Editors' ChoiceBiostatistics

A New Look at Longitudinal Data

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Science Translational Medicine  21 Apr 2010:
Vol. 2, Issue 28, pp. 28ec64
DOI: 10.1126/scitranslmed.3001165

Time changes everything. Indeed, time is a key variable in clinical trials and epidemiological and health-outcomes research. Longitudinal data are collected on the same subject over an extended period with the goal of characterizing patterns that manifest or modify over time. In many situations, changes over time can be studied by using longitudinal linear regression. But in other cases, such as assessing a patient’s changing viral load in HIV research or hormone patterns over the menstrual cycle in fertility research, the longitudinal pattern is complex and not well fit by using existing longitudinal linear regression models. In these examples, semiparametric longitudinal regression models offer a useful alternative strategy. In such models, the change over time is described by a highly flexible curve along with a set of parameters that shift the curve for different covariate values, such as age. This idea is similar to the most commonly cited semiparametric model in medical research, the Cox proportional hazards model for survival data.

Recently, Li et al. developed a Bayesian approach to semiparametric longitudinal regression modeling. This allows for more flexible modeling of between-subject variation by relaxing the normality assumption made in classic longitudinal linear and semiparametric regression approaches. In addition, they offer advice on how best to choose and model the alternatives to the normal distribution (that is, the prior distributions) to yield less biased and more robust results, a difficult aspect of performing Bayesian analyses. Using their approach, they fit a new model of changes in urine progesterone concentrations over the menstrual cycle and confirmed the low and stable estimates with a peak in concentration at approximately day 23 of a standard 28-day cycle. In contrast to other analyses, they find that the pattern changes with age. This difference is probably a result of their ability to more appropriately model the variation that exists between subjects and more flexibly characterize the progesterone pattern over time. These results may have important implications in our understanding of the transition to menopause and changes in bone health as women age.

The biostatistician will find this research useful because it expands the statistical models available to analyze longitudinal data. And for the medical researcher, the work offers a new way to achieve a more appropriate fit of their data with less biased estimates of subject variation, which can change the scientific conclusions drawn from some studies. The major limitation of this approach is that it does not offer the clinical investigator a simple single number to characterize the pattern of change over time.

Y. Li et al., Bayesian inference in semiparametric mixed models for longitudinal data. Biometrics 66, 70–78 (2010). [Abstract]

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