Joint Longitudinal Models for Dealing With Missing at Random Data in Trial-Based Economic Evaluations

Published:February 18, 2021DOI:


      • Standard methods to handle missing data in trial-based economic evaluations discard some of the observed responses. In this article, we illustrate how joint longitudinal models provide an alternative and potentially less biased approach for handling missing data with respect to current practice under a missing at random assumption.
      • Methods that ignore some of the available information may be associated with biased results and mislead the decision-making process. Given the common problem of missing data, many study conclusions could be based on imprecise economic evidence.
      • This is a potentially serious issue for those who use these evaluations in their decision making, thus possibly leading to incorrect policy decisions about the cost-effectiveness of new treatment options.



      In trial-based economic evaluation, some individuals are typically associated with missing data at some time point, so that their corresponding aggregated outcomes (eg, quality-adjusted life-years) cannot be evaluated. Restricting the analysis to the complete cases is inefficient and can result in biased estimates, while imputation methods are often implemented under a missing at random (MAR) assumption. We propose the use of joint longitudinal models to extend standard approaches by taking into account the longitudinal structure to improve the estimation of the targeted quantities under MAR.


      We compare the results from methods that handle missingness at an aggregated (case deletion, baseline imputation, and joint aggregated models) and disaggregated (joint longitudinal models) level under MAR. The methods are compared using a simulation study and applied to data from 2 real case studies.


      Simulations show that, according to which data affect the missingness process, aggregated methods may lead to biased results, while joint longitudinal models lead to valid inferences under MAR. The analysis of the 2 case studies support these results as both parameter estimates and cost-effectiveness results vary based on the amount of data incorporated into the model.


      Our analyses suggest that methods implemented at the aggregated level are potentially biased under MAR as they ignore the information from the partially observed follow-up data. This limitation can be overcome by extending the analysis to a longitudinal framework using joint models, which can incorporate all the available evidence.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic and Personal


      Subscribe to Value in Health
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • EQ-5D-3L
        User guide: Basic information on how to use the EQ-5D-3L instrument.
        • Rubin D.
        Multiple Imputation for Nonresponse in Surveys.
        John Wiley & Sons, New York, NY1987
        • Noble S.
        • Hollingworth W.
        • Tilling K.
        Missing data in trial-based cost-effectiveness analysis: the current state of play.
        Health Econ. 2012; 23: 187-200
        • Gabrio A.
        • Mason A.
        • Baio G.
        Handling missing data in within-trial cost-effectiveness analysis: a review with future recommendations.
        Pharmacoecon Open. 2017; 1: 79-97
        • Leurent B.
        • Gomes M.
        • Carpenter J.
        Missing data in trial-based cost-effectiveness analysis: an incomplete journey.
        Health Econ. 2018; 27: 1024-1040
        • Little R.
        • Rubin D.
        Statistical Analysis With Missing Data.
        John Wiley & Sons, Hoboken, NJ2002
        • Little R.
        Modeling the drop-out mechanism in repeated-measures studies.
        J Am Stat Assoc. 1995; 90: 1112-1121
        • White I.
        • Thompson S.
        Adjusting for partially missing baseline measurements in randomized trials.
        Stat Med. 2005; 24: 993-1007
        • Sullivan T.
        • White I.
        • Salter A.
        • Ryan P.
        • Lee K.
        Should multiple imputation be the method of choice for handling missing data in randomized trials?.
        Stat Methods Med Res. 2016; 27: 2610-2626
        • Little R.
        Regression with missing x’s: a review.
        J Am Stat Assoc. 2012; 87: 1227-1237
        • Carpenter G.
        • Kenward M.
        Multiple Imputation and Its Applications.
        John Wiley & Sons, Chichester, UK2012
        • Van Buuren S.
        Flexible Imputation of Missing Data.
        Chapman and Hall/CRC, Boca Raton, FL2013
        • Brooks S.
        • Gelman A.
        • Jones G.
        • Meng X.
        Handbook of Markov Chain Monte Carlo.
        CRC Press, Boca Raton, FL2011
        • Daniels M.
        • Hogan J.
        Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis.
        Chapman and Hall, New York, NY2008
        • Drummond M.
        • Schulpher M.
        • Claxton K.
        • Stoddart G.
        • Torrance G.
        Methods for the Economic Evaluation of Health Care Programmes.
        3rd ed. Oxford University Press, Oxford, UK2005
        • Mason A.
        • Gomes M.
        • Grieve R.
        • Carpenter J.
        A Bayesian framework for health economic evaluation in studies with missing data.
        Health Econ. 2018; 27: 1670-1683
      1. Gabrio A, Mason A, Baio G. A full Bayesian model to handle structural ones and missingness in economic evaluations from individual-level data. Stat Med. 38(8):1399-1420.

