Lack of identification in semiparametric instrumental variable models with binary outcomes

Stephen Burgess*, Raquel Granell, Tom M. Palmer, Jonathan A C Sterne, Vanessa Didelez

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)


A parameter in a statistical model is identified if its value can be uniquely determined from the distribution of the observable data. We consider the context of an instrumental variable analysis with a binary outcome for estimating a causal risk ratio. The semiparametric generalized method of moments and structural mean model frameworks use estimating equations for parameter estimation. In this paper, we demonstrate that lack of identification can occur in either of these frameworks, especially if the instrument is weak. In particular, the estimating equations may have no solution or multiple solutions. We investigate the relationship between the strength of the instrument and the proportion of simulated data sets for which there is a unique solution of the estimating equations. We see that this proportion does not appear to depend greatly on the sample size, particularly for weak instruments (ρ2 ≤ 0.01). Poor identification was observed in a considerable proportion of simulated data sets for instruments explaining up to 10% of the variance in the exposure with sample sizes up to 1 million. In an applied example considering the causal effect of body mass index (weight (kg)/height (m)2) on the probability of early menarche, estimates and standard errors from an automated optimization routine were misleading.

Original languageEnglish
Pages (from-to)111-119
Number of pages9
JournalAmerican Journal of Epidemiology
Issue number1
Publication statusPublished - 1 Jul 2014


  • Avon Longitudinal Study of Parents and Children
  • generalized method of moments
  • identifiability
  • identification
  • instrumental variables
  • semiparametric methods
  • structural mean model
  • weak instruments


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  • ConDuCT-II

    Blazeby, J.


    Project: Research

  • IEU Theme 3

    Windmeijer, F., Tilling, K. M. & Tilling, K. M.


    Project: Research


    Golding, J.


    Project: Research

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