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(Chest. 2003;124:1694-1701.)
© 2003 American College of Chest Physicians

Prediction of the Apnea-Hypopnea Index From Overnight Pulse Oximetry*

Ulysses J. Magalang, MD, FCCP; Jacek Dmochowski, PhD; Sateesh Veeramachaneni, MD; Azmi Draw, MD; M. Jeffery Mador, MD; Ali El-Solh, MD and Brydon J. B. Grant, MD, FCCP

* From the Division of Pulmonary, Critical Care, and Sleep Medicine (Drs. Magalang, Draw, and El-Solh), Department of Medicine (Dr. Veeramachaneni); Department of Social and Preventive Medicine (Dr. Dmochowski), University at Buffalo; and Veterans Affairs Medical Center (Drs. Mador and Grant), Buffalo, NY.

Correspondence to: Brydon J. B. Grant, MD, FCCP, Veterans Affairs Medical Center (111-S), 3495 Bailey Ave, Buffalo, NY 14215; e-mail: grant{at}buffalo.edu


   Abstract
TOP
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
Study objectives: To compare the relative usefulness of the different indexes derived from pulse oximetry in the diagnosis of obstructive sleep apnea (OSA), and to determine if a combination of these indexes improves the prediction of the apnea-hypopnea index (AHI) measured by polysomnography.

Design: Prediction model developed from 224 patients, validated prospectively in 101 patients from the same center (group 1) and in 191 patients from a different sleep center (group 2).

Setting: Two independent sleep clinics run by university sleep specialists.

Participants: Patients who underwent polysomnography for suspicion of OSA.

Interventions: The following indexes were calculated from pulse oximetry recordings performed simultaneously during polysomnography: (1) {Delta} index, the average of the absolute differences of oxygen saturation between successive 12-s intervals; (2) desaturation events per hour to 2%, 3%, and 4% levels; and (3) cumulative time spent below 90%, 88%, 86%, 84%, 82%, and 80% saturation.

Measurements and results: The best predictor was the {Delta} index, although desaturation events provided similar levels of diagnostic accuracy. An aggregation of multivariate models using combination of indexes reduced the prediction error (r2 = 0.70) significantly (p < 0.05) compared to using the {Delta} index alone (r2 = 0.60). The proportion of subjects from the validation groups within 95% confidence interval (CI) of the derivation group was 90% (95% CI, 83 to 95%) and 91% (95% CI, 86 to 95%) for groups 1 and 2, respectively. The overall likelihood ratios for the aggregated model in all patient groups were 4.2 (95% CI, 3.3 to 15.3), 3.4 (95% CI, 2.7 to 4.3), 3.0 (95% CI, 2.2 to 4.1), and 6.7 (95% CI, 4.9 to 9.2) for normal (AHI < 5/h), mild (AHI 5 to < 15/h), moderate (AHI 15 to < 30/h), and severe (AHI >= 30/h) disease, respectively.

Conclusions: The {Delta} index and oxygen desaturation indexes provided similar levels of diagnostic accuracy. The combination of indexes improved the precision of the predicted AHI and may offer a potentially simpler alternative to polysomnography.

Key Words: bootstrap aggregation • clinical prediction rules • multivariate adaptive regression splines • overnight polysomnography • pulse oximetry • sleep apnea syndrome


   Introduction
TOP
 Abstract
 Introduction
Materials and Methods
 Results
 Discussion
 Appendix
 References
 
The obstructive sleep apnea (OSA) syndrome is a major health problem affecting 2 to 4% of the middle-aged population.1 At present, polysomnography is considered the reference standard diagnostic test for this condition.2 However, polysomnography is costly and time consuming. As a result, primary care providers may be reluctant about ordering polysomnography and patients unwilling to attend their tests. Overnight pulse oximetry has been proposed as a simpler alternative to polysomnography in the diagnosis of OSA because it is readily available, relatively inexpensive, and could potentially meet the large demand for diagnostic testing in the community. It can be easily done at home and repeated, if need be, which is not the case with polysomnography even performed at home.

