Tailor the longitudinal anaysis for nih longitudinal normal brain developmental study

There are imminent needs for longitudinal analysis to make physiological inferences on NIH MRI study of normal brain development. But up to date, two critical aspects for longitudinal analysis, namely the selections of mean and covariance structures have not been addressed by the neuroimaging community. For the mean structure, we employed a linear free-knot B-spline regression in combination with quasi-least square estimating equations to approximate a nonlinear growth trajectory with piecewise linear segments for a friendly physiological interpretation. For covariance structure selection, we have proposed a novel time varying correlation structure considering not only the time separation between the repeated measures but also when these acquisitions occurred. We have demonstrated that the proposed covariance structure has a lower Akaike information criterion value than the commonly used Markov correlation structure.