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Validity of a Physical Activity Questionnaire in Shanghai


Medicine & Science in Sports & Exercise: December 2010 - Volume 42 - Issue 12 - p 2222-2230
doi: 10.1249/MSS.0b013e3181e1fcd5

Purpose: In large epidemiologic studies, physical activity (PA) is often assessed using PA questionnaires (PAQ). Because available PAQ may not capture the full range of PA in which urban Chinese adults engage, a PAQ was developed for this purpose. We examined the validity of this PAQ and the 1-yr stability of PA in 545 urban Shanghai adults.

Methods: The PAQ was interview-administered twice, approximately 1 yr apart, and participants also wore an accelerometer and completed a PA-log for seven consecutive days every 3 months during the same year. The intraclass correlation coefficient (ICC) was used to evaluate the stability of PA across questionnaire administrations, and Spearman correlation coefficients (ρ) and mean differences and 95% limits of agreement were used to examine the validity of the questionnaire compared against accelerometry and the PA-log.

Results: When measured by accelerometry, estimates of time spent in moderate-to-vigorous PA were lower and estimates of time spent sedentary were higher than when self-reported on the PAQ (P < 0.001). Total PA (ICC = 0.65) and PA domains (ICC = 0.45-0.85) showed moderate to high stability across PAQ administrations. Total PA (ρ = 0.30), moderate-to-vigorous activity (ρ = 0.17), light activity (ρ = 0.36), and sedentary behavior (ρ = 0.16) assessed by PAQ and by accelerometry were significantly and positively correlated, and correlations of the PAQ with the PA-log (ρ = 0.36-0.85) were stronger than those observed with accelerometry.

Conclusions: The PAQ significantly overestimated time spent in moderate-to-vigorous activity and underestimated time spent in light activity and sedentary behavior compared with accelerometry, but it performed well at ranking participants according to PA level.

1National Cancer Institute, Division of Cancer Epidemiology and Genetics, Bethesda, MD; 2MRC Epidemiology Unit, Institute of Metabolic Science, Cambridge, England, UNITED KINGDOM; 3Division of Epidemiology, Department of Medicine, Vanderbilt Epidemiology Center, Institute for Medicine and Public Health, Vanderbilt-Ingram Cancer Center, Vanderbilt University School of Medicine, Nashville, TN; 4Shanghai Cancer Institute, Shanghai, CHINA; and 5Department of Epidemiology and Preventive Medicine, University Medical Center Regensburg, GERMANY

Address for correspondence: Ulf Ekelund, MRC Epidemiology Unit, Institute of Metabolic Science, Box 285, Addenbrooke's Hospital, Hills Road,Cambridge, CB2 0QQ, England, United Kingdom; E-mail:

Submitted for publication August 2009.

Accepted for publication March 2010.

Reduced daily energy expenditure from nonrecreational PA including occupational and transport activities after urbanization and mechanization (28-30) may have profound consequences on the increasing prevalence of noncommunicable disease in China (40). This transition is particularly important because participation in activities of daily life is less easily altered than leisure time activity (4), and the prevalence of leisure time physical activity (PA) is low in China (14,16,19).

PA is a complex multidimensional behavior that is difficult to accurately assess in epidemiologic studies. PA questionnaires (PAQ) are the method of choice for low-cost assessment of PA in large etiologic studies and are capable of capturing the type and context of activity. However, current self-report methods often focus on specific domains of PA such as occupational or recreational activity as opposed to total PA and may not assess all parameters of activity, including intensity, frequency, and duration. Furthermore, available PAQ may not sufficiently capture the full range of PA in which urban Chinese adults engage. For example, the International Physical Activity Questionnaire provides a brief assessment of PA levels for surveillance purposes, but it has shown a low validity in a Chinese population (20). These considerations highlight the importance of culturally relevant instruments (21) and support the need to examine the validity of an instrument in a population representative of that in which it will be used.

Accordingly, we developed a comprehensive PAQ inquiring about PA across domains (household, transportation, occupation, caring for others, leisure and recreation, and stair climbing), incorporating activities common in urban Shanghai. We herein examined the validity of this PAQ using objective monitoring of PA by accelerometry as our criterion validation method, and we compared the PAQ with a 7-d PA-log. Owing to differences in the time frame of the PAQ (past year) and the accelerometer measurement, we also assessed the stability of PA over time by readministering the instrument 1 yr later.

