**Purpose**:
Clinical decisions on treatment are usually based on short-term records of consecutive measurements of structure and function. Useful models for analyzing average trends and a description of statistical methods for classifying individual subjects on the basis of subject-specific trend progressions are presented.

**Methods**:
Random effects trend models allow intercepts and slopes of the trend regression to vary across subjects around group-specific mean intercepts and mean slopes. Model results assess whether average intercepts and slopes and subject variability in intercepts and slopes are the same across groups. Fisher's discriminant functions are used for classification.

**Results**:
Methods are presented and illustrated on structural visual data from a multiyear perimetry study. Average thickness of the ganglion cell layer from the optical coherence tomography macula scan and of the retinal nerve fiber layer from the optic disc scan for both glaucoma patients on optimal treatment and normal subjects are analyzed. The random effects trend model shows that average intercepts of glaucoma patients and normal subjects are quite different, but that average slopes are the same, and that the subject variability in both intercepts and slopes is larger for the glaucoma group. These findings explain why the subject-specific trend progression is not a good classifier; it is the level of the measurement (intercept or baseline value) that carries useful information in this particular cohort example.

**Translational Relevance**:
Clinicians base decisions on short-term records of consecutive measurements and need simple statistical tools to analyze the information. This paper discusses useful methods for analyzing short time series data. Model results assess whether there exist significant trends and whether average trends are different across groups. The paper discusses whether clinical measures classify patients reliably into disease groups, given their variability. With ever more available data, classification plays a central role of personalized medicine.

*n*consecutive measurements

^{1}

*i*th subject in group

*j*(

*j*= 1 for normal,

*j*= 2 for disease) at time

*t*with

*i*is from the normal group (

*i*is from the glaucoma group (

^{2}and Searle et al.

^{3}Estimation of such models can be carried out with the PROC MIXED procedure of the SAS Statistical Software,

^{4}or with the R Statistical Software

^{5}through its libraries nlme and lme4. Parameter estimates are usually obtained through restricted maximum likelihood (REML).

^{6}

*k*features, and information about group membership (healthy group and diseased group) is available on each subject (that is, one deals with supervised learning). If the slope of the progression is the only feature to be considered, then

*k*= 1. If the baseline and the slope of the trend model are used to describe the state of a subject, then

*k*= 2. The baseline may be a useful feature as it measures the subject's starting level of the measured characteristic. The Fisher

^{7}linear discriminant analysis classifies a patient with feature vector

*x*into group 2 (disease) if

*k*) for group 1 (healthy) and group 2 (diseased), and they are estimated with the sample mean vectors of features for subjects in groups 1 and 2. The common covariance matrix of the features

*k*×

*k*]) is estimated with the pooled covariance matrix

^{8}and Chapter 12 of Ledolter.

^{9}If

*k*= 1, Fisher's linear discriminant analysis classifies a subject with feature

*x*into the group with the closest mean.

^{7}quadratic discriminant function classifies a subject with feature vector

*x*into group 2 (disease) if

*k*-variate distributions are normal—an assumption that is often violated. Several nonparametric classification approaches that do not rely on normality are available, among them the Support Vector Machine (SVM) approach. We refer the interested reader to the contributions by Boser et al.

^{10}and Christianini and Shawe-Taylor,

^{11}and readily available computer software such as Package e1071 in the R Statistical Software

^{5}and LIBSVM, an extensive library for SVMs.

*P*< 0.05 [fifth percentile] or two adjacent locations at

*P*< 0.01 [first percentile]). Cases were not required to have elevated intraocular pressure, but they were excluded if there were cataracts causing visual acuity worse than 20/30, they were younger than 19 years, or they had a pupil size of less than 2.5 mm. If both eyes qualified, one eye was randomly selected for inclusion in the study.

*P*= 0.107). The average rate of change for the glaucoma group is actually smaller (0.145 – 0.089 = 0.056 micron unit reduction per year), but the difference is not statistically significant. The second model M2 with a common average slope implies a reduction of 0.109 units per year (SE = 0.069;

*P*= 0.11). In summary, we find that the average RNFL baseline of the glaucoma group is considerably thinner than the average RNFL baseline of the normal group (as expected), some evidence for an overall average reduction over time (probability value around 0.10), no statistically significant difference between the average slopes in the normal and the glaucoma groups, and larger subject variability among the slopes in the glaucoma group.

^{17–22}Model results assess whether there exist significant trends and whether average trends are different across groups.

^{12}Similarly, the RNFL contains the axons of the retinal ganglion cells, and their axoplasmic contents may be influenced by the characteristics of axoplasmic flow and status of the axon,

^{12–16}which in turn may cause dynamic changes in the thickness of this layer. The present analysis raises important questions about the increase in variance of the distribution of slopes of the GCL and RNFL in glaucoma patients compared to normal subjects. Specifically, future investigation is warranted to better understand the reason why some subjects with glaucoma show an increase in thickness of the layers of the inner retina over time that the normal group does not.

**J. Ledolter**, None;

**R.H. Kardon**, None

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