Several quantitative indexes derived from overnight pulse oximetry have been used to predict the presence of OSA. These indexes include the number of oxyhemoglobin desaturations below a certain threshold, usually 3% or 4% decline from baseline,3 4 5 6 the cumulative time spent below an oxyhemoglobin saturation of 90%,4 and the {Delta} index, a measure of the variability of the oxyhemoglobin saturation.7 One study has suggested that the number of desaturations > 4% as well as the 12-s {Delta} index also predicts the response to continuous positive airway pressure (CPAP) therapy in patients with OSA.8 Although these quantitative indexes appear to hold more promise than visual inspection of the overnight pulse oximetry tracing, there has been no systematic comparison of their relative utility in the diagnosis of OSA. As a result, physicians select different parameters to interpret overnight pulse oximetry results.

Most published studies utilizing these quantitative oximetry indexes have been performed at a single institution. Thus, the applicability of these indexes to the general population remains uncertain.9 In addition, their accuracy has been validated using different threshold values of the apnea-hypopnea index (AHI) due to a lack of established criterion for the diagnosis of OSA. In practice, most physicians tend to modify the initiation of treatment for OSA depending on the patient’s symptoms and clinical characteristics. Prediction of the actual AHI from overnight pulse oximetry is likely to be more useful than using threshold values to define OSA that has been customary in all but a few studies involving pulse oximetry.3 4 5 6 7 10 11 The objectives of this study were to compare the relative utility of the different quantitative oximetry indexes that are used to confirm the presence of OSA, and to determine if a combination of these indexes may be superior to a single index for predicting the AHI from overnight pulse oximetry data.


   Materials and Methods
TOP
 Abstract
 Introduction
 Materials and Methods
Results
 Discussion
 Appendix
 References
 
Patient Population
Five hundred sixteen patients suspected of having OSA were enrolled into this prospective study. Patients were recruited from two independent sleep clinics in Buffalo, NY: the Associated Sleep Center (ASC) and the Buffalo Veterans Affairs Medical Center (VAMC) Sleep Center. The eligibility criteria were all patients who underwent overnight polysomnography for suspected sleep apnea. The exclusion criteria were age < 18 years; oxygen supplementation was used during the sleep study, or CPAP titration was performed on the same night as the diagnostic study (split-night study). Eighty-four patients (20.5%; 95% confidence interval [CI], 17 to 24%) who were scheduled for polysomnography at the ASC and 71 patients (27%; 95% CI, 22 to 32%) who were scheduled for polysomnography at the Buffalo VAMC did not show up for testing.

The derivation group consisted of 224 consecutive eligible patients referred to the ASC. The prediction model developed from this derivation group was then validated in the subsequent 101 consecutive patients studied at the ASC (validation group 1). In order to test whether the prediction model will be applicable at another sleep laboratory, the model was further validated in 191 consecutive patients studied at the Buffalo VAMC Sleep Center (validation group 2). The study was approved by the Institutional Review Boards of the University at Buffalo and the Buffalo VAMC. Informed consent was obtained from patients studied at ASC, but it was not required by the Institutional Review Board of the Buffalo VAMC for this particular study.

Polysomnography
All patients underwent standard overnight polysomnography with recordings of EEG, electro-oculogram, submental and bilateral leg electromyograms, and ECG. Airflow was measured qualitatively by an oral-nasal thermistor and respiratory effort by thoracoabdominal piezoelectric belts. Measurement of arterial oxyhemoglobin saturation was performed with a pulse oximeter (ASC: Nellcor N-200, Nellcor Puritan Bennett, St. Louis, MO; and Buffalo VAMC: Biox 3740, Ohmeda, Boulder, CO) with the probe placed on the patient’s finger. All signals were collected and digitized on a computerized polysomnography system (ASC: Rembrandt, Aerosep Corporation, Buffalo, NY; and Buffalo VAMC: Acquitron, Mallinckrodt, St. Louis, MO).