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Shanghai cohort studies.

The Shanghai Women's Health Study (SWHS) and Shanghai Men's Health Study (SMHS) are population-based prospective cohort studies of 74,943 adult women (aged 40-70 yr at baseline) and 61,582 adult men (aged 40-75 yr at baseline). Study participants were permanently residing in one of seven (SWHS) or eight (SMHS) communities in Shanghai, China, and were recruited to the studies between 1997 and 2006 (1997-2000 for the SWHS and 2001-2006 for the SMHS). All participants provided written informed consent, and the study protocol was approved by the institutional review boards of all participating institutions.

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Shanghai PA study.

The Shanghai PA study was conducted in a subset of participants from the SWHS and the SMHS, with potential study members randomly selected from two communities of the parent studies. Participant enrollment began in December 2005, and data collection was completed in September 2008. Of the 1101 participants contacted, 619 (56%) participated in the PA study, including 310 women and 309 men.

Participants were enrolled in the study for 1 yr. At the beginning of the study, participants completed a questionnaire (PAQ1, described below) that assessed PA patterns during the past year. They were also asked to wear an ActiGraph accelerometer and to complete a PA-log for seven consecutive days, four times during the study (i.e., at baseline (month 1), in months 4-5, in months 9-10, and in month 12). In addition, the PAQ was readministered during the final ActiGraph wear period (PAQ2, month 12).

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Past year PAQ.

To capture the full range of activity behaviors in which adults in Shanghai typically engage, we adopted the Typical Week Physical Activity Survey that was developed by Ainsworth et al. (2) in the Cross-Cultural Activity Participation Study. Specifically, we developed a PAQ that assessed participation during the past year in PA common to residents of Shanghai. Compared with the Typical Week Physical Activity Survey (2), our questionnaire inquired in greater depth about walking and cycling, which are typically considered major modes of transportation in the Shanghai general population, and provided culturally appropriate examples for questions about exercise participation (e.g., traditional Chinese exercises such as Tai Chi, sword and fan dancing). Cultural input was obtained by collecting comprehensive information on PA common among both the SWHS and SMHS cohorts, which was used to tailor the PAQ to the study population. After development of an initial draft of the instrument, small-scale pilot testing among cohort members was conducted to revise the questionnaire's instructions and word choices by checking the translation from English and by obtaining feedback regarding the comprehension of the questions by study participants.

The instrument was composed of 26 items divided into the following categories of PA: household; transportation; occupation and volunteer work; caring for others; leisure, recreation, and exercise; and stair climbing. For each questionnaire item, participants were asked to report in an open-ended format the number of months per year, the days per month, and the hours and minutes per day spent in each activity on days when they engaged in that particular behavior. Summary measures were calculated using reported frequency (months per year and days per month), duration (converted to minutes per day), and intensity (METs) of PA using standard methods (1). For activities unique to the Shanghai population, MET values were assigned using analogous activities from the compendium of PA (1), e.g., "Mind/body exercise and light effort: slow run, Tai Chi, Mulan, sword dancing and fan dancing" was assigned a value of 4.3 METs because compendium values for similar activities range from 4.0 to 4.5 METs. Time (min·d−1) spent sedentary (<1.5 METs) and in light (2.0-3.0 METs) and moderate-to-vigorous (>3.0 METs) activity was calculated, as was total PA (MET·h·d−1, ≥2.0 METs).

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Objective measurement of PA.

Participants wore an ActiGraph accelerometer (Model 7164; MTI ActiGraph, Fort Walton, FL) for seven consecutive days up to four times during the study. Participants were instructed to wear the monitor on the left side of the hip (attached by an elastic belt) at all times except when sleeping, showering, and swimming. Study personnel distributed and collected the monitors in person, recorded the dates of ActiGraph distribution and collection, checked monitor calibration status, and recalibrated monitors as required.

