Severe cases of spinal deformities such as scoliosis are usually treated by a surgery where instrumentation (hooks, screws and rods) is installed to the spine to correct deformities. Even if the purpose is to obtain a normal spine curve, the result is often straighter than normal. In this paper, we propose a fast statistical reconstruction algorithm based on a general model which can deal with such instrumented spines. To this end, we present the concept of multilevel statistical model where the data are decomposed into a within-group and a between-group component. The reconstruction procedure is formulated as a second-order cone program which can be solved very fast (few tenths of a second). Reconstruction errors were evaluated on real patient data and results showed that multilevel modeling allows better 3D reconstruction than classical models.