[R] "time series", "longitudinal data" or "trajectories"

[Robert A LaBudde]

At 04:54 AM 6/6/2009, Christophe Genolini wrote:
>Thanks for yours answers. So if I understand:
>- Trajectories are continuous, the other are discrete.
>- The difference between time series and longitudinal is that time 
>series are made at regular time whereas longitudinal are not ?
>- Repeated measures are over a short period of time.
>
>
>So if I measure the  weight of my patient daily during one week, it 
>will be repeated measure ; if I measure it once a week during one year,
>it will time series ; if I measure it once a week during one year 
>but with some "missing week", it will longitudinal data ?
>Well I guess it is not as simple at that, but is it the idea ?
><snip>

Not exactly.

If you measure weight daily for a week, that is a "time series" 
(equally spaced time measurements over an arbitrary period) and 
"repeated measurements" (multiple measurements on the same subject, 
whether on time or at random or in some other way).

If you measure weight weekly for each week in a year this is a "time 
series" (equally spaced time measurements) and would generally be 
called a "longitudinal" study (measurements over a lengthy enough 
time period that time-related changes are expected).

Missing data are common in "repeated measures" or "longitudinal 
studies". In "longitudinal studies", an additional problem of 
"dropouts" is present, which may be correlated with the unobserved 
measurement (i.e., "missing, not at random" or "non-ignorable, 
non-random"). Also, the long time period of a "longitudinal study" 
may create issues of measurement bias (due to drift in technique or 
clinicians over time) and change in the subject baseline state.

"Time series" is typically used in my experience for measurements 
that have a great degree of regularity (equally-spaced times, few or 
no missing data).

"Trajectory" is a term for "continuous time curve".

Examples:

Study to measure blood pressure measurement fluctuations: N subjects 
measured by M operators every 8 hr during a week. Note there is a 
general expectation of a constant mean value for each subject during 
the period, with probably short-time fluctuations. This would be 
called a "repeated measure" study, Although it could also be called a 
"time series" study, the expectation of no total time period effect 
and the possibility of missing measurements would argue against that 
term. On the other hand, if a posteriori there were little or no 
missing data, and regular time-dependent patterns were observed, its 
name might be shifted to a "time series" study.

Cohort study to measure blood pressure changes over a ten year time 
frame for treated and untreated subjects: There will be significant 
amounts of missing data, dropouts from the study and a long time 
period of observation. This would almost universally be known as a 
"longitudinal" study.

Controlled experiment to measure rates of gelation of batches of 
different gelatins: N lots of gelatin, each measured in solution at 
the same M time periods for viscosity. A continuous underlying 
viscosity vs. time curve is expected (the "trajectory") for each lot. 
Time periods are equal, and there are few missing data. The goal is 
to compare gelation trajectories. This is a "repeated measure" study, 
and might more particularly be characterized as a "time series" study.

When the subjects are living entities, usually the terms "repeated 
measures" or "longitudinal" are used. If measurements are taken at a 
single point in time, the term "cross-sectional" study is used. If 
there is a single response across time, the term "time series" is 
used. If there are multiple responses all measured at the same times 
for the subjects, the term "panel data" is used.

For controlled experiments, the terms "repeated measures" and "time 
series" are common. "Longitudinal" could be used, but generally is not.



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Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
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