Abstract
A statistical note on analyzing and interpreting individual-level epidemiological data.
Highlights
The first issue is Cox regression modeling with rare events
It is well known that the maximum likelihood estimator (MLE) becomes unreliable under “monotone likelihood”
For a simple univariate case, such monotone likelihood occurs when a failed individual with the rare event has the highest or lowest value for a covariate in the risk set at each failure time, which happens in the case of a linear combination of independent variables.[1,2]
Summary
Parameters of interest can be estimated by the maximum likelihood method. It is well known that the maximum likelihood estimator (MLE) becomes unreliable under “monotone likelihood” (ie, during the iterative calculation, the likelihood converges while some estimated parameters diverge to infinity).[1] For a simple univariate case, such monotone likelihood occurs when a failed individual with the rare event has the highest or lowest value for a covariate in the risk set at each failure time, which happens in the case of a linear combination of independent variables.[1,2] The resultant estimates commonly produce large estimates and standard errors (SE).
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