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Lumley et al. specify that the estimating equations for the Cox regression are the same as those used in the conditional logistic regression for the case-crossover design and that we applied them to the same data.
It can be seen that the estimating errors of all the methods improve as N increases.
It can be shown that the estimating equation for β ̂ I 1 is equivalent to the following nonlinear equations for {b lm, for l=0,1, m=1,⋯,k}, ∑ m = 1 k ∑ a ∈ A y alm λ alm − e b lm ∑ a ∈ A t alm λ alm = 0, ∑ l = 0, 1 ∑ a ∈ A y alm λ alm − e b lm ∑ a ∈ A t alm λ alm = 0, for l=0,1 and m=1,…,k−1.
Statistical theory and our simulations suggest that the estimating equations estimates of β have approximately normal distributions at sample sizes above 20 or 30.
We see that the estimating function is not "well-behaved" in any of the cases: none of the functions is monotonic (either increasing for all values of the CRR or decreasing for all values).
Results with regard to potential bias are shown in Figures 1 and 2, and in Tables 1 and 2. Figure 1 suggests that the estimating equations produce unbiased estimates of μ regardless of exposure frequency when the model is correctly specified, even if sample sizes are very small.
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I can get on board with that – the estimated 300,000 people that fled probably just wanted a change of scenery.
He added that the estimated $4 billion cost is reasonable given the requirements of the project.
It can be seen from this table that the estimated d is significantly lower than the maximum theoretical value (2.0).
The latter ensures that the estimated posterior probabilities are normalized.
The results showed that the estimated baseline vectors were similar.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com