We develop a statistical line of response (LOR) estimator of the three-dimensional interaction positions of a pair of annihilation photons in a PET detector module with depth of interaction capability. The three-dimensional points of interaction of a coincidence pair of photons within the detector module are estimated by calculation of an expectation of the points of interaction conditioned on the signals measured by the photosensors. This conditional expectation is computed from estimates of the probability density function of the light collection process and a model of the kinetics of photon interactions in the detector module. Our algorithm is capable of handling coincidences where each annihilation photon interacts any number of times within the detector module before being completely absorbed or escaping. In the case of multiple interactions, our algorithm estimates the position of the first interaction for each of the coincidence photons. This LOR estimation algorithm is developed for a high-resolution PET detector capable of providing depth-of-interaction information. Depth of interaction is measured by tailoring the light shared between two adjacent detector elements. These light-sharing crystal pairs are referred to as dMiCE and are being developed in our lab. Each detector element in the prototype system has a 2 x 2 mm(2) cross section and is directly coupled to a micro-pixel avalanche photodiode (MAPD). In this set-up, the distribution of the ratio of light shared between two adjacent detector elements can be expressed as a function of the depth of interaction. Monte Carlo experiments are performed using our LOR estimation algorithm and compared with Anger logic. We show that our LOR estimation algorithm provides a significant improvement over Anger logic under a variety of parameters.