A Statistical Method to Detect Abnormal Observations in Multivariate Longitudinal Data Measurements

Abstract

 

Purpose

 

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.

 

Methods

 

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.

 

Results

 

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.

 

Conclusions

 

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.