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Testing for bias in weighted estimating equations. (English) Zbl 1154.62353
Summary: It is very common in regression analysis to encounter incompletely observed covariate information. A recent approach to analyse such data is weighted estimating equations [J.M. Robins, A. Rotnitzky and L.P. Zhao, J. Am. Stat. Assoc. 89, No. 427, 846-866 (1994; Zbl 0815.62043); L.P. Zhao, S. Lipsitz and D. Lew, Biometrics, 52, No. 4, 1165–1182 (1996; Zbl 0925.62304)]. With weighted estimating equations, the contribution to the estimating equation from a complete observation is weighted by the inverse of the probability of being observed. We propose a test statistic to assess if the weighted estimating equations produce biased estimates. Our test statistic is similar to the test statistic proposed by W.H. DuMouchel and G.J. Duncan [J. Am. Stat. Assoc. 78, 535–543 (1983: Zbl 0533.62011)] for weighted least squares estimates for sample survey data. The method is illustrated using data from a randomized clinical trial on chemotherapy for multiple myeloma.

MSC:
62J12 Generalized linear models (logistic models)
62G05 Nonparametric estimation
62G10 Nonparametric hypothesis testing
62P10 Applications of statistics to biology and medical sciences; meta analysis
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