Bayesian growth curve model useful for high-dimensional longitudinal data

Traditional inference on the growth curve model (GCM) requires ‘small p large n’ ( $ n \gg p $ n≫p) and cannot be applied in high-dimensional scenarios, where we often encounter singularity. Several methods are proposed to tackle the singularity problem, however there are still limitations and gaps. We consider a Bayesian framework to derive a statistic for testing a linear hypothesis on the GCM. Extensive simulations are performed to investigate performance and establish optimality characteristics. We show that the test overcomes the challenge of high-dimensionality and possesses all the desirable optimality characteristics of a good test - it is unbiased, symmetric and monotone with respect to sample size and departure from the null hypotheses. The results also indicate that the test performs very well, possessing a level close to the nominal value and high power in rejecting small departures from the null. The results also show that the test overcomes limitations of a previously proposed test. We illustrated practical applications using a publicly available time course genetic data on breast cancer, where we used our test statistic for gene filtering. The genes were ranked according to the value of the test statistic and the top five genes were annotated.