Introduction to the Analysis of Longitudinal Data
Lesa Hoffman in Longitudinal Analysis, 2015
The purpose of this chapter was to introduce some of the recurring themes in longitudinal analysis. In terms of levels of analysis, longitudinal data provide information about between-person relationships (i.e., level-2, time-invariant relationships for attributes measured only once, or for their average values over time), as well as about within-person relationships (i.e., level-1, time-varying relationships for attributes measured repeatedly that vary over time). Longitudinal data can be organized along a continuum ranging from within-person fluctuation, which is often the goal of short-term studies (e.g., daily diary or ecological momentary assessment studies), to within-person change, which is often the goal of longer-term studies (e.g., data collected over multiple years in order to observe systematic change). In reality, however, these distinctions may not always be so obvious and will need to be examined empirically.
Joint Modeling of Longitudinal and Survival Data with a Cure Fraction
Yingwei Peng, Binbing Yu in Cure Models, 2021
Longitudinal data consist of repeated outcome measurements from the same subjects over time and are frequently collected in medical and social science studies along with time to event data from the subjects. Even though longitudinal data and time to event data can be analyzed separately by existing statistical models, a joint analysis of the longitudinal and survival data becomes very popular in recent years because it may provide more efficient estimation than the separate analyses when longitudinal data and survival data are highly correlated (Ibrahim et al., 2010; Rizopoulos, 2012; Gould et al., 2015). In this chapter, we will introduce some methods for a joint analysis of longitudinal data and survival data when some subjects are cured and thus a cured fraction has to be properly taken into account in the joint analysis. The chapter is organized as follows: Section 5.2 introduces examples of longitudinal data and survival data from the same group of study subjects and notations that will be used in this chapter. Section 5.3 and 5.4 discuss a shared random effects approach to jointly model longitudinal continuous and proportional data and survival data with a cured fraction. Section 5.5 presents another approach for the joint model by including the trajectory of the longitudinal model in the cure model for survival data. Finally, applications of some joint models to data from in a breast cancer clinical trial are given in Section 5.6.
Dynamic Structural Equation Models of Change
Jason T. Newsom, Richard N. Jones, Scott M. Hofer in Longitudinal Data Analysis, 2013
Aging, health, and social science researchers often spend considerable time and resources on longitudinal data collection to study the dynamic interplay of variables over time. The use of longitudinal data helps make the important distinction between differences between individuals and changes within an individual (McArdle, 2009).* Studying the longitudinal relationships between variables, however, remains a data analysis challenge for many researchers. This prevents adequate use of these valuable data to test hypotheses about directionality of effects. Aging, health, and social science researchers often resort to modeling longitudinal change in one variable using a growth curve model and using another dynamic variable as a static predictor of change parameters. But this approach ignores the longitudinal change in the other variable. It also falls short of being able to test any hypothesis about longitudinal relationships between the variables.
Clustering of longitudinal interval-valued data via mixture distribution under covariance separability
Published in Journal of Applied Statistics, 2020
Seongoh Park, Johan Lim, Hyejeong Choi, Minjung Kwak
The longitudinal data are a subset of repeatedly measured data over time [12]. Thus, the longitudinal interval-valued data can be understood as data for which the response of each experimental subject is observed as an interval on multiple occasions. More formally, the observations of longitudinal interval data for the ith subject, for q repeated measurements, have the matrix form of a 1) and can be vectorized as (2). The analysis of longitudinal interval-valued data also depends on the type of interval data, the ME-type and MM-type, discussed in Section 1. In this paper, we only focus on the MM-type data, which is the type of our blood pressure example presented in Section 4.
Improved kth power expectile regression with nonignorable dropouts
Published in Journal of Applied Statistics, 2022
In population health, biological researches, economics, social sciences, data are often collected from every sampled subject at many time points, which are referred to as longitudinal data. Our study is motivated by the following longitudinal data from the AIDS Clinical Trial Group 193A (ACTG 193A), which was a study of HIV-AIDS patients with advanced immune suppression. After the treatment was applied, the CD4 counts were scheduled to be collected from each patient in every 8 weeks. However, because of adverse events, low-grade toxic reactions, the desire to seek other therapies, death and some other reasons, the dropout rates of the first four follow-up times are 31.5%, 42.4%, 55.4% and 65.3%, respectively. In addition, previous experiences from doctors and Cho et al. [3] indicated that a steep decline in the CD4 cell counts indicates the disease progression, and patients with low CD4 cell counts are more likely to drop out from the scheduled study visits compared to patients with normal CD4 cell counts. Therefore, nonresponse of the CD4 cell counts is likely related to itself and is nonignorable [31]. On the other hand, it can be checked that the distribution of CD4 cell counts is skewed. Hence, the response mean regression may not appropriately assess the longitudinal change in the CD4 cell counts.
Conditional standards for the quantification of foetal growth in an ethnic Chinese population: a longitudinal study
Published in Journal of Obstetrics and Gynaecology, 2022
Jian Jiang, Xiaodan Zhu, Linyu Zhou, Shanyu Yin, Weilian Feng, Tian’an Jiang
There are two types of raw data that can be used to construct the standard or reference of foetal biometry: cross-sectional data and longitudinal data. In cross-sectional studies, each foetus is observed only once, thus it can only assess foetal size (Royston 1995). Longitudinal data are derived from serial scans and thus reflect the dynamic process of foetal growth. Longitudinal data is a multilevel data that has two levels of variation: within foetuses and between foetuses. Utilising the multilevel modelling, longitudinal data can calculate conditional percentile that can be used to assess foetal growth (Royston and Altman 1995; Owen and Ogston 1998). The conditional percentile is an adjusted growth interval based on the previous measurements of the same foetus earlier in pregnancy and individualised growth trajectory (Hiersch and Melamed 2018).
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