Imputing accelerometer non-wear time when assessing children's moderate-to-vigorous physical activity

BACKGROUND: Moderate-to-vigorous physical activity (MVPA) is an important determinant of children’s physical health, and is commonly measured using accelerometers. A major limitation of accelerometers is non-wear time, which is the time the participant did not wear their device. Given that non-wear time is traditionally discarded from the dataset prior to estimating MVPA, final estimates of MVPA may be biased. Therefore, alternate approaches should be explored. OBJECTIVES: The objectives of this thesis were to 1) develop and describe an imputation approach that uses the socio-demographic, time, health, and behavioural data from participants to replace non-wear time accelerometer data, 2) determine the extent to which imputation of non-wear time data influences estimates of MVPA, and 3) determine if imputation of non-wear time data influences the associations between MVPA, body mass index (BMI), and systolic blood pressure (SBP). METHODS: Seven days of accelerometer data were collected using Actical accelerometers from 332 children aged 10-13. Three methods for handling missing accelerometer data were compared: 1) the “non-imputed” method wherein non-wear time was deleted from the dataset, 2) imputation dataset I, wherein the imputation of MVPA during non-wear time was based upon socio-demographic factors of the participant (e.g., age), health information (e.g., BMI), and time characteristics of the non-wear period (e.g., season), and 3) imputation dataset II wherein the imputation of MVPA was based upon the same variables as imputation dataset I, plus organized sport information. Associations between MVPA and health outcomes in each method were assessed using linear regression. RESULTS: Non-wear time accounted for 7.5% of epochs during waking hours. The average minutes/day of MVPA was 56.8 (95% CI: 54.2, 59.5) in the non-imputed dataset, 58.4 (95% CI: 55.8, 61.0) in imputed dataset I, and 59.0 (95% CI: 56.3, 61.5) in imputed dataset II. Estimates between datasets were not significantly different. The strength of the relationship between MVPA with BMI and SBP were comparable between all three datasets. CONCLUSION: These findings suggest that studies that achieve high accelerometer compliance with unsystematic patterns of missing data can use the traditional approach of deleting non-wear time from the dataset to obtain MVPA measures without substantial bias.

Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.