Accounting for misclassification in binary longitudinal data

Abstract

This thesis proposes new methodology for alternating binary longitudinal responses collected at discrete time points which may not correctly classify the state of the unobservable true process. The model consists of two distinct parts and enables estimation of the probabilities associated with two types of misclassification when supplementary information is available at each observation time. The misclassification part models misclassification probabilities as logistic functions of misclassification predictors available at each observation time and the true process part is modeled as a continuous-time counter model with time-independent covariates.

Parameter identifiability and estimaility issues are investigated when a Type I counter model has exponential state sojourn time distributions. Characteristic functions are used to identify distinct sets of parameter values which yield the same likelihood value for a data set. Estimability issues are discussed when the sampling interval is inadequate or the model is misspecified.

The effect of misclassification on the parameter estimates in the case of constant inter-observation times is next considered. In the absence of covariates and supplementary information, approximated estimators of Type I counter transition probabilities are constructed based on linear functions of known misclassification probabilities. Estimators ignoring misclassification are compared with the approximated and maximum likelihood estimators.

Standard model assessment techniques comparing observed and expected transition counts are applied and may not adequately detect model departures. A simulation study motivates a Type I counter model where one sojourn time has an exponential distribution and the other has a gamma distribution for the data sets considered. Via approximation, the equilibrium probabilities at three consecutive time points are used with misclassification probabilities to calculate expected frequencies. The discrepancy between the expected and observed data at these timepoints is minimized to obtain parameter estimates and estimates for the true state joint equilibrium probabilities.