The ActiGraph measures vertical acceleration 10 times per second, which is integrated during a prespecified epoch (1 min for this study) and converted to activity counts per minute. We estimated monitor wear time using an automated scoring algorithm based on that developed by Troiano et al. (38) using a threshold of ≥60 min for determination of nonwear periods and a modified activity count threshold of ≥50 counts per minute for determination of wear periods (compared with ≥100 counts per minute as per Troiano et al. (38)). We considered a valid day of observation to have ≥10 h of monitor wear time (38), and we excluded all nonvalid days and all measurement weeks with less than two valid days. In summary measures, we calculated average values during valid days for total PA (counts per minute per day ≥ 100 counts per minute), for sedentary time (min·d−1 < 100 counts per minute), and for time (min·d−1) spent in light (100-759 counts per minute) and moderate-to-vigorous activity (≥760 counts per minute) using previously described cut points for sedentary behavior, light activity, and moderate-to-vigorous activity (23-25). We did not evaluate bouts of PA measured by the accelerometer because the PAQ questions did not assess bouts of activity.

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7-d PA-log.

Because the accelerometer does not capture information on the domain or context of PA, we also included the PA-log as a reference instrument in our validation study. Participants completed a PA-log on each of 7 d on four separate occasions, concurrent with accelerometer wear periods. The 7-d PA-log was similar to instruments previously used at baseline in the Shanghai cohorts (17,26). Participants were instructed to complete the PA-log at the end of each day, reviewing a list of PA in which individuals may have engaged during the previous 24 h (self-care and housework, caring for others, transportation, occupational activity, and sports, exercise, or recreational activity). The PA-log evaluated the duration of each type of activity (h·d−1 and min·d−1), and we estimated PA intensity (METs) using standard methods (1). Time (min·d−1) spent sedentary (<1.5 METs) and in light (2.0-3.0 METs) and moderate-to-vigorous (>3.0 METs) activity was calculated, as was total PA (MET·h·d−1, ≥2.0 METs), by averaging across all days of PA-log completion.

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Participant characteristics at baseline.

Exposure assessments were essentially identical in each cohort, except for the collection of reproductive and medical information that was gender specific. For men, demographic (age, education, and occupation) and lifestyle (alcohol intake and cigarette smoking) data were collected during in-person interviews at baseline (2001-2006), whereas women reported this information at baseline on a self-administered questionnaire (1997-2000). For both men and women, anthropometric variables (height, weight, and waist and hip circumferences) were measured in-person by trained interviewers following a standard protocol (35,39).

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Analytic population.

Of 619 potential participants, we excluded 62 individuals without data from both PAQ administrations and 12 persons who did not meet the criteria for sufficient accelerometer data, leaving 545 participants (271 men and 274 women) for analyses.

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Statistical analysis.

Examination of the distribution of total PA, moderate-to-vigorous activity, light activity, and sedentary time by quantile-quantile plots revealed departure from normality. Therefore, all data were analyzed using nonparametric methods, and we report participation in PA and sedentary behavior by medians and interquartile ranges (IQR). Differences in participation in PA subcomponents by gender and by method of assessing PA were investigated using the Kruskal-Wallis test and the Wilcoxon signed-rank test, respectively.

Although reliability of the PAQ could not be appropriately assessed given the study design, the stability of self-reported total PA, various intensities of PA, sedentary behavior, and domains of PA was assessed by the intraclass correlation coefficient (ICC) of log-transformed PA data from each of the two PAQ administrations, estimated by one-way ANOVA.

The validity analysis included only data from PAQ2, so that the criterion measurement period was included within the time frame of reference of the questionnaire (past year). For this same reason, we did not combine data from PAQ1 and PAQ2 to calculate deattenuated correlation coefficients (33). The Spearman correlation coefficient (ρ) was used to estimate the association of accelerometer-measured PA with total PA, moderate-to-vigorous and light activity, sedentary behavior, and various domains of PA assessed by PAQ2. Correlations between PAQ2 and the PA-log were also evaluated to further examine domains of PA. We examined heterogeneity in the relationships of PA and sedentary behavior from PAQ2 with log-transformed estimates from accelerometry and the PA-log by age, gender, body mass index (BMI), and educational attainment by testing the statistical significance of the corresponding interaction term in linear regression models using the Wald test.

For the absolute validity analysis, we calculated the mean difference (PAQ2 − accelerometer), 95% confidence intervals, and 95% limits of agreement (LOA) of time (min·d−1) spent in moderate-to-vigorous activity, light activity, and sedentary behavior between PAQ2 and accelerometry. The ability of the questionnaire to rank participants' activity levels was assessed by calculating the mean counts per minute per day from the accelerometer by quartile of total PA from PAQ2 and the mean sedentary time from the accelerometer (min·d−1) by quartile of sedentary time from PAQ2. Additional analyses were conducted to compare PAQ2 with the PA-log to assess agreement of domains of PA by calculating the mean difference (PAQ2 − PA-log) of time estimates from PAQ2 and the PA-log.

