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In the attention-deficit hyperactivity disorder (ADHD) study, children are prescribed different stimulant medications. The height measurements are recorded longitudinally along with the medication time. Differences among the patients are captured by the parameters suggested the Superimposition by Translation and Rotation (SITAR) model using three subject-specific parameters to estimate their deviation from the mean growth curve. In this paper, we generalize the SITAR model in a Bayesian way with time-invariant covariates. The time-invariant model allows us to predict latent growth factors. Since patients suffer from a common disease, they usually exhibit a similar pattern, and it is natural to build a nonlinear model that is shaped invariant. The model is semi-parametric, where the population time curve is modeled with a natural cubic spline. The original shape invariant growth curve model, motivated by epidemiological research on the evolution of pubertal heights over time, fits the underlying shape function for height over age and estimates subject-specific deviations from this curve in terms of size, tempo, and velocity using maximum likelihood. The usefulness of the model is illustrated in the attention deficit hyperactivity disorder (ADHD) study. Further, we demonstrated the effect of stimulant medications on pubertal growth by gender.

Objective: Association between acute ambient fine particulate matter (PM2.5, aerodynamic diameter less than 2.5 and cardiovascular events are well documented. However, it remains unclear whether acute exposure to PM2.5 acts as a trigger for hemorrhagic (intracerebral or subarachnoid hemorrhage) or non-hemorrhagic (infarct or transient ischemic attack) stroke onset. We, therefore, examined the association between ambient PM2.5 and stroke onset, and whether this relationship differs by stroke subtype, age, sex, and race. Methods: We used a time-stratified case-crossover design to examine the association between exposure to PM2.5 and stroke onset for the calendar year 2010. Data were collected from the Greater Cincinnati Northern Kentucky Stroke Study. We included patients 20 years and older, initially ascertained through hospital ICD-9 discharge codes. Daily ambient concentrations of PM2.5 were estimated from the patient's residential addresses using a spatiotemporal model. Conclusion: Our findings suggest that short-term PM2.5 exposure, particularly at three days before the event, is associated with stroke onset but varies according to stroke subtype, age, sex, and race., Comment: One coauthor didnt want to submit the paper on the arxiv