# Online Analysis of Medical Time Series

This is a short overview of the following paper by Fried et al. (2017):

Fried, Roland, Sermad Abbas, Matthias Borowski, and Michael Imhoff. 2017. “Online Analysis of Medical Time Series.”

Annual Review of Statistics and Its Application4 (1): 169–88. https://doi.org/10.1146/annurev-statistics-060116-054148.

Unfortunately, most of the papers from *Annual Reviews* are not open access. I hope the situation will improve in the future, but in the meantime there is Sci-Hub.

As the title suggests, it is a very complete review of statistical models for studying medical time series in an online setting. It appeared in *Annual Reviews*, which publish very nice reviews of various topics in a wide variety of fields.

Since I work on developing algorithms for a medical device, this is particularly relevant for my job!

## Context: clinical applications and devices, and the need for robust statistical analysis

The goal of online medical time series analysis is to detect relevant patterns, such as trends, trend changes, and abrupt jumps. This is to support online decision support systems.

The paper (section 5) The section explaining the motivation behind the review is at the end of the paper. I find it strange to go straight to the detailed exposition of complex statistical methods without explaining the context (medical time series and devices) in more detail.

goes on to explain the motivation for developing robust methods of time series analysis for healthcare applications.

An important issue in clinical applications is the false positive rates:

Excessive rates of false positive alarms—in some studies more than 90% of all alarms—lead to alarm overload and eventually desensitization of caregivers, which may ultimately jeopardize patient safety.

There are two kinds of medical devices: clinical decision support and closed-loop controllers. *Decision support* aims to provide the physician with recommendations to provide the best care to the patient. The goal of the medical device and system is to go from raw, low-level measurements to “high-level qualitative principles”, on which medical reasoning is directly possible. This is the motivation behind a need for abstraction, compression of information, and interpretability.

The other kind of medical device is *physiologic closed-loop controllers* (PCLC). In this case, the patient is in the loop, and the device can take action directly based on the feedback from its measurements. Since there is no direct supervision by medical practitioners, a lot more caution has to be applied. Moreover, these devices generally work in hard real-time environments, making online functioning an absolute requirement.

## Robust time series filtering

The objective here is to recover the time-varying level underlying the data, which contains the true information about the patient’s state.

We assume that the time series \(y_1, \ldots, y_N\) is generated by an additive model

\[ y_t = \mu_t + \epsilon_t + \eta_t,\qquad t=1,\ldots,N, \]

where \(\mu\) represents the signal value, \(\epsilon\) is a noise variable, and \(\eta\) is an outlier variable, which is zero most of the time, but can take large absolute values at random times.

The paper reviews many methods for recovering the underlying signal via state estimation. Moving window techniques start from a simple running median and go through successive iterations to improve the properties of the estimator. Each time, we can estimate the mean of the signal and the variance.

Going further, regression-based filtering provide an interesting approach to estimate locally the slope and the level of the time series. Of these, the repeated median (RM) regression offers a good compromise between robustness and efficiency against normal noise.

Without using moving windows, Kalman filters I already talked about Kalman filters when I briefly mentioned applications in my post on quaternions.

can also reconstruct the signal by including in their state a steady state, a level shift, slope change, and outliers. However, it is often difficult to specify the error structure.

## Online pattern detection

Instead of trying to recover the underlying signal, we can try to detect directly some events: level shifts, trend changes, volatility changes.

This is generally based on autoregressive modelling, which work better if we can use a small time delay for the detection.

## Multivariate techniques

All the techniques discussed above were designed with a single time series in mind. However, in most real-world applications, you measure several variables simultaneously. Applying the same analyses on multivariate time series can be challenging. Moreover, if the dimension is high enough, it becomes too difficult for a physician to understand it and make decisions. It is therefore very important to have methods to extract the most pertinent and important information from the time series.

The idea is to apply dimensionality reduction to the multivariate time series in order to extract meaningful information. Principal component analysis is too static, so dynamic versions are needed to exploit the temporal structure. This leads to optimal linear double-infinite filters, that

explore the dependencies between observations at different time lags and compress the information in a multivariate time series more efficiently that ordinary (static) principal component analysis.

Graphical models can also be combined with dimensionality reduction to ensure that the compressed variables contain information about the patient’s state that is understandable to physicians.

Finally, one can also use clustering to group time series according to their trend behaviour.

## Conclusions

To summarize, here are the key points studied in the paper.

Context: We have continuous measurements of physiological or biochemical variables. These are acquired from medical devices interacting with the patient, and processed by our medical system. The system, in turn, should either help the physician in her decision-making, or directly take action (in the case of a closed-loop controller).

There are several issues with the basic approach:

- Measurements are noisy and contaminated by measurement artefacts that impact the ability to make decisions based on the measurements.
- We often measure a multitude of variables, which means a lot of complexity.

The article reviews methods to mitigate these issues: extracting the true signal, detecting significant events, and reducing complexity to extract clinically relevant information.

The final part of the conclusion is a very good summary of the challenges we face when working with medical devices and algorithms:

Addressing the challenges of robust signal extraction and complexity reduction requires:

- Deep understanding of the clinical problem to be solved,
- Deep understanding of the statistical algorithms,
- Clear identification of algorithmic problems and goals,
- Capabilities and expertise to develop new algorithms,
- Understanding of the respective medical device(s) and the development environment,
- Acquisition of clinical data that is sufficient to support development and validation of new algorithms.
The multitude of resulting requirements cannot be addressed by one profession alone. Rather, close cooperation between statisticians, engineers, and clinicians is essential for the successful development of medical devices embedding advanced statistical algorithms. Moreover, regulatory requirements have to be considered early on when developing algorithms and implementing them in medical devices. The overarching goal is to help make patient care more efficient and safer.

The complex interplay between mathematical, technical, clinical, and regulatory requirements, and the need to interact with experts in all these fields, are indeed what makes my job so interesting!

## References

I didn’t include references to the methods I mention in this post, since the paper itself contains a lot of citations to the relevant literature.

Fried, Roland, Sermad Abbas, Matthias Borowski, and Michael Imhoff. 2017. “Online Analysis of Medical Time Series.” *Annual Review of Statistics and Its Application* 4 (1): 169–88. https://doi.org/10.1146/annurev-statistics-060116-054148.