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More than 80% of our study population had accelerometer data for three or more measurement periods (mean ± SD; 3.22 ± 0.87), with more than 5 d of data for each measurement week (5.78 ± 1.67). Participants had at least 10 h (600 min) of accelerometer wear time for 71% of days measured (854.6 ± 151.1 min), more than 95% of the study population completed four PA-logs.

On average, participants were 53.4 yr, with a mean BMI of 23.7 kg·m−2 at baseline, and 47% of the study population reported at least a high school education (Table 1). Compared with men, women were younger and had a higher average BMI. Women were also less likely than men to be educated at a high school level or above, and they were less likely to drink alcohol and to smoke cigarettes.



Time spent in moderate-to-vigorous activity was higher, and time spent sedentary was lower when moderate-to-vigorous activity and sedentary behavior were self-reported than when measured by accelerometry (P < 0.05; Table 2). Median time spent in moderate-to-vigorous activity ranged from 79.5 min·d−1 (IQR = 57.2-105.7 min·d−1) by accelerometry to 93.7 min·d−1 on the PAQ (IQR = 58.2-147.8 min·d−1) and 97.9 min·d−1 (IQR = 65.9-138.6 min·d−1) on the PA-log. Because men and women differed with respect to time spent in PA and sedentary behavior, results are also presented by gender. Compared with men, women self-reported a greater amount of total PA and time spent in moderate-to-vigorous activity (P < 0.05), although accelerometer-measured total activity and time spent in moderate-to-vigorous activity did not differ by gender. For all three instruments, women were less sedentary and spent more time in light activity than men (P < 0.001). In Table 2, we also present time spent in various domains of PA from PAQ2 and the PA-log. We observed gender differences for self-reported activity across domains because women reported more time spent walking and doing household chores, whereas cycling was the only activity more common among men than women (P < 0.001). Time spent in occupational or leisure time activity did not differ by gender (P > 0.05).



On average, 402 d separated the two PAQ administrations, with slightly less time between administrations for women than for men (mean = 395 vs 410 d, respectively, P = 0.03). Estimates of PA and sedentary behavior did not systematically differ between the two PAQ, and the stability of PA was not influenced by time between PAQ (data not shown). Self-reports of total PA were moderately consistent over time (ICC = 0.65), as was assessment of PA intensity levels (ICC = 0.48-0.61) and domains (ICC = 0.40-0.86; Table 3). Occupational activity (including sitting, ICC = 0.85) and leisure time activity (ICC = 0.66) were most stable across PAQ assessments.



The stability of self-reported total PA, moderate-to-vigorous activity, and sedentary behavior over time did not systematically differ by education level (middle school or less vs high school or above), BMI (<24 kg·m−2 vs ≥24 kg·m−2), or age (<60 vs ≥60 yr; data not shown). However, compared with men, intraclass correlations for sedentary behavior and walking were weaker among women, whereas correlations for occupational activity were stronger among women (Table 3). The stability of household activity was similar among men and women (ICC = 0.51).

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Validity of the PAQ.

Total PA as assessed by PAQ2 showed reasonable correlations with total PA measured by accelerometry (ρ = 0.30), and correlations between methods were weaker for moderate-to-vigorous activity (ρ = 0.17) than for light activity (ρ = 0.36; Table 4). Self-reported sedentary behavior correlated weakly with accelerometer-measured time spent sedentary (ρ = 0.16), and all PA variables from PAQ2 except household activity were inversely correlated with sedentary behavior from accelerometry. Because the accelerometer is likely to underestimate bicycling, we also evaluated the correlation of time spent in moderate-to-vigorous activity by accelerometer with self-reported moderate-to-vigorous activity after excluding time spent cycling, and we observed slight attenuation of the correlation coefficient (ρ = 0.14; data not shown). Table 4 also shows correlations between PA from PAQ2 and PA variables reported on the PA-log, which were more pronounced (ρ = 0.36-0.85) than those observed between PAQ2 and accelerometry.



