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Title: Learning to Treat Sepsis with Multi-Output Gaussian Process Deep Recurrent Q-Networks

Paper content:
Sepsis is a life-threatening complication from infection and a leading cause of mortality in hospitals.
While early detection of sepsis improves patient outcomes, there is little consensus on exact treatment guidelines, and treating septic patients remains an open  problem.
In this work we present a new deep reinforcement learning method that we use to learn optimal personalized treatment policies for septic patients.
We model patient continuous-valued physiological time series using multi-output Gaussian processes, a probabilistic model that easily handles missing values and irregularly spaced observation times while maintaining estimates of uncertainty.
The Gaussian process is directly tied to a deep recurrent Q-network that learns clinically interpretable treatment policies, and both models are learned together end-to-end.
We evaluate our approach on a heterogeneous dataset of septic spanning 15 months from our university health system, and find that our learned policy could reduce patient mortality by as much as 8.2\% from an overall baseline mortality rate of 13.3\%.
Our algorithm could be used to make treatment recommendations to physicians as part of a decision support tool, and the framework readily applies to other reinforcement learning problems that rely on sparsely sampled and frequently missing multivariate time series data.
Sepsis is a poorly understood complication arising from infection, and is both a leading cause in patient mortality BID8 ) and in associated healthcare costs BID37 ).
Early detection is imperative, as earlier treatment is associated with better outcomes BID33 , BID21 ).
However, even among patients with recognized sepsis, there is no standard consensus on the best treatment.
There is a pressing need for personalized treatment strategies tailored to the unique physiology of individual patients.
Guidelines on sepsis treatment previously centered on early goal directed therapy (EGDT) and more recently have focused on sepsis care bundles, but none of these approaches are individualized.Before the landmark publication on the use of early goal directed therapy BID31 ), there was no standard management for severe sepsis and septic shock.
EGDT consists of early identification of high-risk patients, appropriate cultures, infection source control, antibiotics administration, and hemodynamic optimization.
The study compared a 6-hour protocol of EGDT promoting use of central venous catheterization to guide administration of fluids, vasopressors, inotropes, and packed red-blood cell transfusions, and was found to significantly lower mortality.
Following the initial trial, EGDT became the cornerstone of the sepsis resuscitation bundle for the Surviving Sepsis Campaign (SCC) and the Centers for Medicare and Medicaid Services (CMS) BID6 ).Despite
the promising results of EGDT, concerns arose. External
validity outside the single center study was unclear, it required significant resources for implementation, and the elements needed to achieve pre-specified hemodynamic targets held potential risks. Between
2014-2017, a trio of trials reported an all-time low sepsis mortality, and questioned the continued need for all elements of EGDT for patients with severe and septic shock BID28 , ARISE & Group (2014) , BID27 ). The trial
authors concluded EGDT did not improve patient survival compared to usual care but was associated with increased ICU admissions BID0 ). As a result
, they did not recommend it be included in the updated SCC guidelines BID30 ).Although the
SSC guidelines provide an overarching framework for sepsis treatment, there is renewed interest in targeting treatment and disassembling the bundle BID22 ). A recent metaanalysis
evaluated 12 randomized trials and 31 observational studies and found that time to first an-tibiotics explained 96-99% of the survival benefit BID17 ). Likewise, a study of
50,000 patients across the state of New York found mortality benefit for early antibiotic administration, but not intravenous fluids BID33 ). Beyond narrowing the
bundle, there is emerging evidence that a patient's baseline risk plays an important role in response to treatment, as survival benefit was significantly reduced for patients with more severe disease BID17 ).Taken together, the poor
performance of EGDT compared to standard-of-care and improved understanding of individual treatment effects calls for re-envisioning sepsis treatment recommendations. Though general consensus
in critical care is that the individual elements of the sepsis bundle are typically useful, it is unclear exactly when each element should be administered and in what quantity.In this paper, we aim to directly address this problem using deep reinforcement learning. We develop a novel framework
for applying deep reinforcement learning to clinical data, and use it to learn optimal treatments for sepsis. With the widespread adoption
of Electronic Health Records, hospitals are already automatically collecting the relevant data required to learn such models. However, real-world operational
healthcare data present many unique challenges and motivate the need for methodologies designed with their structure in mind. In particular, clinical time series
are typically irregularly sampled and exhibit large degrees of missing values that are often informatively missing, necessitating careful modeling. The high degree of heterogeneity presents
an additional difficulty, as patients with similar symptoms may respond very differently to treatments due to unmeasured sources of variation. Alignment of patient time series can also
be a potential issue, as patients admitted to the hospital may have very different unknown clinical states and can develop sepsis at any time throughout their stay (with many already septic upon admission).Part of the novelty in our approach hinges
on the use of a Multi-output Gaussian process (MGP) as a preprocessing step that is jointly learned with the reinforcement learning model. We use an MGP to interpolate and to impute
missing physiological time series values used by the downstream reinforcement learning algorithm, while importantly maintaining uncertainty about the clinical state. The MGP hyperparameters are learned end-to-end
during training of the reinforcement learning model by optimizing an expectation of the standard Q-learning loss. Additionally, the MGP allows for estimation of
uncertainty in the learned Q-values. For the model architecture we use a deep recurrent
Q-network, in order to account for the potential for non-Markovian dynamics and allow the model to have memory of past states and actions. In our experiments utilizing EHR data from septic
patients spanning 15 months from our university health system, we found that both the use of the MGP and the deep recurrent Q-network offered improved performance over simpler approaches.
In this paper we presented a new framework combining multi-output Gaussian processes and deep reinforcement learning for clinical problems, and found that our approach performed well in estimating optimal treatment strategies for septic patients.
The use of recurrent structure in the Q-network architecture yielded higher expected returns than a standard Q-network, accounting for the nonMarkovian nature of real-world medical data.
The multi-output Gaussian process also improved performance by offering a more principled method for interpolation and imputation, and use of the full MGP posterior improved upon the results from just using the posterior mean.In the future, we could include treatment recommendations from our learned policies into our dashboard application we have developed for early detection of sepsis.
The treatment recommendations might help providers better care for septic patients after sepsis has been properly identified, and start treatments faster.
There are many potential avenues for future work.
One promising direction is to investigate the use of more complex reward functions, rather than the sparse rewards used in this work.
More sophisticated rewards might take into account clinical targets for maintaining hemodynamic stability, and penalize an overzealous model that recommends too many unnecessary actions.
Our modeling framework is fairly generalizable, and can easily be applied to other medical applications where there is a need for data-driven decision support tools.
In future work we plan to use similar methods to learn optimal treatment strategies for treating patients with cardiogenic shock, and to learn effective insulin dosing regimes for patients on high-dose steroids.

assistant: text: We combine Multi-output Gaussian processes with deep recurrent Q-networks to learn optimal treatments for sepsis and show improved performance over standard deep reinforcement learning methods,