Abstract
Objective:
To compare forecasted changes in mean deviation (MD) on perimetry for patients with normal-tension glaucoma (NTG) and high-tension glaucoma (HTG) at different target intraocular pressures (IOPs) using a machine-learning technique called Kalman Filtering (KF).
Design:
Retrospective cohort study.
Participants:
496 patients with HTG from the Collaborative Initial Glaucoma Treatment Study or the Advanced Glaucoma Intervention Study and 262 patients with NTG from Japan.
Methods:
Using the first 5 sets of tonometry and perimetry measurements, we classified each patient as a fast-progressor, slow-progressor, or non-progressor. Using KF, we generated personalized forecasts of MD changes on perimetry over 2.5 years of follow-up for fast-progressors and slow-progressors with HTG and NTG whose IOPs were maintained at hypothetical IOP targets of 9-21 mmHg. We also assessed future MD loss with different percentage reductions in IOP from baseline (0-50%) for the groups.
Main Outcome Measures:
Mean change in forecasted MD at different target IOPs.
Results:
The mean ± SD age of patients with NTG and HTG were 63.5±10.5 years and 66.5±10.9 years, respectively. At target IOPs of 9, 15, and 21, fast progressors with NTG had mean forecasted MD losses of 2.3±0.2, 4.0±0.2, and 5.7±0.2 dB and slow progressors had mean forecasted MD losses of 0.63±0.02, 1.02±0.03, and 1.49±0.07 dB over 2.5 years of follow up, respectively. At target IOPs of 9, 15, and 21, fast progressors with HTG had mean forecasted MD losses of 1.8±0.1, 3.4±0.1, and 5.1±0.1 dB and slow progressors had mean forecasted MD losses of 0.55±0.06, 1.04±0.08, and 1.59±0.10 dB over 2.5 years of follow up. Fast progressors with NTG experienced a greater MD decline than fast progressors with HTG at each target IOP (p≤0.007 for all). The MD decline for slow progressors with HTG and NTG were similar at each target IOP (p≥0.24 for all). Fast progressors with HTG experienced greater MD loss than those with NTG with IOP reductions of 0-10% from baseline (p≤0.01 for all) but not 25% (p=0.07) or 50% (p=0.76).
Conclusions:
Machine learning algorithms using KF techniques demonstrate promise at forecasting future values of MD at different target IOPs for patients with NTG and HTG.
Précis
We leverage machine learning techniques to develop personalized forecasts of perimetric changes at different target intraocular pressures for patients with normal- and high-tension glaucoma.
Introduction
The American Academy of Ophthalmology’s Preferred Practice Pattern for Primary Open Angle Glaucoma emphasizes the importance of establishing a target intraocular pressure (IOP) for each patient with glaucoma.1 A target IOP is the level of IOP that the clinician feels is sufficiently low such that the patient is unlikely to experience disease progression.1 Although guidelines highlight the importance of setting target IOPs, the literature offers little guidance of what specific level or range of IOP is appropriate for a particular patient. If a clinician were to choose a target IOP that is higher than is actually necessary, the patient may be at risk of experiencing glaucomatous progression. Likewise, if the clinician selects a target IOP that is lower than is actually needed, aggressively lowering the patient’s IOP to such a target may result in subjecting the patient to unnecessary interventions, which can have adverse effects and may be costly. Complicating matters further, a target IOP which is safe for one particular eye may be too high or low for another eye.
Kalman filtering (KF) is a machine learning methodology that has been used extensively in the aerospace and aviation industry to dynamically forecast flight courses of airplanes from one destination to another.2 More recently, researchers have begun to apply KF methods to assist with forecasting the trajectory of chronic diseases.3-5 Kalman filters generate personalized forecasts of the disease trajectory for a particular patient by integrating past data from that specific patient along with data from a population of patients with the same disease entity. The more the KF learns about the past behavior of the actual patient of interest, the more this helps guide the algorithm’s predictions.
Past research from our group has demonstrated that KF can be effective at forecasting conversion to glaucoma in patients with ocular hypertension6, and disease progression for patients with high tension open-angle glaucoma (HTG)7 and normal tension glaucoma (NTG).8 We have also shown that it is possible to generate personalized menus of target IOPs to guide care in patients with HTG.7 The objectives of this study are 1) to assess whether it is possible to employ KF to forecast future values of mean deviation (MD) and pattern standard deviation (PSD) at different target IOPs for patients with NTG, 2) to assess MD loss over time at different percentage reductions in IOP from baseline levels for patients with NTG and HTG, and 3) to compare the amount of forecasted decline in MD on perimetry over time for patients NTG to others with HTG whose IOP is maintained at comparable target IOP levels.
Methods
This study was approved by the University of Michigan and Fukui-ken Saiseikai Hospital institutional review boards and faithfully adhered to the tenets of the Declaration of Helsinki. We performed all machine learning methods using MATLAB version 9.4.0.813654 and all statistical analyses using R version 3.5.2.
