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Using a Box–Cox transformation in the analysis of longitudinal data with incomplete responses

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  • S. R. Lipsitz
  • J. Ibrahim
  • G. Molenberghs

Abstract

We analyse longitudinal data on CD4 cell counts from patients who participated in clinical trials that compared two therapeutic treatments: zidovudine and didanosine. The investigators were interested in modelling the CD4 cell count as a function of treatment, age at base‐line and disease stage at base‐line. Serious concerns can be raised about the normality assumption of CD4 cell counts that is implicit in many methods and therefore an analysis may have to start with a transformation. Instead of assuming that we know the transformation (e.g. logarithmic) that makes the outcome normal and linearly related to the covariates, we estimate the transformation, by using maximum likelihood, within the Box–Cox family. There has been considerable work on the Box–Cox transformation for univariate regression models. Here, we discuss the Box–Cox transformation for longitudinal regression models when the outcome can be missing over time, and we also implement a maximization method for the likelihood, assumming that the missing data are missing at random.

Suggested Citation

  • S. R. Lipsitz & J. Ibrahim & G. Molenberghs, 2000. "Using a Box–Cox transformation in the analysis of longitudinal data with incomplete responses," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(3), pages 287-296.
  • Handle: RePEc:bla:jorssc:v:49:y:2000:i:3:p:287-296
    DOI: 10.1111/1467-9876.00192
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    Cited by:

    1. Tan, W. D. & Gan, F. F. & Chang, T. C., 2004. "Using normal quantile plot to select an appropriate transformation to achieve normality," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 609-619, April.
    2. Gurka, Matthew J. & Edwards, Lloyd J. & Nylander-French, Leena, 2007. "Testing transformations for the linear mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4297-4307, May.
    3. Jiang, Jiakun & Lin, Huazhen & Zhong, Qingzhi & Li, Yi, 2022. "Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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