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2014 ; 15
(4
): 745-56
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Almost efficient estimation of relative risk regression
#MMPMID24705141
Fitzmaurice GM
; Lipsitz SR
; Arriaga A
; Sinha D
; Greenberg C
; Gawande AA
Biostatistics
2014[Oct]; 15
(4
): 745-56
PMID24705141
show ga
Relative risks (RRs) are often considered the preferred measures of association
in prospective studies, especially when the binary outcome of interest is common.
In particular, many researchers regard RRs to be more intuitively interpretable
than odds ratios. Although RR regression is a special case of generalized linear
models, specifically with a log link function for the binomial (or Bernoulli)
outcome, the resulting log-binomial regression does not respect the natural
parameter constraints. Because log-binomial regression does not ensure that
predicted probabilities are mapped to the [0,1] range, maximum likelihood (ML)
estimation is often subject to numerical instability that leads to convergence
problems. To circumvent these problems, a number of alternative approaches for
estimating RR regression parameters have been proposed. One approach that has
been widely studied is the use of Poisson regression estimating equations. The
estimating equations for Poisson regression yield consistent, albeit inefficient,
estimators of the RR regression parameters. We consider the relative efficiency
of the Poisson regression estimator and develop an alternative, almost efficient
estimator for the RR regression parameters. The proposed method uses near-optimal
weights based on a Maclaurin series (Taylor series expanded around zero)
approximation to the true Bernoulli or binomial weight function. This yields an
almost efficient estimator while avoiding convergence problems. We examine the
asymptotic relative efficiency of the proposed estimator for an increase in the
number of terms in the series. Using simulations, we demonstrate the potential
for convergence problems with standard ML estimation of the log-binomial
regression model and illustrate how this is overcome using the proposed
estimator. We apply the proposed estimator to a study of predictors of
pre-operative use of beta blockers among patients undergoing colorectal surgery
after diagnosis of colon cancer.
|*Models, Statistical
[MESH]
|*Regression Analysis
[MESH]
|*Risk
[MESH]
|Adrenergic beta-Antagonists/therapeutic use
[MESH]
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