Analyzing left-truncated right-censored data with uncertain onset time with parametric models

Prevalent sampling is an efficient and focused approach to the study of the natural history of disease. Right-censored time-to-event data observed from prospective prevalent cohort studies are often subject to left-truncated sampling. Left-truncated samples are not randomly selected from the population of interest and have a selection bias. Extensive studies have focused on estimating the unbiased distribution given left-truncated samples. However, in many applications, the exact date of disease onset was not observed. For example, in an HIV infection study, the exact HIV infection time is not observable. However, it is known that the HIV infection date occurred between two observable dates. Meeting these challenges motivated our study. We propose parametric models to estimate the unbiased distribution of left-truncated, right-censored time-to-event data with uncertain onset times. We first consider data from a length-biased sampling, a specific case in left-truncated samplings. Then we extend the proposed method to general left-truncated sampling. With a parametric model, we construct the full likelihood, given a biased sample with unobservable onset of disease. The parameters are estimated through the maximization of the constructed likelihood by adjusting the selection bias and unobservable exact onset. Simulations are conducted to evaluate the finite sample performance of the proposed methods. We apply the proposed method to an HIV infection study, estimating the unbiased survival function and covariance coefficients. ^

Slope estimation in a parametric measurement error model: A simulation study

In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^

A multiplicative model for standardizing vital rates without using external standards

Standardization is a common method for adjusting confounding factors when comparing two or more exposure category to assess excess risk. Arbitrary choice of standard population in standardization introduces selection bias due to healthy worker effect. Small sample in specific groups also poses problems in estimating relative risk and the statistical significance is problematic. As an alternative, statistical models were proposed to overcome such limitations and find adjusted rates. In this dissertation, a multiplicative model is considered to address the issues related to standardized index namely: Standardized Mortality Ratio (SMR) and Comparative Mortality Factor (CMF). The model provides an alternative to conventional standardized technique. Maximum likelihood estimates of parameters of the model are used to construct an index similar to the SMR for estimating relative risk of exposure groups under comparison. Parametric Bootstrap resampling method is used to evaluate the goodness of fit of the model, behavior of estimated parameters and variability in relative risk on generated sample. The model provides an alternative to both direct and indirect standardization method. ^