Defense Date


Document Type


Degree Name

Master of Science



First Advisor

Viswanathan Ramakrishnan


Most studies on maturation and body composition using the Fels Longitudinal data mention peak height velocity (PHV) as an important outcome measure. The PHV is often derived from growth models such as the triple logistic model fitted to the stature (height) data. The age at PHV is sometimes ordinalized to designate an individual as an early, average or late maturer. In theory, age at PHV is the age at which the rate of growth reaches the maximum. Theoretically, for a well behaved growth function, this could be obtained by setting the second derivative of the growth function to zero and solving for age. Such a solution would obviously depend on the parameters of the growth function. An estimate of the age at PHV would be a function of estimates of these parameters. Since the estimates of age at PHV are ultimately used as a predictor variable for analyzing adulthood outcomes, the uncertainty in the estimation of the PHV inherent due to the uncertainty in the estimation of the growth model need to be accounted for. The asymptotic s.e. of the age at maximum velocity in simple growth models such as the logistic and the Gompertz models could be explicitly obtained because explicit formulas for the age at maximum velocity are available. In this thesis a numerical method is proposed for computing the s.e. of the age at PHV for those that do not lead to explicit solutions for the age at PHV. The accuracy of this method is demonstrated by computing the s.e. using the explicit method as well as the proposed numerical methods and by comparing them. Incorporating the estimates of the s.e. in regression models that use age at PHV as predictor is illustrated using the FELS data.


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Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

May 2010

Included in

Biostatistics Commons