Data Sources
Patients with HTG
Patients with HTG were participants in the Advanced Glaucoma Intervention Study (AGIS) or the Collaborative Initial Glaucoma Treatment Study (CIGTS) randomized clinical trials who met the eligibility criteria outlined below. Briefly, all participants in AGIS and CIGTS had primary or secondary forms of HTG with elevated IOPs at enrollment in 1 or both eyes. All AGIS participants had IOPs at trial entry of >22 mmHg, glaucomatous loss on standard automated perimetry (SAP), and glaucomatous appearing optic nerves.9 In CIGTS, participants were eligible if they had untreated IOPs >21 mmHg along with evidence of glaucomatous damage on SAP and optic nerves demonstrating glaucomatous damage.10 Patients from both trials had 5 to 11 years of longitudinal monitoring with SAP and IOP measurements obtained approximately every 6 months.9,10 The cohort of patients with HTG we recruited from these 2 trials have been described previously.7,8 None of the participants from AGIS or CIGTS had NTG.
Patients with NTG
Patients with NTG were identified from a convenience sample of patients who were receiving care at the Fukui-ken Saiseikai Hospital in Fukui, Japan. All of these patients were under the clinical care of one of our study authors (K.N.) and had 4 to 6 years of longitudinal monitoring with SAP and IOP measurements approximately every 6 months between June 1, 2009, and May 31, 2015. Patients in this group had documentation of open angles on gonioscopy, changes to the optic nerve consistent with glaucomatous optic neuropathy, glaucomatous visual field loss on SAP, and >3 baseline untreated IOP measurements <21 mmHg and no baseline readings ≥21 mmHg. Student’s t tests and Pearson x2 tests were used to compare the NTG and HTG groups for differences in continuous and categorical parameters, respectively.
Inclusion and Exclusion Criteria
For this study, at least 5 Swedish Interactive Threshold Algorithm Standard 24-2 Humphrey VFs (HVFs) (Carl Zeiss Meditec, Dublin, CA) and 5 IOP measurements are required by our KF to generate forecasts. As such, we excluded patients from both groups who had fewer than 5 HVFs or IOPs. If an incisional glaucoma surgery occurred during a patient’s follow-up period, we censored all IOP and HVF measurements after the date of surgery. We censored these data because incisional surgery can dramatically affect IOP and disease progression dynamics, and this adds complexity to the training of our forecasting algorithms. If both eyes of a patient were eligible, we randomly selected 1 eye. For all patients, on the occasions when testing was unable to be performed in a 6-month interval (e.g., a patient missed a clinical visit) linear interpolation was used to obtain evenly spaced readings.
Kalman Filtering
Kalman filtering is a machine learning technique that considers the underlying behavior of a population of patients with a given disease entity along with the unique dynamics of the individual patient. In chronic disease management, the KF leverages population data on the disease of interest and baseline patient information to make an initial forecast of the disease trajectory for that particular patient. The KF dynamically updates these forecasts as it gains more information on the status of the specific patient during follow-up visits. With additional information on the patient, the model’s prediction error is reduced over time. We previously developed and validated KF models for use in predicting future disease trajectory (levels of MD, PSD, IOP) for patients with HTG and NTG.7,8 Briefly, the KF model uses a disease state vector which includes MD, PSD, and IOP measurements for each patient, as well as the velocities and accelerations of these measurements. The KF learns and predicts how changes in one variable will affect the other variables, and it can extend this prediction multiple time periods into the future.
Kalman Filter Training
To parameterize the KF for this particular study, we randomly divided the HTG sample into 2 halves. One half of the sample was used to train the KF and the other half was used as a test set. The training and testing sets had similar distributions of sex, race, and trial participation (AGIS vs. CIGTS). Our KF parameters were calculated using an expectation maximization algorithm.11
Tuning of Kalman Filter Parameters
In our past research, we tested and validated a single set of KF parameters and used that model to perform all of the necessary predictions for a given project. To improve the accuracy of our predictions, for this set of analyses we developed 4 different KF parameter sets—a general one and one each to forecast progression dynamics for eyes that are behaving as fast progressors (MD loss greater than 1 dB/year), slow progressors (MD loss between 0 and 1 dB/year), and non-progressors (no decline in MD) during the 6-month period immediately preceding a given prediction.7,12-15
The model first calculates a patient’s MD rate of decline by fitting a linear regression to the patient’s history of past MD readings up to the current period. We use the slope of this regression to describe the patient’s progression rate for that particular time period. Then, the model uses this slope to classify the patient as either a fast, slow, or non-progressor, and applies the corresponding KF parameter set to make its predictions. The specialized parameters were trained on the subset of data only including patients of that progression type based on their entire history of MDs. In effect, the KF is leveraging knowledge of an individual patient to make predictions based on a subset of data from all patients whose glaucoma is behaving similarly to his or hers.
