Add post on Online Analysis of Medical Time Series

bib/bibliography.bib

@@ -454,3 +454,18 @@
   doi =		 {10.1007/978-3-319-20735-3},
   isbn =	 9783319207346,
 }
+
+@article{fried2017_onlin_analy_medic_time_series,
+  author =	 {Roland Fried and Sermad Abbas and Matthias Borowski
+                  and Michael Imhoff},
+  title =	 {Online Analysis of Medical Time Series},
+  journal =	 {Annual Review of Statistics and Its Application},
+  volume =	 {4},
+  number =	 {1},
+  pages =	 {169-188},
+  year =	 {2017},
+  doi =		 {10.1146/annurev-statistics-060116-054148},
+  url =
+                  {https://doi.org/10.1146/annurev-statistics-060116-054148},
+  DATE_ADDED =	 {Tue Nov 17 08:59:07 2020},
+}

posts/online-analysis-of-medical-time-series.org

@@ -0,0 +1,193 @@
+---
+title: "Online Analysis of Medical Time Series"
+date: 2020-11-17
+toc: false
+---
+
+This is a short overview of the following paper by
+cite:fried2017_onlin_analy_medic_time_series:
+
+#+begin_quote
+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]].
+#+end_quote
+
+[fn:: {-} 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 [[https://en.wikipedia.org/wiki/Sci-Hub][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 [[https://www.annualreviews.org/][/Annual Reviews/]], which publish very nice reviews of
+various topics in a [[https://www.annualreviews.org/action/showPublications][wide variety of fields]].
+
+Since I work on developing algorithms for a [[https://www.sysnav.fr/markets/heathcare/?lang=en][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)[fn:section5] goes on to explain the motivation
+for developing robust methods of time series analysis for healthcare
+applications.
+
+[fn:section5] {-} 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.
+
+
+An important issue in clinical applications is the false positive
+rates:
+#+begin_quote
+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.
+#+end_quote
+
+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 [[https://en.wikipedia.org/wiki/State_observer][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 [[https://en.wikipedia.org/wiki/Repeated_median_regression][repeated median]] (RM) regression offers a good
+compromise between robustness and efficiency against normal noise.
+
+Without using moving windows, [[https://en.wikipedia.org/wiki/Kalman_filter][Kalman filters]][fn:kalman] 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.
+
+[fn:kalman] {-} I already talked about Kalman filters when I briefly
+mentioned applications [[./quaternions.html#applications][in my post on quaternions]].
+
+* 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 [[https://en.wikipedia.org/wiki/Autoregressive_model][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 [[https://en.wikipedia.org/wiki/Dimensionality_reduction][dimensionality reduction]] to the multivariate time
+series in order to extract meaningful information. [[https://en.wikipedia.org/wiki/Principal_component_analysis][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
+#+begin_quote
+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.
+#+end_quote
+
+[[https://en.wikipedia.org/wiki/Graphical_model][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 [[https://en.wikipedia.org/wiki/Cluster_analysis][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:
+
+#+begin_quote
+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.
+#+end_quote
+
+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.