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# lec1 - STAT 8630 Advanced Statistical Applications II...

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STAT 8630 — Advanced Statistical Applications II Lecture Notes Introduction to Longitudinal Data Terminology: Longitudinal data consist of observations (i.e., measurements) taken re- peatedly through time on a sample of experimental units (i.e., individuals, subjects). The experimental units or subjects can be human patients, animals, agricultural plots, etc. Typically, the terms “longitudinal data” and “longitudinal study” refer to situations in which data are collected through time under uncontrolled circumstances. E.g., subjects with torn ACLs in their knees are assigned to one of two methods of surgical repair and then followed through time (examined at 6, 12, ,18, 24 months for knee stability, say). Longitudinal data are to be contrasted with cross-sectional data . Cross-sectional data contain measurements on a sample of subjects at only one point in time. Repeated measures: The terms “repeated measurements” or, more sim- ply, “repeated measures” are sometimes used as rough synonyms for “lon- gitudinal data”, however, there are sometimes slight differences in meaning for these terms. Repeated measures are also multiple measurements on each of several individuals, but they are not necessarily through time. E.g., mea- surements of chemical concentration in the leaves of a plant taken at different locations (low, medium and high on the plant, say) can be regarded as repeated measures. 1

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In addition, repeated measures may occur across the levels of some controlled factor. E.g., crossover studies involve repeated mea- sures. In a crossover study, subjects are assigned to multiple treat- ments (usually 2 or 3) sequentially. E.g., a two period crossover ex- periment involves subjects who each get treatments A and B, some in the order AB, and others in the order BA. Another rough synonym for longitudinal data is panel data. The term panel data is more common in econometrics, the term longitudinal data is most commonly used in biostatistics, and the term repeated measures most often arises in an agricultural context. In all cases, however, we are referring to multiple measurements of essen- tially the same variable(s) on a given subject or unit of observation. We’ll often use the more generic term clustered data to refer to this situation. Advantages and Disadvantages of Longitudinal Data: Advantages: 1. Although time effects can be investigated in cross-sectional studies in which different subjects are examined at different time points, only longitudinal data give information on individual patterns of change. 2. Again, in contrast to cross-sectional studies involving multiple time points, longitudinal studies economize on subjects. 3. In investigating time effects in a longitudinal design or treatment effects in a crossover design, each subject can “serve as his or her own control”. That is, comparisons can be made within a subject rather than between subjects. This eliminates between-subjects sources of variability from the experimental error and makes inferences more efficient/powerful (think paired t -test versus two-sample t -test).
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