The definition of sleep quality that encompasses the ramifications of its implications is hard to achieve given its subjective nature. It is like describing “sweetness”; the description is based on a subjective personal history of exposure to “sweet” things. However, despite the variance of the actual manifestation, sleep quality can be generally regarded as the relative amount of satisfaction derived from a sleep episode.

In some research, sleep quality is defined in terms of the subjective Pittsburgh Sleep Quality Index (PSQI) as a statistical measure introduced by Buysse et al. in 1988 [1] and has now taken on a life of its own in the different localized varia tions such as the “Persian PSQI”, “Hungarian PSQI (PSQI-HUN)”, “Korean PSQI (PSQI-K)” and other non-distinct morphological variants [2, 3].

In introducing the Pittsburgh Sleep Quality Index (PSQI), Buysse et al., cited the difficulty of establishing a general definition of “sleep quality” which has qualitative aspects. This is because qualitative aspects of sleep are hard to quantify, for example, “restfulness”. In fact, one might argue that qualitative factors like “restfulness” are equally as important as quantitative factors like “sleep duration”, “number of interruptions” etc. in the perception of sleep quality.

The PSQI was also motivated by the need for a formal taxonomy in sleep quality research that captures both statistical and clinical factors. The PSQI is a score derived from the answers to 19-questions in a sleep questionnaire [4]. PSQI, however, has not been rigorously adopted as a standard by the mainstream even though it has been the subject of many research publications given the amount of citations. The reason is not far-fetched, while the PSQI is groundbreaking from an ontological viewpoint. It is not a significant improvement from what was already in use in mainstream sleep medicine, i.e. the use of questionnaires to establish sleep history. Although in scientific research, there has been reliance on questionnaires when studying phenomenon strongly correlated with behavioral or individual patterns, in many clinical applications, precision is a principal criterion. This criterion excludes data based solely on the ability of the subject to remember accurately and understand questions correctly. The exclusion of data gathered in this manner is due to its highly subjective nature which makes generalization difficult. Furthermore, varying subjectivity does not foster further development in the ontology of sleep research and consequently limits its usefulness in enabling emerging technologies in the 21^st century.

For considerable progress to be made in sleep research, there is a need for more reliable and externally valid data sources which can be used to develop various statistical models in cadence with technology trends. This research will lean towards a rather vague but more clinically acceptable definition of sleep quality given by the Encyclopedia of Pharmacology which views Sleep Quality (SQ) as the outcome of polysomnography [5]. Subsequently, an ensemble of statistical learning models that collaborate to predict Sleep Quality (SQ) from polysomnography is presented.

Predicting Sleep Quality (SQ) requires the ability to forecast future inputs for the “sleep stage” classification model since Sleep Quality (SQ) is a function of the time spent in the sleep stages. The higher the amount of time spent in stage 3-5, the higher the SQ value. The goal is to demonstrate that the power spectrum derived from the ECG signal of an individual can be learned by a regression model and used to forecast future trends which are then classified by a Support Vector Machine (SVM) model and evaluated as a Sleep Quality (SQ) value using the equation below:

An intuitive way of conceptualizing the SQ formulae is that it is a function from the predicted sleep hypnogram (or the corresponding confusion matrix) to the real numbers. A summary of the performance of the SVM model for all data in the test set is presented in the confusion matrix in Table 3.

The confusion matrix in Table 3 represents the overall result of the classification performed for all 100 patients in the test set. The rows represent the distribution of the predictions in the different sleep stages in cadence with the actual observations which are in the columns. For examples, row 0, column 0 translates to the total amount of points predicted or classified to be stage 0 “Awake” that is actually stage 0. Similarly, row 0, column 1 translates to the total amount of points classified to be stage 0 that is actually stage 1. The number in each cell represents the total for the entire test set. Mathematically, each cell is calculated as follows:

Where 0 ≤ i ≤ 5

0 ≤ j ≤ 5,  N = cardinality of test set

The average performance characteristics are reported as follows:

Average SVM Accuracy in the test set 85%

To determine the accuracy, the number of correctly classified points are determined by checking the predicted sleep stages and wake stage against the actual stages in the clinical annotations. As such, for every sample patient, the accuracy of the classified wake stage and sleep stages is evaluated as follows:

For all in a set of predictions, and in a set of actual measured observation,

where:

N = cardinality of test set.

