  The intra-cluster correlation coefficient (ICC) plays an important role while
designing the cluster randomized trials (CRTs). Often optimal CRTs are designed
assuming that the magnitude of the ICC is constant across the clusters.
However, this assumption is hardly satisfied. In some applications, the precise
information about the cluster specific correlation is known in advance. In this
article, we propose an optimal design with non-constant ICC across the
clusters. Also in many situations, the cost of sampling of an observation from
a particular cluster may differ from that of some other cluster. An optimal
design in those scenarios is also obtained assuming unequal costs of sampling
from different clusters. The theoretical findings are supplemented by thorough
numerical examples.
