Maximum Likelihood Estimation of Binary Regression Model Under Proxy Response Bias

Sammanfattning

Proxy responses are commonly used in health and social care surveys when sampled individuals are unable to respond directly, but such responses are prone to outcome misclassification and selective missingness. When proxy use is non-random, these features can distort inference in binary regression models. This thesis develops and evaluates a Maximum Likelihood Estimator (MLE) for binary outcomes subject to proxy-induced misclassification under a Missing at Random (MAR) mechanism. The estimator is derived from a fully parametric likelihood and explicitly models both the self-response process and proxy reporting error. Using Monte Carlo simulations across varying sample sizes (n=50–10,000) and varying MAR response model parameters (0.2–0.8), the MLE is compared with Complete Case Analysis, Proxy Substitution, Multiple Imputation, and Inverse Probability of Treatment Weighting. A sensitivity analysis on proxy misclassification rates showed that while effect magnitudes varied moderately (up to 15%), the direction of all associations remained stable, indicating robust substantive conclusions. Furthermore, MLE consistently achieved lower bias and mean squared error than other competing methods in most cases. Application to real data from 2017 Swedish National Board of Health and Welfare home care survey (≈43% proxy responses) confirms these findings. Overall, the results demonstrate that explicitly modelling proxy misclassification is essential for valid inference in proxy-heavy survey data.