New approaches to obtaining individual peak height velocity and age at peak height velocity from the SITAR model. (September 2018) - Cao, Zhiqiang; Hui, L.L.; Wong, M.Y.
Highlights: Three new methods, the model method, the quadratic function method and the numerical method, for calculating the individual peak height velocity (PHV) and the age at peak height velocity (APHV) from the SITAR model, are proposed and compared. When the growth curves of all individuals are well fitted by the SITAR model, the quadratic function method is more superior since it does not produce unreasonable APHV estimates compared to the model method and costs less computation time compared to the numerical method. When the growth curves of some individuals are not well fitted by the SITAR model, the numerical method should be adopted for getting most robust estimates of PHV and APHV. The model method generates unreasonable APHV estimates, particularly when the growth curves are not well fitted. Abstract: Objective: We compared three methods for estimating the individual peak height velocity (PHV) and age at peak height velocity (APHV) from the SuperImposition by Translation and Rotation (SITAR) model. Methods: We fitted the SITAR model using simulated data and heights of 12 girls from the Chard Growth Study and obtained individual PHVs and APHVs from three methods: the model method, the quadratic function method and the numerical method, which are available in our newly developed R package"iapvbs". The mean, interquartile range, range of biases in estimated APHV and PHV as well as the rates of warning and unreasonable cases, i.e. estimated APHVs being outside the range of age measurements, from the three methods were presented and compared. Results: When the growth curves of all individuals were well fitted by the SITAR model, all three methods estimated individual APHVs with similarly small biases, with a few unreasonable cases (0.16%) observed when the model method was used while more computation time required for the numerical method. When the growth curves of some individuals were not very well fitted, the model method generated more unreasonable individual APHV (8.15%) and more bias in PHV and APHV, compared to those estimated by the numerical method and quadratic function method. In line with the observations from the simulated data, the real data analysis demonstrated that the numerical method generated more reliable PHV and APHV for individuals with growth curve not well fitted by the SITAR model. Conclusion: The performance of different methods estimating individual APHV depends largely on how well the growth curves are fitted by the SITAR model. The quadratic function method is more superior when growth curves of all individuals are well fitted by the SITAR model; otherwise, the numerical method should be adopted for getting most robust estimates of PHV and APHV. The model method generates unreasonable APHV estimates, particularly when the growth curves are not well fitted.