Sleep stages were scored in 30-s epochs using standard criteria.12 Each epoch was analyzed for the number of apneas, hypopneas, EEG arousals, oxyhemoglobin desaturation, and disturbances in cardiac rate and rhythm. Apnea was defined as the absence of airflow for at least 10 s. Hypopnea was defined as a visible reduction in airflow lasting at least 10 s associated with either a 4% decrease in arterial oxyhemoglobin saturation or an EEG arousal. An arousal was defined according to the criteria proposed by the Atlas Task Force.13 Apneas and hypopneas were classified as obstructive if respiratory effort was present, and central if respiratory effort was absent during the event. The AHI was defined as the number of apneas and hypopneas per hour of sleep. Only one person in each sleep laboratory, blinded to the off-line analysis of pulse oximetry data, scored the sleep studies.

Pulse Oximetry
Pulse oximetry data were collected as part of the polysomnography. Oximetry data were digitized and collected at 8 Hz and 10 Hz at the ASC and Buffalo VAMC, respectively, into a computerized polysomnography system along with the other sleep study parameters. The recording time was defined as lights-off to lights-on (approximately 10 PM to 6 AM). Recording time was used as the denominator for the various indexes of overnight pulse oximetry rather than total sleep time since EEG will not be available when oximetry is to be utilized outside of the sleep laboratory. The oximeters in both sleep laboratories employed a moving average of 3 s. The oximetry data were then extracted from the computerized polysomnography system for further off-line analysis. Oximetry data were averaged over 2-s sampling intervals. Artifacts were removed by eliminating all changes of oxygen saturation between consecutive sampling intervals of > 4%/s,14 and any oxygen saturation < 20%. The definition of a desaturation event was also based on the work of Taha and colleagues.14 Every data point was examined sequentially to determine if criteria were met to define an event. The criteria for an event were a decrease of at least the set amount (2%, 3%, or 4%) in oxygen saturation from the initial data value for at least 10 s, and at a rate that is > 0.1%/s. In addition, the oxygen saturation must return within 60 s to within 1% of the initial value, or increase from its nadir by 1.5 times or more of the set amount of the dip. Once the criteria were met, a new search for an event was initiated at the next data point after the event. The {Delta} index was calculated as the average of absolute differences of oxygen saturation between successive 12-s intervals (sum of the absolute differences between two successive points, divided by the number of intervals measured).7 The index quantifies oxygen saturation variability. In OSA, oxygen desaturations associated with respiratory events cause fluctuations in the oxygen saturation signal leading to high {Delta} index values. A total of 10 indexes were calculated for each patient in the derivation group using a computer program: {Delta} index, number of desaturation events (to 2%, 3%, and 4% levels) per hour of recording time, and the cumulative time spent below 90%, 88%, 86%, 84%, 82%, and 80% saturation as a proportion of total recording time.

Prediction of the AHI
We used modern multivariate regression techniques to develop a prediction model15 of the AHI from the calculated quantitative indexes with commercially available software (Multivariate Adaptive Regression Splines; Salford Systems; San Diego, CA). The various indexes of overnight oximetry correlated with each other. As a result, we anticipated that the models may be unstable and that the structure of the model would depend heavily on the cases used in the derivation set. To address this issue, we used one of a new group of techniques ("committee of experts") that used the aggregated result from 20 different models.16 Details of the approach that we used are provided in the appendix. The prediction model was validated in two independent facilities so that it could be used as a predictive instrument.

Statistical Analysis
The characteristics of the patients in the derivation and two validation groups were compared using nonparametric one-way analysis of variance. If a significant difference was found, a multiple comparison procedure (Dunn method) was used to determine a source of the difference (Sigmastat; SPSS; San Rafael, CA).

