Abstract
Longitudinal data analysis had been widely developed in the past three decades. Longitudinal data are common in many fields such as public health, medicine, biological and social sciences. Longitudinal data have special nature as the individual may be observed during a long period of time. Hence, missing values are common in longitudinal data. The presence of missing values leads to biased results and complicates the analysis. The missing values have two patterns: intermittent and dropout. The missing data mechanisms are missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). The appropriate analysis relies heavily on the assumed mechanism and pattern. The parametric fractional imputation is developed to handle longitudinal data with intermittent missing pattern. The maximum likelihood estimates are obtained and the Jackkife method is used to obtain the standard errors of the parameters estimates. Finally a simulation study is conducted to validate the proposed approach. Also, the proposed approach is applied to a real data.
Highlights
Longitudinal studies are common in many fields, where data are collected from each subject repeatedly over time, or under different conditions
The missing data mechanism is missing completely at random (MCAR) if the probability of missingness is not related to the unobserved and the observed values. It is missing at random (MAR) if the probability missingness is related to the observed values and if the probability of missingness is related to both observed and unobserved values, it is denoted as missing not at random (MNAR)
Many techniques have been proposed to deal with incomplete longitudinal data such as; the complete case analysis (CC) which depends on analyzing the cases without missing and ignoring the others with missing (Donders., et al, 2006)
Summary
Longitudinal studies are common in many fields, where data are collected from each subject repeatedly over time, or under different conditions. There are three models obtained by different factorization of the joint distribution of the response variable Y, and the missing indicator R. Many techniques have been proposed to deal with incomplete longitudinal data such as; the complete case analysis (CC) which depends on analyzing the cases without missing and ignoring the others with missing (Donders., et al, 2006). The likelihood based methods depend on maximizing the log-likelihood function of the joint model of the complete data. The aim of this paper is to develop the PFI method to estimate the parameters in the presence of the intermittent missingness.
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