedure from SAS 28) using body weight, lean body mass, REE, PA, and different interactions between these variables. A number of different models were explored to identify the best choice, with the lowest value of AIC (Akaike's Information Criterion)43 used as the criterion. The model with the lowest AIC had the independent variables, lean body mass, and the interaction between REE and PA (we included the REE and PA main effects when working with this model). We conducted a variance decomposition on the total variance of TEE from this model using estimated mean squares from a Type I ANOVA Table, calculated using the proc mixed procedure from SAS 28, and methods described in Searle et al. 44.

To estimate the effect of AM removal and/or the imputation procedures, TEE was estimated by substituting the PA from 24 HR with the estimates from the different simulations (A1, A2, B1, B2, C1, C2, and D).

Differences in the mean values for PA and TEE between the 24 HR reference dataset and the different simulations were compared using paired t-tests (paired by subject) and/or coefficients of variation (CV; standard deviation of the difference between 24 HR and a simulation divided by the mean, multiplied by 100). Preliminary analyses indicated the some of the data were not normally distributed 45, so analyses were performed on both raw and log-transformed data (log-transforming the daily means, which normalizes their distribution).

Adherence was estimated to be 15.8 ± 3.4 hrs/day, with a range of 1.3 to 24.0 hrs/day (Fig 1B). Adherence was minimally influenced by the selection of the 20 min cut-off (15.5 ± 3.3 hrs/day for 15 min to 16.3 ± 3.6 hrs/day for 30 min). The estimated adherence by day of week was 14.9 (0.1), 16.1 (0.1), 16.1 (0.1), 16.1(0.1), 16.2 (0.1), 16.3 (0.1), and 15.0 (0.1) hrs/day (Sunday to Saturday). Sunday and Saturday adherences were significantly lower than each of the weekdays (p < 0.0001), but Sunday and Saturday were not different from each other, as were each of the weekdays also not different from each other. Lastly, gender differences in adherence were virtually non-existent. The data from one of the subjects were lost, due to an AM malfunction.

There is no consensus in the literature regarding many hours a day a subject must wear an AM to represent a "day", so we define a day as being 12.4 hrs. This definition of a day was calculated by removing days that were lower than 1 SD below the mean (based on a mean adherence of 15.8 ± 3.4 hrs/day). After omitting days where adherence was less than 12.4 hrs/day, daily adherence was 11.7 ± 2.0 days (out of 13 to 15 possible)(Fig 1C). Figure 1A indicates that although most AM removals likely occurred during sleep, approximately 30% of the removals occurred between 6:00 am and 10:00 pm.

When compared to 24 HR, imputing zeroes for sleep (Simulation A1) and deleting sleeping hours (Simulation B1) resulted in significant under-and over predictions of PA (p < 0.05), respectively, while imputing a constant value for sleeping hours (Simulation C1) reduced the bias. The under- and over-predictions of PA did not have a substantial effect on the prediction of TEE. Log-transformation of the data reduced the CV in all simulations.

Simulation of an AM removal (by imputing zeroes) for a single waking hour in Simulation A2 (zeroes imputed for sleep) resulted in a CV of approximately 7%, with each additional hour of missing data resulting in an increase of 5 – 10% per hour. A single hour of AM removal during waking hours resulted in a CV of approximately 21% for Simulation B2 (sleeping hours deleted). The additional hourly AM removals in B2 resulted in a curvilinear increase in the CV, where two to six hours of removals actually produced a lower CV than the CV produced with only a single hour deleted. This occurred because the different ways missing sleeping and waking hours were handled tended to offset each other when 2 – 6 hrs of waking data were removed.

The consistently lowest CV's throughout the entire range of missing data was observed for Simulation D (imputation of a constant for sleep and imputation of missing data during waking hours). We found the autoregressive parameter significant in 68.5% of the simulations (Wald test) when only one hour was imputed, but this value decreased to 39.2% when 10 hours was imputed. This means that our imputation procedure was effective in a majority of the cases when missing data were observed (although the effectiveness decreases as missing data increase).

As with the results from Table 3, log-transforming the data reduced the CV in all simulations.

The largest component of explained variance was lean body mass (71.5%). The contribution of the sum of other effects was small (7.1%), composed of PA (0%), REE (2.0%) and the interaction between PA and REE (5.1%). Unexplained variation (by the model) was 21.3% of the total.