Chapter 9 Conclusions/ Final Thoughts

9.1 Strengths

This practical guide offers a relatively simple and easy-to-implement approach to assessing bias from non-ignorable LTFU in both observational and experimental research. The approach presented here integrates MCAR, MAR and MNAR mechanisms in a manner which reflects real-world co-existence of multiple missing data mechanisms. Combined with clear assumptions and instructions for selecting offset parameters, we hope this guide will encourage the use and reporting of pattern-mixture modeling for sensitivity analyses of MNAR mechanisms.

Furthermore, while authors have previously applied pattern-mixture modeling to analyze the impact of LTFU caused by the outcome, we extend it here to LTFU caused by an entirely unmeasured confounder. This additional scenario of MNAR outcome data helps researchers to assess situations in which those LTFU have different common causes of the outcome than those not LTFU. If researchers have a reason to believe that this type of missing data mechanism exists in their data, then this additional scenario and corresponding implementation in R will help them to more fully assess bias in their causal effect estimate.

9.2 Limitations

While this practical guide provides a sound methodology for evaluating the effects of non-ignorable LTFU, some limitations remain. First, pattern-mixture modeling will only provide useful results if the offset parameters are plausible. This is not to say that externally collected data are a must; instead, this method relies on the knowledge and experience of the user, which can be prone to error. Second, when causal effect estimates are calculated according to plausible offset parameters, we assume that causes of the outcome are similar in both the observed and LTFU groups. In reality, it is impossible to verify this assumption unless a sub-study is conducted to report empirically on the group that was LTFU. Finally, our methods for simulating an unmeasured confounder may be limited by the fact that it was initially modeled using a multiply imputed outcome variable. Future methods for conducting sensitivity analyses of MNAR mechanisms could employ more advanced simulations of the unmeasured confounder.

9.3 Opportunities for extending methods presented

Due to the simplicity and flexibility of pattern-mixture modeling, these methods can be extended to various other applications, including:

  • Categorical outcomes

  • A scenario in which LTFU causes the outcome

  • A scenario in which the relationship between outcome and LTFU operates in both directions

  • Missing exposure or covariate data in addition to missing outcome data, requiring multiple imputation by chained equations (MICE) or joint modeling