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S. Dubuc, W. Wittich, J. B. Santo, J. E. Gomolin, O. Overbury; Hierarchical Linear Modeling of Anatomical Change Over Time: Bevacizumab With or Without PDT. Invest. Ophthalmol. Vis. Sci. 2008;49(13):547. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
To apply Hierarchical Linear Modeling (HLM) as a novel statistical technique to the analysis of anatomical outcome after treatment using anti-VEGF medication. Unlike traditional statistical approaches, such as analysis of variance (ANOVA), which requires discrete groups and follow-ups at arbitrary time points, HLM maintains time as a continuous variable. This allows for the inclusion of unequal numbers of follow-ups. Furthermore, instead of having to group individuals by treatment, HLM can consider participant characteristics as continuous variables, making the analysis more sensitive to subtle treatment interaction effects. Given its flexibility, it is hypothesized that HLM will detect effects that would otherwise remain hidden using ANOVA.
Retinal thickness and macular volume were measured by Optical Coherence Tomography (OCT) among patients treated with bevacizumab alone or in combination with Photodynamic Therapy (PDT) for exudative Age-related Macular Degeneration. The anatomical status of the treated eye of 17 patients (age 46-88), was monitored by OCT at each visit. The number of follow-ups ranged from 2-5 over a period ranging from 2 months to 4 years. For the 2x3 mixed ANOVA, data were reduced to 2 groups (bevacizumab or bevacizumab/PDT) and three time groups (pre-, post-1, post-2). For HLM, a 2-level model was utilized. At Level 1, anatomical change was predicted by time. At Level 2, number of bevacizumab and PDT treatments were used to predict variability of Level 1 parameters.
The ANOVA did not reveal any significant effects. However, for the HLM analysis, at Level 1, time accounted for a significant amount of variance. At Level 2, there was a significant effect of treatment type as a function of time for retinal thickness and volume. Patients who received repeated PDT treatments in combination with more frequent bevacizumab demonstrated a greater decrease on measures of retinal thickness and volume. This effect became more pronounced as the follow-up continued over time.
This study has demonstrated that HLM provides an advantage as a statistical procedure over ANOVA. Had ANOVA been utilized, several effects would have gone undetected. The beneficial effect of bevacizumab is well accepted. However, traditional analysis of the data would have contradicted this belief. Even with a relatively small sample, HLM can accommodate more complex hypotheses as long as sufficient measures over time are available.
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