Compared with accelerometry, the PAQ significantly overestimated time spent in moderate-to-vigorous activity and underestimated time spent in light activity and sedentary behavior (Table 5). The 95% LOA varied by subcomponents of activity but indicated underestimation of moderate-to-vigorous activity, light activity, and sedentary behavior by more than 2 h·d−1 and overestimation of moderate-to-vigorous activity, light activity, and sedentary behavior by nearly 3 h·d−1. We did not observe heterogeneity in the association of self-reported and accelerometer-measured moderate-to-vigorous activity, light activity, and sedentary behavior across strata of gender, education, or BMI (data not shown). However, the mean difference between the PAQ and accelerometry for each PA variable was less for younger (40-59 yr) than for older (≥60 yr) participants, although 95% LOA were wide irrespective of age.



When comparing PAQ2 with the PA-log (Table 5), PAQ2 significantly overestimated total PA and underestimated light activity and sedentary behavior, and although the mean difference for moderate-to-vigorous activity was not statistically significant, 95% LOA were wide. With respect to domains of PA, PAQ2 significantly overestimated time spent walking, in active transport, and cycling but underestimated time spent in household and leisure time activity. No difference was observed for occupational activity (P > 0.05).

Table 6 shows a positive association of mean total PA, moderate-to-vigorous activity, light activity, and sedentary behavior measured by accelerometry with quartiles of corresponding variables from the PAQ. Trends for all PA variables and for sedentary behavior were statistically significant (P < 0.05).



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We observed modest validity of a comprehensive PAQ, developed to assess the full range of PA common among adults in urban Shanghai. The correlation coefficient of 0.30 for total PA in our study is similar to previous validation studies of both global (8,9,20) and comprehensive (11) PAQ using accelerometry as the criterion method. Although the PAQ assessments correlate modestly to weakly with the criterion measurements, the PAQ performed well at ranking individuals according to categories of total PA, moderate-to-vigorous activity, light activity, and sedentary behavior. The ability of the PAQ to discriminate quartiles of PA levels indicates that the instrument is suitable for use in etiologic studies.

Although the PAQ was able to rank individuals according to PA level, it showed weak to modest absolute validity when compared with accelerometer-measured PA and sedentary behavior. The ability of the PAQ to assess individual-level estimates of moderate-to-vigorous activity, light activity, or sedentary behavior is poor, as indicated by the mean differences between instruments. Furthermore, we noted greater mean differences between the PAQ and accelerometry among persons older than 60 yr. One explanation is that misreporting increases with age, although the observation of low validity of the PAQ for assessing sedentary behavior suggests that the PAQ may better ascertain dynamic activities, which are more likely engaged in by younger than older persons.

Our observation of overestimation of PA and underestimation of sedentary behavior by self-report methods is consistent with the literature (18,27,31,34). Yet the relative contribution of participants misreporting PA versus the accelerometer failing to capture certain behaviors remains unclear. The structure of our PAQ, interrogating the spectrum of activities in which an adult in urban Shanghai might participate, may have encouraged overreporting of PA, whereas failure of the accelerometer to capture certain behaviors such as cycling and upper body movement may have underestimated those types of PA. However, contrary to expectations, exclusion of self-reported time spent cycling did not improve correlations between the PAQ and accelerometry. Yet self-reported household PA, which likely involves upper body movement, was inversely correlated with accelerometer-measured total activity and moderate-to-vigorous activity in our study. This supports previous observations that accelerometry underestimates domestic activity (13), despite use of a lower threshold (760 counts per minute) for moderate-to-vigorous activity that intended to capture this type of activity (23). It is also possible that household activity suffers from overreporting (32), and lower validity of the PAQ among older women may result from greater participation in household activity by this population subgroup (16). In addition, the large differences between the PAQ and accelerometry in measuring sedentary behavior suggest that the PAQ may underascertain physical inactivity.

We also observed stronger correlations with accelerometry for self-reported light PA than for moderate-to-vigorous activity, in contrast with some (17,26), but not all (41), previous studies that showed superior validity of self-reported vigorous than nonvigorous activities. Differences in the criterion methods and the PAQ used across studies likely contribute to this inconsistency.

