ORIGINAL ARTICLE
Hierarchical Linear Modeling of Visual Acuity
Change Over Time: Rate of Functional Recovery
After Macular Hole Surgery
WALTER WITTICH, MA, OLGA OVERBURY, PhD, MICHAEL A. KAPUSTA, MD, FRCSC,
and DONALD H. WATANABE, MSc
Department of Neurology and Neurosurgery-Neuroscience, McGill University, Montreal, Quebec, Canada (WW), Sir Mortimer B. Davis
Jewish General Hospital, Lady Davis Institute for Medical Research, Montreal, Quebec, Canada (WW, OO), Department of
Ophthalmology, McGill University, Montreal, Quebec, Canada (OO, MAK), and Department of Psychology, Concordia University,
Montreal, Quebec, Canada (DHW)
ABSTRACT
Purpose. To examine acuity recovery rate after Macular Hole (MH) surgery, using Hierarchical Linear Modeling (HLM)
with linear and curvilinear regression analysis.
Methods. Preoperative MH diameter (OCT) and acuity (ETDRS) were recorded in 20 eyes. Acuities were tested during
follow-up (6 to 23 months), with three to eight measurements per eye. The resulting 95 acuities were analyzed using HLM.
Variability at the level of the person was explained by change over time, using a natural logarithm conversion. Across
patients, MH diameter was used to predict slopes and intercepts at the level of the individual.
Results. MH diameter was able to account for significant amounts of variability in preoperative acuity (intercept) and
significantly influenced rate of functional recovery (slope). A nonlinear approach to the data accounted for the largest
amount of variance.
Conclusions. Participants with larger MHs recovered relatively more acuity sooner while eyes with smaller MHs had
better absolute acuity outcome. HLM provides important insight into the recovery process after MH surgery and is more
flexible with follow-up data. In the context of MH treatment, most recuperation occurred during the initial 6 months.
(Optom Vis Sci 2007;84:872–878)
Key Words: visual acuity, Hierarchical Linear Modeling, growth curve analysis, rate of recovery, macular hole, visual
acuity
T
he primary goal of Macular Hole (MH) surgery is to close
the retinal defect by reattaching the edges of the macular
tissue around the hole and to restore a continuous retinal
layer.
1
As a result, visual acuity is likely to improve to a certain
degree and this beneficial effect has been demonstrated across sev-
eral studies.
2
Initially, MH stages proposed by Gass
3,4
greatly fa-
cilitated how MHs were classified. Subsequently, the advent of
Optical Coherence Tomography (OCT) provided more detailed
information about the structural aspects of MHs.
5,6
What remains
difficult is to predict functional outcome after anatomically suc-
cessful treatment based on preoperative MH characteristics. One
of the most frequently reported structural components of MHs is
their size, commonly expressed as their central diameter.
The association of preoperative acuity with MH size has not
been consistent in the literature and has been reported as signifi-
cant,
7–9
strong,
10,11
moderate
12–14
or not significant.
15,16
This
inconsistency, however, may be due to small sample sizes, various
acuity charts that were used, as well as variability in the accuracy of
anatomical measurement techniques. Successful anatomical clo-
sure of MHs has been associated with MH diameter and symptom
duration.
13
In addition, other factors that are related to visual
function after surgery have been identified, including preoperative
acuity,
10
MH diameter,
9,12
duration of symptoms,
17
as well as
compliance to face-down positioning.
18
It has been frequently re-
ported that larger MHs are less likely to recover normal or near-
normal acuity after treatment.
5,9,17,19
Few studies have evaluated the pattern with which vision con-
tinues to improve beyond the initial 6 months after treatment.
Previous work by Krasnik et al.,
20
as well as Leonard et al.,
21
has
demonstrated that acuity improvement after MH surgery is a dy-
1040-5488/07/8409-0872/0 VOL. 84, NO. 9, PP. 872–878
OPTOMETRY AND VISION SCIENCE
Copyright © 2007 American Academy of Optometry
Optometry and Vision Science, Vol. 84, No. 9, September 2007