Since previous research suggests that at least 5 SAP results should be obtained before assigning a patient into 1 of these 3 progression categories13 our model does not classify a patient’s progression type in the first 5 periods. Instead, each patient’s data is initially processed through our KF using the general parameters, which were developed using the entire training set. After the first 5 tests, the model classifies each patient as a fast progressor, slow progressor, or non-progressor and applies the appropriate KF parameter set. We refer to this initial classification as the baseline classification. With each additional SAP test result, the linear regression slope updates. As a result, patients can change classification type over time and thus change which specialized KF parameters will be used for their subsequent forecasts. For clarity, we use the baseline classification of a patient as the progression type in all statistical analyses and figures reported in the Results section. Because the KF is a forecasting tool, using the baseline classification most closely resembles the information available to a clinician at the time of clinical decision-making.
Kalman Filter Testing and Validation
After training our models, we generated forecasts on the testing set. The testing set consisted of the other half of the patients with HTG as well as all of the patients with NTG. As one of the study objectives was to determine how well our KF models developed using data from patients with HTG might perform on another distinct patient cohort, we included all patients with NTG as a part of the testing set, and applied our HTG-trained KF to understand their progression dynamics.
To apply our KF to the patients in the testing set, we defined a 5-period warm-up interval to help our KF learn the unique progression dynamics for a given patient. All KF predictions are made after this warm-up interval. Next, for each patient we predicted the MD for the next 5 periods (2.5 years) and compared the KF’s forecasted MD value to the true value recorded during the patient’s time in AGIS/CIGTS for those with HTG and during clinical follow-up for those with NTG for each period. We defined prediction error as the difference between this predicted value from the KF and the observed value. To understand whether the predictive accuracy of our HTG-trained model applied also to new patient populations (such as patients with NTG), we compared the mean prediction error at each forecasted time period between the patients in the testing set with HTG and patients with NTG using two-sided t-tests. We also compared mean prediction errors between patients with HTG and NTG stratified by baseline progression classification type.
Target Intraocular Pressure Analysis
Once we parameterized, trained, and validated our KFs, we used them to estimate changes in MD over time at different target IOPs. After the warm-up period, we asked the models to assume that the patient’s IOP would remain at 1 of 5 specified levels (9, 12, 15, 18, or 21 mmHg) over the course of the next 2.5 years. The KFs then forecasted what would happen to the patient’s MD at each of those target IOP levels over that 2.5 year timeframe. We generated forecasts of MD at each IOP level for each patient with NTG and each patient with HTG in the testing set. We also compared the mean decline in MD between the end of the warm-up period to the end of the 2.5-year follow-up for patients with HTG vs. NTG.
In addition to assessing changes in MD at specified target IOP levels, we also used our models to estimate changes in MD over time if the patient’s IOP were reduced varying percentages from its baseline level. After the warm-up period, we had our models assume that the patient’s IOP is immediately reduced by 1 of 5 levels (0%, 5%,10%, 25%, 50%) from baseline and held at this IOP over the course of the next 2.5 years. We then used the KFs to forecast what would happen to the patient’s MD during the next 2.5 years at each of those percentage reductions in IOP from baseline. In this analysis, baseline is defined as prediction period 0, which is the fifth and final visit of the warm-up period.
We generated 95% confidence intervals for the mean MD decline at each target IOP level and each percentage IOP reduction from baseline for patients with NTG and HTG of each baseline progression type. We performed two-sided t-tests to compare the testing set patients with NTG and HTG and among progression types to assess if there were statistical differences in mean forecasted MD decline between groups at each target IOP level and each percentage reduction in IOP from baseline. Statistical significance was p<0.05.
Results
Patients with HTG
The cohort of patients with HTG included 496 eyes of 496 participants. Half of these participants were included in the training set (n=248) and the other half were included in the testing set (n=248). (Table 1) Patients with HTG had a mean ± SD age at baseline of 66.5 ± 10.9 years. The racial composition included 243 (49%) blacks, 237 (48%) whites, and 16 (3%) Asians. At baseline, among the 248 patients with HTG in the training set, 66 (27%), 82 (33%), and 100 (40%) were fast, slow, and non-progressors, respectively. At baseline, of 248 patients with HTG in the testing set 62 (25%), 82 (33%), and 104 (42%) were fast, slow, and non-progressors, respectively. There were no significant differences between the HTG training and HTG testing sets regarding race, sex, age, baseline MD, baseline PSD, or baseline IOP (p>0.05 for all).
