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Abstract
Conclusions from studies vary regarding the association of weight loss among obese people and measures of health and/or mortality. Total weight loss for individuals in a population may be a combination of intentional weight loss (IWL) and unintentional weight loss (UWL). Among people who have no intention to lose weight, the total weight loss observed is UWL. Among people who have intention to lose weight, the total weight loss is assumed to be UWL and IWL. Note that total weight loss among subjects intending to lose weight is observable but IWL itself is not and, therefore, the latent variable that is of interest.
This research reformulates Coffey et al. (2005) using the potential outcomes framework which help to clarify nonestimable quantities, in particular, tighten bounds for nonestimable correlation parameter and a causal parameter in a linear model under certain assumptions. Also, the positive definiteness requirement of a correlation matrix with covariate(s) is helpful in order to tighten the bounds for nonestimable quantities, and this is demostrated using the mice data example from Coffey et al. (2005). A parametric bootstrap is used to investigate sampling variability of estimated bounds for the causal parameter.
Finally, a matched pairs design is considered in order to get more information for a nonestimable parameter. Three data examples are considered; a data set from an experiment on eye treatments, the mice data set, and a data set from a study on twins. With the mice data set, the base line weight is used to assign mice to matched pairs. Some pairs are created from mice in different treatment groups, and other pairs from mice in the same treatment group. The latter helps to assess "quality of matching".
