= Death-only rate correction under exponential censoring
{title2=$\widehat\lambda_{\text{plug-in}}=\widehat\pi\widehat s$}
Under independent exponential death and censoring, a rate fit using only observed-death times estimates $s=\lambda+\gamma$. Multiplying by the observed death fraction consistently estimates $\lambda$. This plug-in correction generally differs in a finite sample from the full maximum-likelihood estimate, which uses observed exposure from both deaths and censored subjects.
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