Table 1:
Description of the Study Samples
| HTG Training Group |
HTG Testing Group |
NTG Testing Group |
P Valuea | |
|---|---|---|---|---|
| Patientsb, N | 248 | 248 | 262 | |
| Sex | 0.004 | |||
| Female | 126 (51%) | 123 (50%) | 103 (39%) | |
| Male | 122 (49%) | 125 (50%) | 159 (61%) | |
| Race | < 0.0001 | |||
| Asian | 8 (3%) | 8 (3%) | 262 (100%) | |
| Black | 133 (54%) | 110 (44%) | 0 (0%) | |
| White | 107 (43%) | 130 (52%) | 0 (0%) | |
|
No. of patient visits, Mean (SD) |
11.0 (5.0) | 11.3 (5.3) | 10.3 (0.9) | 0.001 |
|
Baselinec
Age (years), Mean (SD) |
66.1 (10.6) | 66.8 (10.9) | 63.5 (10.5) | < 0.0001 |
|
Baselinec
MD (dB), Mean (SD) |
−7.9 (6.7) | −8.0 (6.2) | −7.0 (6.5) | 0.09 |
|
Baselinec
PSD (dB), Mean (SD) |
6.6 (3.9) | 6.6 (3.8) | 8.6 (4.6) | < 0.0001 |
|
Baselinec
IOP (mmHg), Mean (SD) |
17.5 (3.4) | 17.2 (3.6) | 12.5 (2.2) | < 0.0001 |
| Baseline Progression Typed, N (%) | < 0.0001 | |||
| Fast | 66 (27%) | 62 (25%) | 22 (8%) | |
| Slow | 82 (33%) | 82 (33%) | 102 (39%) | |
| Non | 100 (40%) | 104 (42%) | 138 (53%) |
Abbreviations: NTG = normal tension glaucoma, HTG = high tension glaucoma, MD = mean deviation, PSD = pattern standard deviation, IOP = intraocular pressure, SD = standard deviation, dB = decibels.
P values shown are for tests between NTG and HTG testing groups. P values for categorical variables were computed using Pearson’s x2 test for independence. P values for continuous variables were computed using Student’s independent-samples t test. There were no significant differences (α = 0.05) between the HTG training and test groups.
Each patient contributed only 1 eye.
Baseline refers to the reading at the end of the 5 measurement warm-up period (i.e., the measurement taken in prediction period 0).
Baseline progression type is based on the slope of a linear regression fitted to filtered patient readings in the warm-up period. Patients with a slope less than −1.0 dB change per year were considered fast progressors. Patients with a slope between −1.0 dB and 0 dB change per year were considered slow progressors. All other patients were considered non-progressors.
Patients with NTG
The cohort of patients with NTG in the testing set included 262 eyes of 262 participants. Patients with NTG had a mean ± SD age at baseline of 63.5±10.5 years. There were 103 (39%) females and all the patients were Asian. At baseline, among the 262 patients with NTG, 22 (8%), 102 (39%), and 138 (53%) were fast, slow progressors, and non-progressors, respectively. Patients in the testing set with NTG had significantly more males than those in the testing set with HTG (p=0.004). Patients with NTG in the testing set also had a significantly lower mean patient age (p<0.0001) and baseline IOP (p<0.0001), and a significantly higher mean PSD at baseline (p<0.0001) than those with HTG. There was no significant difference in the baseline MD between the groups (p=0.09). A Pearson x2 test showed that the proportion of patients behaving as fast, slow, and non-progressors at baseline differed between patients in the testing set with NTG and HTG (p<0.0001).
Kalman Filter Prediction Error
Figure 1 shows the distribution of prediction errors for patients in the testing set with NTG and HTG from 6 months to 2.5 years into the future. The mean±SD prediction error was 0.56±2.43 dB across all 5 periods for patients with NTG and −0.07±2.21 dB for patients with HTG. The mean prediction error for patients with NTG was statistically different from 0 using a two-sided t-test (p<0.0001). This suggests that the model tends to underestimate declines in MD for patients with NTG. Supplemental Figures 1 and 2 show prediction errors by baseline progression type for patients with NTG and HTG, respectively. For both HTG and NTG testing groups, our models generally had smaller errors when predicting the MD change of slow- and non-progressing patients when compared to fast-progressing patients.
Figure 1: Amount of Prediction Error of Mean Deviation for Patients in the Testing Set with Normal and High Tension Glaucoma.
Abbreviations: NTG = normal tension glaucoma, HTG = high tension glaucoma, MD = mean deviation, dB = decibels.
A prediction period is defined as a 6 month interval after the 5 measurement warm-up period. The Kalman filter uses the warm-up measurements to predict future patient MD change. The error is defined as the predicted MD minus the true MD. The boxes represent the 25th-75th percentiles and the whiskers extend to the most extreme points within 1.5x the interquartile range.