Estimates of PA from the PAQ showed superior agreement with the PA-log than with the accelerometer, as previously observed for a global PAQ in a Chinese population (20). Considering the similar structure and content of the PAQ and the PA-log in our study, which are both self-report instruments, modest to strong correlations (ρ = 0.36-0.85) between the PAQ and the PA-log across PA domains could be anticipated. However, the potential that the errors in the PAQ and the PA-log are correlated suggests that the PA-log may not be the most suitable criterion method for assessing the validity of the PAQ (10). Yet the PA-log is the most practical instrument for examination of the validity of PA domains because objective methods such as accelerometers cannot distinguish the type or context of activity.

The stability of PA between PAQ administrations did not vary by intensity level of PA. Previous reports have observed that high- versus low-intensity PA is either better captured by PAQ or better reported by participants (5,7,15,34,36,41). Regarding domains of PA, however, occupational and leisure time PA were most consistently reported across PAQ assessments. This observation is consistent with previous reports of more consistent recall of routine activities compared with less structured activities, e.g., walking (17,26,36). Although the extent of time elapsed between PAQ administrations may have attenuated estimates (3,6,15,32), our results correspond to test-retest estimates in the range of 0.31-0.73 from previous reports with intervals lasting ≥1 yr (3,17,26,32). Considering the duration of time between PAQ1 and PAQ2 (∼1 yr), changes in PA behavior are feasible.

Overall, PA was stable across subgroups defined by gender, age, education level, and BMI. However, modest differences in the consistency of walking and sedentary behavior by gender may indicate subgroup-specific differences in participation in these activities between the two PAQ administrations.

We must consider several other limitations of our study and the potential implications for our results. Neither accelerometry nor the PA-log represents a "gold standard" method of PA measurement, and neither instrument directly and independently captures total PA, activity intensity, and domains of PA. Yet the use of objective methods such as accelerometry in a validation study limits the potential for correlated error that likely exists when comparing the PAQ with another self-report method, e.g., the PA-log. However, it is possible that participants' reporting on the PA-log may have been influenced by wearing accelerometers during the same period, or vice versa, that activity patterns were altered by completing the PA-log, although the influence of a PA-log on questionnaire validity has been shown to be minor (37). In addition, the quality of accelerometer data may have been improved by requiring at least three valid days of monitor wear; yet we observed exceptional compliance with the study protocol, and we collected more than five valid days of data for each measurement week for 80% of our study population. In our study, PAQ2 showed stronger correlations with the PA-log than did PAQ1 (data not shown), indicating that participants' reporting on the PAQ may have successively improved after quarterly completion of the PA-log. Alternatively, such a difference may result from the fact that the time frame of reference of PAQ1 did not overlap with the time of PA-log completion. Regardless, the correlations of PAQ1 and PAQ2 with accelerometry were similar (data not shown), suggesting that our results do not overestimate the validity of the PAQ when compared with an objective criterion. Another potential limitation is the possibility that the cut points chosen to distinguish accelerometer intensity levels influenced estimates of the absolute validity of the PAQ (12,22), although the ability of the PAQ to rank PA levels is unlikely to be sensitive to small changes in accelerometer cut point within a given intensity level. Moreover, the ability of counts per minute per day to rank total PA does not depend on accelerometer cut points.

The PAQ evaluated in this study was designed to assess the range of types (household, transportation, occupation and volunteer work, caring for others, recreation and exercise, and stair climbing) and parameters (intensity, frequency, and duration) of PA typical of adults in Shanghai. Strengths of our study include the study design, with two administrations of the PAQ and repeated measures of the accelerometer, and the PA-log during a 1-yr period. In addition, we observed a high rate of compliance by participants and good quality and completeness of PA data.

In summary, the PAQ is valid for classifying individuals into quartiles of total PA and certain PA subcomponents. The potential for underascertainment of sedentary behavior and light activity and the limited validity of the PAQ among older persons should be considered, but the PAQ will be useful to assess PA as an exposure in etiologic studies among adults in urban China.

The study was supported in part by the Intramural Research Program of the National Institutes of Health (NIH) and by NIH grants R01 CA70867 (Shanghai Women's Health Study) and RO1 CA82729 (Shanghai Men's Health Study), which supported the parent cohort studies. The ActiGraph accelerometer is a product of MTI ActiGraph, Fort Walton, FL.

The authors have no conflicts of interest to declare.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.

The authors would like to acknowledge Dr. Stephen Sharp for statistical assistance.

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