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CPS2169 Carmen D. Tekwe et al.
p-values(p0.05 for all of the estimated coefficients). Point-wise bootstrap
confidence intervals were obtained at the 95% confidence level. The estimated
functional coefficient illustrates the curvilinear patterns of SDEE over time,
indicating that the patterns of physical activity is not constant across time.
Thus, the FLRM provides more flexibility in the estimations when compared to
the LRM in our application. The confidence intervals also support the
conclusion that there is insufficient evidence in our data to indicate that SDEE
is predictive of BMI values at 18 months post baseline among the children.

Results from CFQRM
At each quantile, measures of energy expenditure were reduced to linear
combinations of splines and basis functions. Similar to the FLRM, the final
numbers of basis functions were selected by comparing the AIC values
computed under varying numbers of basis functions at each quantile. The AIC
comparisons led to the choice of Kn=;4 at the 10th, 50th and 85 th quantiles,
Kn =6 at the 25th quantile, while Kn=7 was selected at the 95th and 99th
quantiles. We did not detect any statistically significant associations between
SDEE and the conditional quantile functions of our response across all the
quantile regressions considered (p>0.05 for all the spline coefficients). Figure
3 provides plots of the estimated functional coefficients on SDEE and their
corresponding 95% point-wise confidence intervals. The plots also illustrate
the patterns of physical activity behaviour across time under each quantile
regression. Varying patterns in the physical activity behaviour were observed
under the six quantile functions.

4. Discussion and Conclusion
Three regression-based methods were used to investigate the impact of
baseline SDEE on BMI values at 18 months post baseline among elementary
school-aged children recruited from a Texas school district. Using the LRM, we
assessed the impact of overall mean SDEE on the outcome of interest. A
potential disadvantage of this approach is that it does not account for
potential diurnal patterns of physical activity behaviour and the focus of the
analyses is on assessments of the covariate on the conditional mean of the
outcome. Using splines in the FLRM provided more flexibility by modelling the
objective measures of SDEE as curves, while the outcome was also the
conditional mean of BMI at 18 months post baseline. We note that unlike the
spline methodology employed, the use of overall mean SDEE to represent
physical activity behaviour at baseline resulted in loss of information. While
both the LRM and FLRM enable evaluations of covariate effects on the
conditional mean of BMI, the CFQRM enables assessments of covariate effects
across the entire distribution of the outcome.

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