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. 2014 Jul 1;180(1):111-9.
doi: 10.1093/aje/kwu107. Epub 2014 May 23.

Lack of identification in semiparametric instrumental variable models with binary outcomes

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

Lack of identification in semiparametric instrumental variable models with binary outcomes

Stephen Burgess et al. Am J Epidemiol. .

"VSports app下载" Abstract

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 VSports手机版. 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 (ρ(2) ≤ 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. .

Keywords: Avon Longitudinal Study of Parents and Children; generalized method of moments; identifiability; identification; instrumental variables; semiparametric methods; structural mean model; weak instruments. V体育安卓版.

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Figures

Figure 1.
Figure 1.
Estimating function for the example from Palmer et al. (20) demonstrating lack of identification. Two distinct parameter values for the causal risk ratio (0.81 and 4.95) satisfy the estimating equation formula image, where formula image is the average value of G in the population.
Figure 2.
Figure 2.
Percentage of simulated data sets with no solution (solid color), 1 solution (shaded), and multiple solutions (no color) from A) multiplicative generalized method of moments, and B) linear generalized method of moments methods with different strengths of instrument as measured by the squared correlation between the instrument and exposure (ρ2) and different sample sizes (n). For each value of ρ2, the first column is n = 5,000, the second column is n = 10,000, the third column is n = 20,000, and the fourth column is n = 50,000.
Figure 3.
Figure 3.
Estimating functions for the applied example from the multiplicative generalized method of moments method (in A, B, and C), and the linear generalized method of moments method (in D, E, and F) for the following 3 instruments: in A and D, a variant from the fat mass and obesity associated (FTO) gene; in B and E, the Speliotes score; and in C and F, the Speliotes score with the FTO genetic variant omitted. Avon Longitudinal Study of Parents and Children, 1991–1997.
See this image and copyright information in PMC

References

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