  Health economic evaluations face the issues of non-compliance and missing
data. Here, non-compliance is defined as non-adherence to a specific treatment,
and occurs within randomised controlled trials (RCTs) when participants depart
from their random assignment. Missing data arises if, for example, there is
loss to follow-up, survey non-response, or the information available from
routine data sources is incomplete. Appropriate statistical methods for
handling non-compliance and missing data have been developed, but they have
rarely been applied in health economics studies. Here, we illustrate the issues
and outline some of the appropriate methods to handle these with an application
to a health economic evaluation that uses data from an RCT.
  In an RCT the random assignment can be used as an instrument for treatment
receipt, to obtain consistent estimates of the complier average causal effect,
provided the underlying assumptions are met. Instrumental variable methods can
accommodate essential features of the health economic context such as the
correlation between individuals' costs and outcomes in cost-effectiveness
studies. Methodological guidance for handling missing data encourages
approaches such as multiple imputation or inverse probability weighting, that
assume the data are Missing At Random, but also sensitivity analyses that
recognise the data may be missing according to the true, unobserved values,
that is, Missing Not at Random.
  Future studies should subject the assumptions behind methods for handling
non-compliance and missing data to thorough sensitivity analyses. Modern
machine learning methods can help reduce reliance on correct model
specification. Further research is required to develop flexible methods for
handling more complex forms of non-compliance and missing data.
