Analysis of Mixed Discrete and Heavy Tailed Longitudinal Data with Non-random Missingness Using Stochastic Variants of the EM Algorithm

Abdallah S. A. Yaseen^1,

¹The National Centre for Social and Criminological Research, Cairo, Egypt

Cite this paper:
Abdallah S. A. Yaseen. Analysis of Mixed Discrete and Heavy Tailed Longitudinal Data with Non-random Missingness Using Stochastic Variants of the EM Algorithm. American Journal of Applied Mathematics and Statistics. 2022; 10(1):28-38. doi: 10.12691/ajams-10-1-5

Abstract

Interstitial cystitis (IC) is a chronic inflammatory condition that results in recurring discomfort or pain in the bladder and the surrounding pelvic region. In interstitial cystitis data base (ICDB) cohort study, the main target is to determine the influence of covariates, such as the demographic clinical characteristics of patients, on the longitudinal outcomes including the pain score (p), urinary urgency (u) and urinary frequency (f) which are three main indices reflecting IC symptoms. The ICDB data are mixed (discrete and continuous) longitudinal data. In longitudinal studies the continuous response may be non-normal, heavy tailed for example. The analysis of mixed longitudinal data is challenging due to several inherent features: (1) more than one outcome are followed for each subject over a period of time. (2) The longitudinal outcomes are subject to missingness that may be missing not at random (MNAR). This article proposes the analysis of mixed discrete and heavy tailed longitudinal outcomes subject to MNAR missingness using two different alternative algorithms. The continuous outcome is assumed to follow non-normal heavy tailed distribution. The proposed methodology is an extension of [1] and [2]. The proposed techniques are applied to Interstitial Cystitis data. Also, three simulation studies are conducted to validate the proposed techniques.

Keywords:
stochastic expectation maximization parametric fractional imputation interstitial cystitis longitudinal data maximum likelihood missing data

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