The Two-Part Model and the Standard Error of the Treatment Effect Estimate

Researchers in health economics often seek to evaluate the effect of a policy or medical intervention on healthcare costs by employing a two-part model. While the model readily provides the treatment effect estimate, obtaining its standard error could be slightly more involved.

Depending on the study design, the effect of treatment on the treated could be estimated in a variety of different ways. For the purpose of this presentation, we will consider a design which involves a treatment group and a control group whose characteristics, including healthcare costs, are observed for several pre- and several post-treatment periods. As commonly seen in such types of data, a relatively large fraction of the respondents have zero reported medical costs.

Considering the features of this research design and data, one would seek for a modeling strategy that would account for the large fraction of zeros and also utilize the pre-post and treatment-control nature of the data. A possibility is to employ a difference-in-differences (DID) cost estimator derived from a two-part model (TPM). The caveat here is that the zero costs are generated by a different process from the one that generated the rest of the observed costs (e.g. no utilization vs. utilization). However, this should be a plausible assumption as it is practically impossible for someone to receive medical care at a zero cost.

Obtaining the DID estimate following this strategy is not particularly difficult.  However, computing its standard error could be somewhat more challenging.

Clearly, looking for the analytical standard error would be impractical. An alternative approach in these circumstances would be to compute empirical standard errors. This amounts to repeatedly sampling with replacement of entire patient records separately from the treatment and control groups, re-estimating the TPM, and re-calculating the DID estimate. This procedure produces the empirical distribution of the DID estimate, which can then be used to obtain, among other interesting statistics, the standard error of the treatment effect.

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