Although our goal was to provide a prediction model of AHI, we did use a threshold value to define OSA as a summary comparison and to facilitate quantitative comparisons with previous studies. Sensitivity, specificity, and receiver operator characteristic (ROC) curves were generated for each of the quantitative oximetry indexes using an AHI threshold value of >= 15 events/h based on the polysomnography to define the presence of OSA. Comparison of the diagnostic accuracy of the univariate oximetry indexes was assessed from the area under the ROC curve. The area under the ROC curve was estimated by the c index,17 and is calculated using a sampling with replacement (bootstrap) method with our own software.18 95% CI was used in all analysis of confidence limits. All values represented by ± are SE unless stated otherwise. A logarithmic transformation of predicted and actual AHI was used in order to achieve a normal distribution of residuals as previously done.19 The validity of the prediction models developed using the aggregation of models was tested by calculating the proportions of patients in the validation groups that were within the confidence limits of the derivation group. In addition, we compared the positive likelihood ratios of the aggregated model and the {Delta} index, an approach previously used by others.20 Positive likelihood ratios were calculated from the true positive rate predicted from oximetry compared with polysomnography for that level of severity of sleep apnea divided by the false-positive rate.


   Results
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
Discussion
 Appendix
 References
 
Patient Characteristics
A total of 224 patients were entered into the derivation group. Another 101 patients were enrolled in validation group 1, and 191 patients were enrolled in validation group 2. Therefore, a total of 516 patients were included in the analysis. The patient characteristics of the derivation and two validation groups are shown in Table 1 . All groups have similar body mass index and AHI. The patients in validation group 2 were significantly older compared to the derivation group and validation group 1, and have a larger neck circumference compared to the derivation group.


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  		Table 1. Summary of Patient Characteristics*

 
Relative Utility of Oximetry Indexes
Table 2 shows the c index of the different quantitative indexes calculated from the raw oximetry data in the 224 patients in the derivation group. The best predictor of the presence of OSA using a threshold value of 15 events/h was the {Delta} index (c index, 0.88 ± 0.02), although the number of desaturation events provided similar levels of diagnostic accuracy. In addition, the definition of desaturation events (2%, 3%, or 4%) did not alter the diagnostic accuracy of the desaturation indexes (c index, 0.87 ± 0.02, 0.87 ± 0.02, and 0.85 ± 0.03, respectively). The sensitivity of a {Delta} index of > 0.63 in the diagnosis of OSA was 91% (CI, 84 to 95%), while the specificity was 59% (CI, 49 to 69%).


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  		Table 2. Accuracy of the Indexes Derived From Overnight Oximetry in the Diagnosis of OSA

 
Prediction of the AHI
Derivation Group:
The prediction equation using the {Delta} index alone derived from the multivariate model in the derivation group is as follows (equation 1) :

(1)
where BF1 is the maximal value of either zero or ({Delta} index - 0.57), and BF2 is the maximal value of either zero or (0.570 - {Delta} index). The coefficient of determination (r2) between the actual and predicted AHI was 0.60 using this initial multivariate prediction model involving the {Delta} index alone. The aggregated model using a combination of the various oximetry indexes increased the r2 between the actual and predicted AHI (r2 = 0.70), which was significantly higher than the initial model (p < 0.05). The predicted and actual AHIs of the 224 patients in the derivation group using the aggregated model are shown in Figure 1 .



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  		Figure 1. The aggregated model using a combination of all 10 oximetry indexes to predict the AHI from the derivation group (n = 224). The predicted and actual AHI values are shown on logarithmic scale. The coefficient of determination (r2) between the actual and predicted AHI was 0.70, which is significantly improved compared to 0.60 (data not shown) using the initial model (p < 0.05).

 
In comparison with the derivation model using only the {Delta} index, there was an improvement in terms of diagnostic accuracy using >= 15/h to define OSA with the aggregated model. The area under the ROC curve was increased to 0.9 ± 0.02 with a sensitivity of 90% (CI, 82 to 95%) and a specificity of 70% (CI, 62 to 78%) using the aggregated model.

