In complex analysis, several research works have been done using the concepts of different growth indicators of entire functions such as order, lower order etc. In past decades, the study of the growth properties regarding entire function has usually been done using the concepts of maximum modulus and maximum term. On the other hand, Biswas (J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 25(3) (2018), pp. 193-201 and Uzbek Math. J., 2018 (2), (2018), pp. 153-160) has initiated to study some growth properties of composite entire functions using the concepts of central index. Considering the idea, here in this paper, we have compared the central index of the composition of two entire functions with their corresponding left and right factors. Mainly, we have established some results related to the growth rates of composite entire functions on the basis of central index using the ideas of (p,q,t)L-th order, (p,q,t)L-th type and (p,q,t)L-th weak type.