EPID 766: Analysis of Longitudinal Data from ... - NCSU Statistics

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CHAPTER 1 Epid 766, D. Zhang 1.5 Why longitudinal studies? 1. A longitudinal study allows us to study the change of the variable of interest over time, either population level or individual level. 2. A longitudinal study enables us to separately estimate the cross-sectional effect (e.g., cohort effect) and the longitudinal effect (e.g., aging effect): Given yij, age ij (j = 1, 2, · · · , ni, j = 1 is baseline). In a cross-sectional study, ni = 1 and we are forced to fit the following model yi1 = β0 + βCage i1 + ǫi1. That is, βC is the cross-sectional effect of age. With longitudinal data (ni > 1), we can entertain the model yij = β0 + βCage i1 + βL(age ij − age i1) + ǫij. Graduate Summer Session in Epidemiology Slide 22
CHAPTER 1 Epid 766, D. Zhang Then yi1 = β0 + βCage i1 + ǫi1 (let j = 1), yij − yi1 = βL(age ij − age i1) + ǫij − ǫi1. That is, βL is the longitudinal effect of age and in general βL �= βC. 3. A longitudinal study is more powerful to detect an association of interest compared to a cross-sectional study, =⇒ more efficient, less sample size (number of subjects). 4. A longitudinal study allows us to study the within-subject and between-subject variations. Suppose b ∼ (µ, σ2 b ) is the blood pressure for a patient population. However, what we observe is Y = b + e, where e ∼ (0, σ2 e) is the measurement error. • σ 2 e = within-subject variation • σ 2 b = between-subject variation Graduate Summer Session in Epidemiology Slide 23
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EPID 766: Analysis of Longitudinal Data from ... - NCSU Statistics

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