Validation Group:
In validation group 1, the actual AHI values of 92 of 101 patients were within the CI of the predictions for the AHI using the aggregated model. The proportion of patients within the CI of the prediction was 90% (CI, 83 to 95%). In validation group 2, actual AHI values of 174 of 191 patients were within the CI of the predicted AHI. The proportion of patients within the CI of the prediction was 91% (CI, 86 to 95%).

Likelihood Ratios
To determine exactly at what levels of disease severity the {Delta} index model and the aggregated model differed, we stratified the data into four groups according to the AHI measured by polysomnography: normal (AHI < 5/h), mild (5 to < 15/h), moderate (15 to < 30/h), and severe (>= 30/h). Figure 2 shows the positive likelihood ratios in all patient groups according to the severity of the AHI of the multivariate prediction models using the {Delta} index alone vs the aggregated model. Both the {Delta} index and the aggregated models improved the prediction mainly at both ends of the AHI spectrum (< 5/h and >= 30/h). The aggregated model was superior to the {Delta} index model in the severe level in the derivation group and the severe level and normal level in validation group 1, but no different in validation group 2 (Fig 2) .



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  		Figure 2. The positive likelihood ratios (± SE) in the derivation group (top, A), validation group 1 (center, B), and validation group 2 (bottom, C) according to the severity of the AHI derived from multivariate prediction models using the {Delta} index alone (filled triangles) vs the aggregated model (filled circles). The aggregated model improved the prediction mainly at both ends of the AHI spectrum (< 5/h and >= 30/h).

 
The likelihood ratios for the aggregated model in the derivation group were 6.9 (95% CI, 4.4 to 10.8), 4.3 (95% CI, 2.8 to 6.5), 3.6 (95% CI, 2.5 to 5.4), and 12 (95% CI, 7.1 to 20) for normal, mild, moderate, and severe disease severity, respectively. The likelihood ratios fell within the 95% CI for the normal and mild levels in validation group 1 and for the moderate and severe levels in validation group 2 (Fig 2) . The likelihood ratios for the {Delta} index model in the derivation group were 5.4 (95% CI, 2.2 to 12.6), 2.5 (95% CI, 1.7 to 5.3), 3.0 (95% CI, 2.1 to 4.4), and 4.0 (95% CI, 3.6 to 6.5) for normal, mild, moderate, and severe disease severity, respectively. The likelihood ratios fell within the 95% CI for the mild level only in validation group 1 and for all levels in validation group 2 (Fig 2) .

To obtain an overall estimate, we combined the results from the derivation and both validation groups for the aggregated model. The overall likelihood ratios for the aggregated model in the derivation group were 4.2 (95% CI, 3.3 to 15.3), 3.4 (95% CI, 2.7 to 4.3), 3.0 (95% CI, 2.2 to 4.1), and 6.7 (95% CI, 4.9 to 9.2) for normal, mild, moderate, and severe disease severity, respectively. The overall likelihood ratios for the {Delta} index were 3.3/h, 2.5/h, 3.0/h, and 4.9/h for normal, mild, moderate, and severe disease severity, respectively. Therefore, the likelihood ratios were at the lower 95% CI in both the normal and severe levels of disease severity.


   Discussion
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
Appendix
 References
 
The major findings of this study are as follows: (1) among the different oximetry indexes, the {Delta} index was the best predictor of the presence of OSA, although desaturation events provided similar levels of diagnostic accuracy; (2) the {Delta} index had good sensitivity but low specificity; (3) a bootstrap aggregation of models involving a combination of all the oximetry indexes (compared to using the {Delta} index alone) improved the precision of the prediction of the AHI; and (4) the prediction model developed in this article was validated in two independent sleep clinics. To our knowledge, there has been no previous study that has compared systematically the relative utility of the various quantitative indexes derived from overnight oximetry in the diagnosis of OSA.

