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

In a recent prospective observational study carried out on a sample of patients with herniated lumbar discs who underwent physiotherapy, the recovery rate of those who had been recommended surgical treatment, but did not comply and chose physiotherapy instead, was not appreciably different from that of the other patients, although their prognosis was worse. In order to investigate whether this finding may be due to a confounding effect induced by unobserved features of the patients, we have fitted to the data a latent class model which considers the joint probability of recovery and two other response variables presumably affected by individual choice (participation rate and compliance) as dependent on a latent variable and a set of covariates. Thus the assumption of conditional independence is relaxed and conditional association is modelled by regressing the outcomes one on the other. The results of our study indicate that the latent classes may be interpreted as dividing the patients according to whether they are highly versus moderately motivated towards therapy. More precisely, conditionally on the rest of the covariates, the more motivated subjects attend a larger number of therapy sessions and seem to benefit much more from the therapy. In addition, the fact that the proportion of less motivated patients among non-compliers is tiny may be due to a selection mechanism, which may explain the surprisingly good performance of physiotherapy for these patients.