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Maximum Likelihood Estimation of Logistic Regression Parameters under Two‐phase, Outcome‐dependent Sampling
Author(s) -
Breslow Norman E.,
Holubkov Richard
Publication year - 1997
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00078
Subject(s) - statistics , logistic regression , stratified sampling , sampling (signal processing) , outcome (game theory) , sampling design , mathematics , econometrics , regression analysis , computer science , mathematical economics , filter (signal processing) , computer vision , demography , sociology , population
Outcome‐dependent sampling increases the efficiency of studies of rare outcomes, examples being case—control studies in epidemiology and choice–based sampling in econometrics. Two‐phase or double sampling is a standard technique for drawing efficient stratified samples. We develop maximum likelihood estimation of logistic regression coefficients for a hybrid two‐phase, outcome–dependent sampling design. An algorithm is given for determining the estimates by repeated fitting of ordinary logistic regression models. Simulation results demonstrate the efficiency loss associated with alternative pseudolikelihood and weighted likelihood methods for certain data configurations. These results provide an efficient solution to the measurement error problem with validation sampling based on a discrete surrogate.