Non-compliance in surgical patients with herniated lumbar discs: an application of an extended latent class model to selection model

In a recent observational study on a sample of patients with herniated lumbar discs who underwent physiotherapy, the recovery rate of those who chose physiotherapy rather than surgery, as recommended, was not appreciably different from that of the other patients, although their prognosis was worse. To investigate whether this finding was due to a confounding effect induced by unobserved features of the patients, we fit a latent class model for the joint distribution of compliance, participation rate and recovery, given the individual attitude (modelled as latent variable) and a set of covariates. The usual assumption of local independence is relaxed in favour of conditional association between the observed variables given the latent one. The results indicate that the latent classes may be interpreted as dividing the patients according to whether they are highly versus moderately motivated towards physiotherapy: conditionally on the covariates, the more motivated subjects attend a larger number of therapy sessions and benefit much more from the therapy. In addition, the fact that the proportion of less motivated patients among non-compliers is very small may be due to a self-selection mechanism, which may explain the surprisingly good performance of physiotherapy for these patients.