Examples of Target Intraocular Pressure Predictions
Figures 2 and 3 show personalized KF predictions of MD decline over the next 2.5 years for sample patients from the testing set with NTG who are exhibiting signs of fast and slow progression, respectively, at baseline. The predictions are shown over a range of different target IOP levels. Figure 2 shows the predicted values of MD over the next 2.5 years for a fast progressing patient with NTG. At baseline (Period 5) this patient’s MD was −22.1 dB. As depicted in the figure, if this patient maintained her IOP at 9 mmHg over the next 2.5 years, our model predicts she would lose 1.5 dB during that timeframe. In contrast, if her IOP was maintained at 21 mmHg for those 2.5 years, our model predicts she would lose 4.9 dB of MD. Figure 3 shows the predicted values of MD over time for a patient with NTG from the testing set who was behaving like a slow progressor at baseline. For this patient, if her IOP consistently stayed at 9 mmHg, our model predicts this patient will lose 0.4 dB on MD during the next 2.5 years. If her IOP remained at 21 mmHg over the 2.5 years of follow-up, her MD is expected to drop 1.2 dB. For comparison, Supplemental Figure 3 shows the prediction of MD at different target IOPs for a fast progressing patient with HTG from the testing test and Supplemental Figure 4 shows comparable predictions for a slow progressing patient with HTG.
Figure 2: Example of Personalized Forecast of Mean Deviation Under Different Target Intraocular Pressures for a Baseline Fast-Progressing Patient in the Testing Set with Normal Tension Glaucoma.
Abbreviations: MD = mean deviation, IOP = intraocular pressure, mmHg = millimeters of mercury, dB = decibels. This figure shows the Kalman Filter (KF) forecast of MD progression for a baseline fast-progressing patient with NTG under different target IOP levels. The first 5 measurements represent the warm-up period. The baseline classification is based on the slope of a linear regression fitted to the MD values in the warm-up period. Actual readings are observed values of IOP and MD during clinical follow-up. Filtered values are the result of the KF’s algorithm to extract out measurement noise.
Figure 3: Example of Personalized Forecast of Mean Deviation Under Different Target Intraocular Pressures for a Baseline Slow-Progressing Patient in the Testing Set with Normal Tension Glaucoma.
Acronyms: MD = mean deviation, IOP = intraocular pressure, mmHg = millimeters of mercury, dB = decibels. This figure shows the Kalman Filter (KF) forecast of MD progression for a baseline slow-progressing patient with NTG under different target IOP levels. The first 5 measurements represent the warm-up period. The baseline classification is based on the slope of a linear regression fitted to the MD values in the warm-up period. Actual readings are observed values of IOP and MD during clinical follow-up. Filtered values are the result of the KF’s algorithm to extract out measurement noise.
Comparison of Target IOP Forecasts for Patients with HTG and NTG Based on Baseline Progression Type
Supplemental Figure 5 compares the mean predicted MD change from baseline to 2.5 years later for fast-progressing testing set patients with NTG vs. HTG. The bands in this figure represent the 95% confidence interval for the mean predicted MD change. At baseline, fast progressors with NTG had a mean ± SD MD of −14.5±1.7 dB and a mean forecasted MD loss of 2.3±0.2, 4.0±0.2, and 5.7±0.2 dB over 2.5 years of follow up under target IOPs of 9, 15, and 21 mmHg, respectively. In contrast, at baseline, fast progressors with HTG had a MD of −12.3±0.7 dB and a mean forecasted MD loss of 1.8±0.1, 3.4±0.1, and 5.1 ±0.1 dB MD at target IOPs of 9,15, and 21, respectively. At each of the target IOPs, the group of fast progressors with NTG experienced greater decline in MD relative to those with HTG (p≤0.007 for all). Supplemental Figure 5 also provides this comparison for slow-progressing patients. At baseline, slow progressors with NTG had an MD of −7.0±0.6 dB and a mean forecasted MD loss of 0.63±0.02, 1.02±0.03, and 1.49±0.07 dB over 2.5 years of follow up under target IOPs of 9, 15, and 21 mmHg, respectively. At baseline, slow progressors with HTG had a MD of −6.8±0.6 dB and a mean forecasted MD loss of 0.55±0.06, 1.04±0.08, and 1.59±0.10 dB under the same target IOPs. Slow progressors with HTG and NTG did not differ in the mean amount of MD decline at target IOPs of 9, 15, or 21 mm Hg (p≥0.24 for all). Similarly, non-progressors with HTG and NTG did not differ in the mean amount of MD decline at target IOPs of 9, 15, or 21 mm Hg (p≥0.19 for all).