At present, there is no definite established AHI criterion for the diagnosis of OSA with the threshold varying from 5 to 20 events per hour. Most clinicians will modify initiation of treatment depending on the symptoms and other clinical characteristics. Reports suggest that even what is considered as mild sleep-disordered breathing is associated with hypertension21 22 and cardiovascular disease,23 and that these patients with mild disease may also benefit from CPAP therapy.24 25 A consensus statement26 recommended that treatment be administered if the AHI is >= 30/h regardless of symptoms. However, results from a published study27 do not support this recommendation since patients with an AHI >= 30/h who did not have daytime sleepiness did not benefit from CPAP therapy. Therefore, we reasoned that a prediction of the actual AHI from overnight oximetry would be more clinically meaningful than a dichotomous answer to the presence of OSA, and that it would be more useful if this prediction can be computerized to eliminate the problem of interobserver and intraobserver variability.

The aggregation method16 resulted in a significant improvement of the precision of the predicted AHI. The methodology belongs to a group of methods that are known as the committee of experts, and has been described only recently and is still being developed. Although modest, this improvement is important because even small improvements in precision can increase the confidence in the prediction.

Comparison to the Results of Others
A study11 using an automated analysis of oximetry data and a desaturation event definition >= 4% lower than baseline reported a very high sensitivity of 98% and specificity of 88%; however, this study used a definition of arousals that differs substantially from the criteria proposed by the Atlas Task Force13 that has come into general use in the United States. As a result, their definition of hypopnea will differ substantially from ours. These investigators found that the addition of arousal-based scoring criteria (using their definition of arousal) for hypopnea causes only small changes in the AHI.28 However, a large study29 found that incorporating arousals based on the Atlas Task Force criteria on the hypopnea definition does impact on the value of the AHI. Table 3 shows the comparison of our results to others using an AHI cutoff value of >= 15/h to define the presence of OSA. Our results are consistent with others in the field, although our specificity was higher using the aggregated model compared to the previously published studies using the {Delta} index.


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  		Table 3. Comparison of Results

 
The study by Levy and colleagues7 reported that the correlation between the {Delta} index and actual AHI was 0.72, whereas in the study by Olson et al10 the Spearman correlation coefficient between the {Delta} index and actual AHI was 0.71. In our study, the correlation (expressed as Pearson correlation) between the predicted and actual AHI was 0.77, which improved to 0.83 when we used a combination of the oximetry indexes. Therefore, our prediction model provides modest improvement compared to using a simple regression between the {Delta} index alone and actual AHI.

Limitations
A limitation to the applicability of our prediction model is that it was validated using overnight pulse oximetry that was obtained simultaneously with polysomnography data in the sleep laboratory. Using the oximetry data performed together with polysomnography has the advantage of eliminating such potential confounders as night-to-night variability of the AHI, as well as ensuring that oximetry data were collected in exactly the same environment as the polysomnography data. Further validation of the prediction model is necessary using overnight oximetry done in the home setting unattended by technicians.

Clinical Applicability and Controversy
The fact that our prediction was validated in two independent sleep laboratories suggests that the model could be potentially applied widely, although its impact on clinical practice has yet to be established. The exact role of our predictive instrument in the clinical management of patients with suspected OSA remains to be elucidated. Overnight oximetry analysis even incorporating a combination of the different quantitative indexes may not take into account hypopneas that were defined on the basis of EEG arousals rather than changes in oxygen saturation. This may partly explain the variance of our AHI prediction. In fact, in both validation groups, most of the discrepancy involved cases where the actual AHI was greater than the predicted AHI as anticipated. An argument can be made that the prediction developed in this article will miss cases of upper airway resistance syndrome, since by definition these patients do not have oxygen desaturation during sleep.30 The existence of this syndrome is controversial.31 The prevalence of the condition remains unknown.32 In addition, the percentage of patients presenting to a sleep clinic for evaluation of daytime sleepiness with upper airway resistance syndrome is also unknown. In view of their significant daytime hypersomnia, these may be the patients that would eventually end up requiring overnight polysomnography despite a low predicted AHI from our model.

