Hi! I have quite a specific question regarding the use of estimating equations - so hope that it’s in place here. Currently I’m reading a paper that uses estimating equations for variance estimation. I’m not familiar with estimating equations and a bit confused about two of the estimating equations used and in search for some help or perhaps some references.

The problem is the following: you have a dataset of N people, and assume that all N people have two repeated measures of an endpoint that is contaminated with measurement error (V_1 and V_2) and additionally, M people (M < N) have an additional (error free) measure of the endpoint, Y. Further, we assume that the expected value of V is equal to \theta_0 + \theta_1Y (and there is no dependence between the two measures V). Using this, we would like to form the estimating equations for the parameters \theta_0 and \theta_1 (and eventually use this information to predict Y in all people without a measure of Y). According to the paper these would respectively be:

N^{-1}\sum^N_i(Y_i-\theta_0-\theta_1V_{1i})I_iN/M = 0

N^{-1}\sum^N_i(Y_i-\theta_0-\theta_1V_{1i})V_{2i}I_iN/M = 0

where I_i is 1 if individual i is contained in the subset consisting of individuals with measures of Y and 0 if not.

I’m a bit confused on why you would only use the first measure (V_1) to form an estimating equation for \theta_0 and then for the estimating equation of \theta_1 you multiply it with the second measure (V_2) (for me it would make more sense to take the mean of the two measures).

Really would appreciate help of any kind!

Best,

Linda