Comparison of Mean Deviation Changes At Different Percentage IOP Reductions from Baseline for Patients with HTG and NTG
Figure 4 compares the change in mean predicted MD when IOP is reduced 0% to 50% from its baseline level. The bands in this figure represent the 95% confidence interval for the mean predicted MD change at each percentage reduction in IOP from baseline. At baseline, fast progressors with NTG and HTG had mean IOPs of 13.11±1.96 mm Hg and 17.51±3.40 mm Hg, respectively. Fast progressors with NTG demonstrated mean forecasted MD reductions of 3.47±0.70, 3.10±0.69, and 1.64±0.69 dB over the course of 2.5 years at IOP reductions of 0%, 10%, and 50% from baseline, respectively. By comparison, fast progressors with HTG experienced mean forecasted MD reductions of 4.14±1.19, 3.65±1.12, and 1.70±0.92 dB over the course of 2.5 years at IOP reductions of 0%, 10%, and 50% from baseline, respectively. Fast progressors with HTG experienced a statistically significant greater decline in MD at 0%, 5%, and 10% IOP reductions from baseline (p≤0.01 for all). However, there was no significant difference in mean forecasted MD change between these 2 groups at 25% (p=0.07) and 50% IOP reductions (p=0.76) from baseline levels. (Supplemental Table 1) Slow progressors with NTG and HTG had a mean baseline IOP of 12.99±1.90 mm Hg and 17.54±3.40 mm Hg, respectively. Slow progressors with NTG experienced mean forecasted MD reductions of 0.86±0.14, 0.78±0.13, and 0.45±0.11 dB over the course of 2.5 years at IOP reductions of 0%, 10%, and 50% from baseline, respectively. Slow progressors with HTG demonstrated mean forecasted MD reductions of 1.01±0.63, 0.90±0.63, and 0.45±0.62 dB over the course of 2.5 years at IOP reductions of 0%, 10%, and 50% from baseline, respectively. The mean forecasted MD change was significantly greater for slow progressors with HTG compared to those with NTG at a 0% IOP reduction from baseline (p=0.04). However, the mean forecasted MD change was not significantly different between slow progressors with NTG and HTG at 5%, 10%, 25%, and 50% IOP reductions from baseline (p≥0.06 for all). (Supplemental Table 1)
Figure 4: Comparison of Predicted Change in Mean Deviation for Fast- and Slow-Progressing Patients in the Testing Set with Normal Tension Glaucoma Versus High Tension Glaucoma by Percent Reduction in Baseline Intraocular Pressure.
Acronyms: NTG = normal tension glaucoma, HTG = high tension glaucoma, MD = mean deviation, IOP = intraocular pressure, dB = decibels.
This figure shows the forecasted mean MD change for patients with NTG and HTG under various target IOP percent reductions maintained over the next 2.5 years. The lines represent the sub-population mean, and the shaded regions represent the 95% confidence interval. The baseline period is the final period of the warm-up period (i.e. period 5, or prediction period 0) The mean baseline MD values for fast-progressing patients were −14.52 dB for patients with NTG and −12.25 dB for patients with HTG. The mean baseline MD values for slow-progressing patients were −6.76 dB for patients with NTG and −12.25 dB for patients with HTG. The mean MD change was not statistically different between fast-progressing patients with NTG vs HTG at IOP reductions of 25% (p=0.07) and 50% (p=0.76), and was statistically significantly different at all other levels (p≤0.01). The mean MD change was not statistically significantly different between slow-progressing patients with NTG vs HTG at IOP reductions of 5%, 10%, 25%, and 50% (p≥0.06) and was statistically significantly different at a 0% IOP reduction (p=0.04).
Discussion
In this study, we assessed how well our KF methodology, which previously was parameterized, trained, and validated on a sample of patients with HTG is able to forecast disease future values of MD for a new population of patients with NTG. After establishing that our previously created KF is capable of predicting future MD values relatively well on this new patient population, we then sought to compare changes in MD over time for fast- and slow-progressing patients in the testing set with HTG to comparable patients with NTG, assuming IOPs during follow-up were maintained at a given target IOP or a given percentage reduction in IOP from baseline levels. We learned that, on average, fast progressors with NTG tended to experience slightly greater declines in MD relative to fast progressors with HTG at a given target IOP. By contrast, fast progressors with HTG experienced, on average, greater declines in MD relative to fast progressors with NTG with no or small reductions in IOP (0-10%) from baseline. However, when the percentage reduction in IOP from baseline was larger (25-50%), fast progressors with HTG and NTG behaved similarly.
Past research has demonstrated that KF is capable of successfully predicting future values of MD, PSD, and IOP for patients with glaucoma.7 However, before machine learning algorithms such as KFs can be safely integrated into clinical practice, it is essential to perform validation studies to determine whether models that are parameterized, trained, and tested on one patient population forecast well on other populations. In this study, we found that our previously created KF, which had been created using data from patients with HTG, performed quite well at predicting future values of MD among a new sample of patients with a different type of glaucoma (NTG). While it is not surprising that the mean prediction error of the NTG group was higher than that of the HTG group for which the model was trained, clearly the KF did an impressive job forecasting future values of MD for both of the groups with mean prediction errors of only 0.56 dB and 0.07 dB, respectively. We suspect that our KF performed well on this new sample of patients with NTG because of the nature by which KFs function. Namely, over time, KF forecasts are less influenced by behavior of the underlying population and more influenced by the past readings from the actual patient. In this case, we suspect our KF was able to recognize that patients with NTG happen to be experiencing declines in MD at lower IOPs than the population with HTG for which the model was trained, and the KF was able to adjust its forecasts accordingly.