A concern with unattended overnight oximetry is that there is no assurance for controlling for technical difficulties and completeness of data collection. However, oximetry is such a simple procedure that a repeat test in the patient’s home on a separate night in the event of technical difficulties would be reasonable. Portable oximeters capable of storing data over a prolonged recording period are now readily available. The oximeter can be sent home with the patient, and after the overnight recording mailed back to the sleep laboratory or physician’s office for downloading of the data and a computer-generated report of the predicted AHI with its 95% CI reported back to the physician through an automated system.

The clinical utility of pulse oximetry can be assessed quantitatively from the likelihood ratios. The Bayesian approach is to multiply the pretest odds by the likelihood ratio to determine the posttest odds. Positive likelihood ratios that cause large changes in the likelihood of disease are > 10, moderate changes 5 to < 10, small changes 2 to < 5, and trivial changes < 2.9 Our data show that pulse oximetry using the aggregated method can produce moderate shifts in the pretest to posttest probability of OSA in the normal and severe ranges of disease severity, but only of limited usefulness in the mild-to-moderate range.

In summary, we have compared the relative utility of different quantitative indexes derived from overnight oximetry in the diagnosis of OSA. To our knowledge, our study is the first to have made this comparison. We have developed a novel prediction model of the AHI using a combination of these quantitative oximetry indexes with a better precision compared to using a single index. We validated this improved prediction in two independent sleep clinics prospectively.


   Appendix
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
References
 
Multivariate Prediction Models
We used multivariate adaptive regression splines (MARS) to develop prediction models.15 The splines used in this study consisted of one or more of a series of linear segments joined at adjacent ends that could be fitted to nonlinear data. MARS is a multivariate nonparametric procedure that builds flexible regression-like models using exhaustive search techniques to test the necessity of different predictors. Interactions between independent variables are simultaneously tested. The model is adaptive because it overfits the data, and then determines the size of the model that optimizes the tradeoff between accuracy (bias) and variance (precision) using a tenfold cross-validation. The final model is obtained through backward elimination to the optimal model size. Predicted value is derived as linear combination of basic functions.

Aggregated Model
The various indices of overnight pulse oximetry (predictor variables) are correlated so that there may be several difference plausible models that could be fitted to the data, and may account for some of the prediction error. To address this issue, we used one of a new group of techniques (committee of experts) that average the predictions of different plausible models to reduce this error. Specifically, we used bootstrap aggregation model averaging ("bagging") by developing 20 random samples (with replacement) from the original data set,16 a process known as bootstrapping. Each of the 20 data sets has the same size as the original data set. Because we used random sampling with replacement, a particular patient could occur more than once in any of the 20 generated data sets, and some may not appear at all. For each of the 20 data sets, a MARS model was generated in a similar form to that shown in equation 1 .

For every patient (P) in the original derivation data set (i), and each of predictive models (m), the predictive value of AHI 0 <= Pi,m <= 360 was determined, so that every patient was assigned 20 predictions. Predictions beyond this range were truncated at the end point values because results outside this range are unachievable. The maximal value, 360/h, would indicate continuous apnea since apnea is defined as an event >= 10 s in duration.

The multiple linear regression model with bootstrap sample predictions as independent variables was fitted to transformed response (equation 2) :

(2)
where AHI is measured for that patient by overnight polysomnography, and e is the error term. The best regression model was found with the all-subsets method. If the model was not included in the final regression model, the corresponding coefficient was assigned as zero. We used the weighted average of the predictions to obtain a single aggregated prediction of AHI for a particular patient (equation 3) :

(3)


   Footnotes
 
Abbreviations: AHI = apnea-hypopnea index; ASC = Associated Sleep Center; CI = confidence interval; CPAP = continuous positive airway pressure; MARS = multivariate adaptive regression splines; OSA = obstructive sleep apnea; ROC = receiver operator characteristic; VAMC = Veterans Affairs Medical Center

Supported by Research for Health in Erie County, Inc. and Veterans Affairs Enhancement Funds.

Received for publication April 23, 2002. Accepted for publication June 16, 2003.


   References
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 

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