Handling incomplete Quality-of-Life Data

Incomplete data sets are often encountered in theanalysis of quality-of-life (QOL) data. The incompleteness arisesfrom two major sources, namely, missing responses and artificialquantification of response categories. Shen and Lai (1998a)propose using Optimal Scaling (OS) to tackle the problem. The OSmethod based on numerical iterative approach attempts to restorethe continuous property of the measurements and provide estimatesfor missing responses. However, the OS leads to convergenceproblem when there are many missing values in the data set; andit incorporates no mechanisms to provide the standard errors ofthe mean estimates when missing values are filled. Hot-deckimputation is therefore suggested. This paper presents asimulation study to show that the random hot-deck imputationyields reasonable estimates for the population mean and generallypreserves the distribution of the population. In addition, whenapplying the random hot-deck imputation, valid estimates for thestandard error of the mean estimate can be obtained using thevariance formula due to Lai (1998). With hot-deck imputationtaking care of the missing responses and OS quantifying theresponse categories, it is postulated that the problem of dataincompleteness can be more satisfactorily handled. By applyingthe proposed techniques to real survey data, this paper alsopresents the change of the QOL of Hong Kong residents in the lastdecade leading to the turning point of the metropolis in 1997.