When comparing the forecasted values of MD over time at different target IOPs, we learned that fast progressors with NTG experienced a decline in MD of approximately 0.5 dB more, on average over the 2.5 years of follow-up, relative to their counterparts with HTG at target IOPs of 9, 15, and 21 mmHg. The clinical relevance of this relatively small difference between the groups depends on the age of the patient and the underlying severity of their disease. For fast progressing patients with NTG who are diagnosed with glaucoma at a relatively young age, a decline of an additional 0.5 dB of MD for every additional 2.5 years of follow-up relative to their counterparts with HTG may result in a considerable amount of visual field deterioration over the course of 20 to 30 years of anticipated life expectancy such that it may impair function. Similarly, fast progressors with NTG who present with visual field loss encroaching on central fixation, may require more aggressive IOP control than their counterparts with HTG to achieve disease stabilization and maintain central fixation. Unlike fast progressors, slow progressors with HTG and NTG exhibited, on average, very similar levels of MD decline at each of the target IOP levels we tested so it may not be necessary to alter the aggressiveness of IOP lowering between these 2 groups of patients.
When it comes to using KF to predict the impact of different percentage reductions in IOP from baseline on future values of MD for patients with HTG versus NTG, our results highlight the importance of the actual level of the baseline IOP. In our analyses, the mean baseline IOP among the fast progressors with HTG (17.5 mmHg) was several points higher than the mean baseline IOP for fast progressors with NTG (13.1 mmHg). If IOPs were to remain at these levels (0% reduction from baseline) over the course of the follow-up, we observed the group with HTG experience a statistically significant greater decline in MD compared to those with NTG. Likewise, with modest reductions in IOP from baseline (5-10%), the difference in mean IOP between the groups continues to be sufficiently large enough to result in statistically significant differences in MD loss over time between these 2 groups. However, when IOP is more substantially reduced from baseline (25-50%), the mean IOPs for fast progressors with HTG would be 8.8 mmHg to 13.1 mmHg while the mean IOPs for fast progressors with NTG would be 6.6 mmHg to 9.8 mmHg, and at these respective levels, we observe no significant difference in rates of further decline in MD over time between the 2 groups. These results highlight how fast progressors with HTG and NTG behave similarly in terms of progression on perimetry only once IOP is lowered sufficiently. This is less important for slow progressors with HTG versus NTG. In this case, both groups experience similar levels of deterioration on perimetry when IOP is lowered any amount from 5% to 50% its baseline level.
Study Limitations
Our study has limitations. First, the number of eligible patients with NTG was relatively small compared to those with HTG. Second, it would have been ideal to have a longer length of follow-up for the patients with NTG to permit us to assess how well our models forecast beyond 2.5 years. Despite these two limitations, the mean prediction error for the group with NTG was only 0.56 dB which is quite good. Third, the standard deviation of the MD prediction error was higher than desirable (above 2.0 dB) for the patients with HTG and NTG. Upon further analysis, we learned that this relatively high standard deviation was primarily driven by a few outlier patients who demonstrated abrupt large improvements or declines in their actual MD, which seem rather difficult to forecast. For example, 5 of the 262 patients with NTG (less than 2% of the sample) accounted for 30% of the standard deviation of the prediction error. These outliers may represent patients who struggle with performing SAP, making it challenging, even for a machine learning algorithm like KF, to generate accurate predictions of their future MD values. Fourth, we excluded patients at the time they underwent incisional glaucoma surgery. As a result, our training data did not include many patients who exhibited large, sudden IOP changes that may occur with such surgery. Additional validation studies are needed to determine how incisional surgery affects our model predictions. Given that KFs are nimble and can quickly adjust to changes in disease progression dynamics over time, we would expect that after a few follow-up readings, the KF would adjust its predictions following surgery, though we have yet to formally study this. Fifth, the ideal way to validate our target IOP predictions would be to run our models on a new sample of patients who have consistently maintained their IOPs at one of the target levels we used in our analyses for prolonged periods of time and compare the MD predictions from our models with the actual values attained during clinical care. Unfortunately, we lack access to a sufficiently large sample of patients whose IOPs exhibited such little fluctuation to be able to perform such a validation. Finally, we acknowledge that we may be able to enhance the accuracy of our predictions by adding additional data into the models such as nerve fiber layer thickness measurements on optical coherence tomography or the presence or absence of disc hemorrhages on each exam. Unfortunately, optical coherence tomography was unavailable during the AGIS and CIGTS trials to permit us to incorporate this into our models for the current set of analyses. We are in the process of using other data sources to build KFs that include measurements from optical coherence tomography to permit us to study how much these structural parameters aid with predicting future perimetric loss.