        • Gomes M.
        • Radice R.
        • Camarena J.
        • Marra G.
        Copula selection models for non-Gaussian outcomes that are missing not at random.
        Stat Med. 2019; 38: 480-496
        • Gabrio A.
        • Daniels M.
        • Baio G.
        A Bayesian parametric approach to handle missing longitudinal outcome data in trial-based health economic evaluations.
        J R Stat Soc Ser A Stat Soc. 2020; 183: 607-629
        • Nixon R.
        • Thompson S.
        Methods for incorporating covariate adjustment, subgroup analysis and between centre differences into cost-effectiveness evaluations.
        Health Econ. 2005; 14: 1217-1229
        • Efron B.
        Nonparametric standard errors and confidence intervals.
        Can J Stat. 1981; 9: 139-172
      2. JAGS: Just Another Gibbs Sampler.
      3. Package R2jags.
      4. Package mice.
        • Gelman A.
        • Hill J.
        Data Analysis Using Regression and Multilevel/Hierarchical Models.
        Cambridge University Press, New York, NY2007
        • Bailey J.
        • Webster R.
        • Hunter R.
        • et al.
        The men’s safer sex project: intervention development and feasibility randomised controlled trial of an interactive digital intervention to increase condom use in men.
        Health Technol Assess Rep. 2016; 20: 1-115
        • Van Hout B.
        • Al M.
        • Gordon G.
        • Rutten F.
        • Kuntz K.
        Costs, effects, and c/e-ratios alongside a clinical trial.
        Health Econ. 1994; 3: 309-319
        • Hassiotis A.
        • Poppe M.
        • Strydom A.
        • et al.
        Clinical outcomes of staff training in positive behaviour support to reduce challenging behaviour in adults with intellectual disability: cluster randomised controlled trial.
        Br J Psychiatry. 2018; 212: 161-168
        • Brand J.
        • van Buuren S.
        • le Cessie S.
        • van den Hout W.
        Combining multiple imimputation and bootstrap in the analysis of cost-effectiveness trial data.
        Stat Med. 2019; 38: 210-220
        • Schomaker M.
        • Heumann C.
        Bootstrap inference when using multiple imputation.
        Stat Med. 2018; 37: 2252-2266
        • O’Hagan A.
        • Stevens J.
        A framework for cost-effectiveness analysis from clinical trial data.
        Health Econ. 2001; 10: 303-315
        • Basu A.
        • Manca A.
        Regression estimators for generic health-related quality of life and quality-adjusted life years.
        Med Decis Making. 2012; 32: 56-69
        • Ng E.
        • Diaz-Ordaz K.
        • Grieve R.
        • et al.
        Multilevel models for cost-effectiveness analyses that use cluster randomised trial data: an approach to model choice.
        Stat Methods Med Res. 2016; 25: 2036-2052
        • Mason A.
        • Richardson S.
        • Plewis I.
        • Best N.
        Strategy for modelling nonrandom missing data mechanisms in observational studies using Bayesian methods.
        J Off Stat. 2012; 28: 279-302
        • Leurent B.
        • Gomes M.
        • Faria R.
        • et al.
        Sensitivity analysis for not-at-random missing data in trial-based cost-effectiveness analysis: a tutorial.
        Pharmacoeconomics. 2018; 36: 1-13