Purchase this article with an account.
Yun Ling, Richard Anthony Bilonick, Gadi Wollstein, Hiroshi Ishikawa, Larry Kagemann, Michelle Gabriele Sandrian, Joel S Schuman; A Statistical Method to Detect Abnormal Observations in Multivariate Longitudinal Data Measurements. Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):5003.
Download citation file:
© ARVO (1962-2015); The Authors (2016-present)
Some abnormal observations can be very influential on longitudinal growth curve parameter estimation (e.g., slope) and the removal of the observations from the dataset can substantially change the growth curve equation. An abnormal observation may indicate a misspecified subject or a measurement error. The purpose of this study is to introduce a statistical method to determine possible abnormal observations in multivariate longitudinal data measurements.
Multivariate linear mixed effect (MLME) model was used to simultaneously model the average retinal nerve fiber layer (RNFL) thickness and ganglion cell complex (GCC) as a function of follow-up days, adjusted for baseline age and diagnosis (healthy, glaucoma suspect and glaucoma). To take into account three kinds of cross correlations, including correlations between two variables, correlation between repeated measurements and correlation between two eyes of one subject, the multivariate conditional Cook’s distance is used to evaluate how “abnormal” is an observation. A higher Cook’s distance indicates a more “abnormal” observation. Figure 1 shows the definition of the multivariate conditional Cook’s distance.<br /> The method was applied on a longitudinal cohort to compare the rate of glaucomatous progression in different diagnosis groups. Total 5,994 observations on 256 subjects (487 eyes) were analyzed. The R statistical software was used to fit the MLME model and compute the Cook’s distance.
The top 10 most “abnormal” observations are listed in Table 1. Figure 2 shows the trajectories of the 10 eyes with the 10 most “abnormal” observations. Each of the 10 observations is far from other measurements of same eye quadrant, and removal of the observation significantly changed the slope of the trajectory of this eye quadrant.
Multivariate Cook’s distance accounts for all the three kinds of cross correlations between RNFL and GCC of each eye, correlations between repeated measurements and correlations between two eyes of each subject, correctly estimating the influence of each observation under multivariate growth curve context.
This PDF is available to Subscribers Only