Similarly, a statistic for the overall performance of the polynomial regression model is presented as follows:

Average adjusted R² for polynomial regression = 0.61

For every sample patient in the test set, a reference point in the wake cycle is selected, the sleep onset latency is determined by predicting Time to Sleep (TTS) and it is added to a target length of sleep episode (sleep time) which is extracted from the clinical annotations, which varies for each patient. The polynomial regression model is then used to model the ideal progression of the power spectrum. The R² is computed to determine the fit of the prediction to the actual model and then adjusted for the number of estimators or predictors, which in this case is 3. The average value of the adjusted R² is calculated as follows for all patients:

where: N = cardinality of test set

After the forecasted power spectrum is classified by the SVM model, the Sleep Quality (SQ) formula which can be conceived as a function from the predicted sleep hypnogram to the set of real numbers, is used to determine a score on the interval (0,1), with 0 meaning poor sleep quality and 1 meaning best sleep quality. The overall R² for Sleep Quality (SQ) for all the patients in the test set is approximately 0.9. This is largely in part to the symmetry of misclassification and the evaluation of Sleep Quality (SQ) focuses on the transitions in the sleep hypnogram that involves only stage 3, 4 and 5.

Furthermore, in Table 3 which summarizes the SVM performance for the whole experiment, the misclassifications distributed within stage 0, 1, 2 for both predicted and actual values will have no impact of the final computation of the Sleep Quality (SQ) values because stages 0, 1, 2 are unused in the Sleep Quality (SQ) equation. Also, the symmetry of the mistake in classifying Stage 2 and 3 improves the outcome, i.e. 10279 actual stage 3 points were misclassified as stage 2 but 13206 actual stage 2 points were also misclassified as stage 3. This results in an offsetting behavior in the Sleep Quality (SQ) equation that focuses on the total time spent in stages 3, 4, 5 and not their exact distribution. It is worthy of mentioning that the 85% test set accuracy for the SVM model is directly influenced by the quality of the forecasted power spectrum by polynomial regression. Considering the average R² is 0.61, meaning only 61% of the variation in the true model is explained, SVM intrinsic behavior of finding a separating hyperplane that maximizes the margin between classes was invaluable in achieving the reported accuracy and also responsible for the near-symmetric misclassification on the border classes of stage 2 and 3. Intuitively, this makes sense, since stage 3 and above is considered, then there is an implicit boundary line between stage 2 and 3. In a typical modal, we expect that the probability of predicting stage 3 when is 2 is the same as the probability of predicting stage 2 when it is 3. Informally, we conceive the error as being normally distributed. In this case, however, there is a slight bias towards stage 3 at the boundary.

Fig. (5) represents a plot of the overall Sleep Quality (SQ) model for all patients in the test set. It is obtained by plotting actual Sleep Quality (SQ) values computed from clinical annotations against the Sleep Quality (SQ) values from the predicted hypnogram. Recall, that the Sleep Quality formula, is a function from the predicted sleep hypnogram to the interval (0, 1) and as a result, the values computed from clinical annotations as well as predicted by the Sleep Quality (SQ) model are consistently between 0 and 1. Although, an informal notion can be introduced to view computed SQ values as probabilities if the outcome is viewed like a Bernoulli trial with binary realizations {good sleep, bad sleep}, SQ values are actually a measure of the goodness or quality of a sleep episode, with 1 being the best sleep possible [9, 13, 14].

As mentioned earlier, the Sleep Quality (SQ) model is influenced principally by the correctness of the forecasted future HRV power spectrum under the current methodology. It follows, therefore, that the general usefulness of the presented approach would depend on the ability of the learning model to generalize over a set of different sleep patterns under the presumption that these patterns are influenced by daily physiological experiences and that most individuals have finite distinct observable physiological experiences. There is also an assumption that the observed physiological patterns of other individuals would account for the variations possible in a single individual.

Fig. (5). Overall SQ predictive model performance [9].

It is no surprise that the result is a mixed bag, ranging from a good fit to wide deviations from the true underlying model. However, in many cases, the performance of the model provides a fair replica of the true underlying Sleep Quality (SQ) model.

Industrial or mainstream adoption might benefit significantly from a calibration step, which will enable pre-trained models to learn the “Wake-Sleep” behavior of the host patient. However, since the quality of ECG recordings from many ambulatory ECG devices is noisy, real-time signal processing and data preprocessing for continuous training might be challenging.