In conclusion, we were able to leverage the machine learning methodology of KF to characterize the disease trajectory patterns of patients with NTG and compare this progression to those with HTG at different target IOPs and different percentage reductions in IOP from baseline levels. We found that fast progressors with NTG exhibited slightly greater drops in MD at a given target IOP relative to their counterparts with HTG, while the drop in MD was similar among slow progressors with NTG and HTG. We hope that soon clinicians can make use of these predictions to help guide them when selecting a target IOP or deciding what percentage reduction in IOP to aim for in caring for patients with glaucoma.
Supplementary Material
Acknowledgments
Financial Support: National Eye Institute R01 EY026641 (M.S.L./J.D.S.) and NSF CAREER: CMMI-1552525 (M.S.L.).
Footnotes
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Meeting Presentation: Presented as a Podium Presentation at the 2019 American Academy of Ophthalmology Annual Meeting San Francisco, CA, October 14, 2019.
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References
- 1.Prum BE, Rosenberg LF, Gedde SJ, et al. Primary Open-Angle Glaucoma. Ophthalmology. 2016;123(1):P41–P111. [DOI] [PubMed] [Google Scholar]
- 2.Leffens EJ, Markley FL, Shuster MD. Kalman filtering for spacecraft attitude estimation. J Guid Control Dyn. 1982;5(5):417–429. [Google Scholar]
- 3.Eberle C, Ament C. The Unscented Kalman Filter estimates the plasma insulin from glucose measurement. Biosystems. 2011;103(1):67–72. [DOI] [PubMed] [Google Scholar]
- 4.Wang Q, Molenaar P, Harsh S, et al. Personalized state-space modeling of glucose dynamics for type 1 diabetes using continuously monitored glucose, insulin dose, and meal intake: An extended Kalman filter approach. J Diabetes Sci Technol. 2014;8(2):331–345. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Lavieri MS, Puterman ML, Tyldesley S, Morris WJ. When to treat prostate cancer patients based on their PSA dynamics. IIE Trans Healthc Syst Eng. 2012;2(1):62–77. [Google Scholar]
- 6.Garcia GGP, Lavieri MS, Andrews C, et al. Accuracy of Kalman Filtering in Forecasting Visual Field and Intraocular Pressure Trajectory in Patients with Ocular Hypertension. JAMA Ophthalmol. 2019;137(12):1416–1423. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 7.Kazemian P, Lavieri MS, Van Oyen MP, Andrews C, Stein JD. Personalized Prediction of Glaucoma Progression Under Different Target Intraocular Pressure Levels Using Filtered Forecasting Methods. Ophthalmology. 2018;125(4):569–577. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8.Garcia GGP, Nitta K, Lavieri MS, et al. Using Kalman Filtering to Forecast Disease Trajectory for Patients With Normal Tension Glaucoma. Am J Ophthalmol. 2019;199:111–119. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Ederer F, Gaasterland DE, Sullivan EK, AGIS Investigators. The advanced glaucoma intervention study (AGIS): 1. Study design and methods and baseline characteristics of study patients. Control Clin Trials. 1994;15(4):299–325. [DOI] [PubMed] [Google Scholar]
- 10.Musch DC, Lichter PR, Guire KE, Standardi CL. The Collaborative Initial Glaucoma Treatment Study: Study design, methods, and baseline characteristics of enrolled patients. Ophthalmology. 1999;106(4):653–662. [DOI] [PubMed] [Google Scholar]
- 11.Dempster AP, Laird NM, Rubin DB. Maximum Likelihood from Incomplete Data Via the EM Algorithm. J R Stat Soc Ser B. 1977;39(1):1–22. [Google Scholar]
- 12.De Moraes CG, Jasien JV., Simon-Zoula S, Liebmann JM, Ritch R. Visual field change and 24-hour IOP-related profile with a contact lens sensor in treated glaucoma patients. In: Ophthalmology. Vol 123. ; 2016:744–753. [DOI] [PubMed] [Google Scholar]
- 13.Gardiner SK, Crabb DP. Examination of different pointwise linear regression methods for determining visual field progression. Investig Ophthalmol Vis Sci. 2002;43(5):1400–1407. [PubMed] [Google Scholar]
- 14.Heijl A, Buchholz P, Norrgren G, Bengtsson B. Rates of visual field progression in clinical glaucoma care. Acta Ophthalmol. 2013;91(5):406–412. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 15.Chauhan BC, Malik R, Shuba LM, Rafuse PE, Nicolela MT, Artes PH. Rates of glaucomatous visual field change in a large clinical population. Investig Ophthalmol Vis Sci. 2014;55(7):4135–4143. [DOI] [PubMed] [Google Scholar]
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