From cd8fff45ff4993e4d38699d686c9c6edd62b0cf4 Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Tue, 17 Nov 2020 18:20:23 +0100 Subject: [PATCH] Add post on Online Analysis of Medical Time Series --- bib/bibliography.bib | 15 ++ ...online-analysis-of-medical-time-series.org | 193 ++++++++++++++++++ 2 files changed, 208 insertions(+) create mode 100644 posts/online-analysis-of-medical-time-series.org diff --git a/bib/bibliography.bib b/bib/bibliography.bib index 4106836..c72659c 100644 --- a/bib/bibliography.bib +++ b/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}, +} diff --git a/posts/online-analysis-of-medical-time-series.org b/posts/online-analysis-of-medical-time-series.org new file mode 100644 index 0000000..b1def3b --- /dev/null +++ b/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.