WO2018051343A1 - Dynamic treatment regime (dtr) implementations - Google Patents

Abstract

A system for analyzing sensor data. The system comprises at least one input interface adapted to receive from at least one sensor a plurality of measurements of at least one biological parameter of a target patient in real time during a period of at least an hour, at one processors, a code, stored in memory coupled to the processor(s). When the code is executed by the processer: recording the plurality of measurements as at least one sequence in the memory, calculating a model according to a first portion of the at least one sequence, calculating a similarity value by placing a second portion of the at least one sequence the model, and performing a check the similarity value against at least one threshold to detect a presence or an absence of a suspicious change.

Description

DYNAMIC TREATMENT REGIME (DTR) IMPLEMENTATIONS

BACKGROUND

The present invention, in some embodiments thereof, relates to change-point detection tools and, more specifically, but not exclusively, to systems and method for change -point detection for treating patients in real time.

In medical research, dynamic treatment regimes (DTRs) are increasingly used to choose effective treatments for individual patients who require long-term patient carel. A DTR (or similarly, policy) is a set of decision rules for how to treat a patient at multiple time-points. At each time -point, a treatment decision is made depending on the patient's medical history up to that point. Thus, DTRs may be considered as personalized medicine techniques tailored to the time-varying states of a patient. A dynamic treatment regime may be an infinite -horizon setting in which the number of decision points is very large. Specifically, long trajectories of patients' measurements recorded over time may be acquired and at each time -point, a decision whether to intervene or not is conditional on whether or not there has been a change in the patient's trajectory.

SUMMARY

According to some embodiments of the present invention, there is provided a system for analyzing sensor data. The system comprises at least one input interface adapted to receive from at least one sensor a plurality of measurements of at least one biological parameter of a target patient in real time during a period of at least an hour, a processor, a code, stored in memory coupled to the processor, wherein when the code is executed by the processer: recording the plurality of measurements as at least one sequence in the memory, calculating a model according to a first portion of the at least one sequence, calculating a similarity value by placing a second portion of the at least one sequence the model, and performing a check the similarity value against at least one threshold to detect a presence or an absence of a suspicious change, and an output interface adapted to output an indication of the presence of the suspicious change based on an outcome of the check.

Optionally, the period is of at least one week. Optionally, the model is generated using a Shiryaev-Roberts formulation.

Optionally, the model is generated by calculating a pre-change density value and a post-change density value when one of these densities is estimated and another is deduced from the first portion.

Optionally, the model is generated according a mean extracted from a plurality of sequences of measurements of the at least one biological parameter of a plurality of other patients which are different from the target patient.

Optionally, the model is generated using a cumulative distribution function.

Optionally, the model is generated by calculating a joint density of at least some of the measurements of the first portion when no change takes place and a second joint density of at least some of the measurements of the second portion

More optionally, the plurality of measurements are sequentially taken in a rate of at least once a minute.

Optionally, the at least one sensor comprises a Neonatal Incubator Sensor; wherein the indication is of a Late-Onset Neonatal Sepsis.

More optionally, the Neonatal Incubator Sensor comprises a member of a group consisting of a heart rate sensor, a respiratory rate sensor, a saturation sensor, a blood pressure sensor, and a temperature.

Optionally, the at least one sensor comprises a glucometer wherein the indication is a glucose level change.

Optionally, the at least one threshold is set according to a combination of an Average Run Length to False Alarm (ARL2FA) an expected time from an appearance of the change in the at least one sequence and a detection thereof.

Optionally, the similarity value is at least one similarity ratio (SR) statistic value.

Optionally, the at least one input interface is adapted to receive the plurality of measurements from each of a plurality of sensors in real time during a period of at least an hour; wherein when the code is executed by the processer the plurality of measurements are recorded as a plurality of sequences in the memory; wherein the calculating a mode, the calculating a similarity value, and the performing a check are performed for each one of the plurality of sequences. More optionally, the output interface is adapted to output the indication based on the outcome of the respective check.

More optionally, the output interface is adapted to output the indication based on a combination of a number of checks each of a different sequence from the plurality of sequences.

According to some embodiments of the present invention, there is provided a method for analyzing sensor data. The method comprises receiving from at least one sensor a plurality of measurements of at least one biological parameter of a target patient in real time during a period of at least an hour, recording the plurality of measurements as at least one sequence in the memory, calculating a model according to a first portion of the at least one sequence, calculating a similarity value by placing a second portion of the at least one sequence the model, performing a check the similarity value against at least one threshold to detect a presence or an absence of a suspicious change, and outputting an indication of the presence of the suspicious change based on an outcome of the check.

Unless otherwise defined, all technical and/or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of embodiments of the invention, exemplary methods and/or materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Some embodiments of the invention are herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of embodiments of the invention. In this regard, the description taken with the drawings makes apparent to those skilled in the art how embodiments of the invention may be practiced. In the drawings:

FIG. 1 a method for real time detection of suspicious events based on a CPD procedure such as a Shiryaev-Roberts CPD procedure that optionally adaptively learn from patient's past observations, according to some embodiments of the present invention;

FIG. 2 is an exemplary system that executes a code for CPD procedure such as a Shiryaev-Roberts CPD procedure, according to some embodiments of the present invention;

FIG. 3 is a graph showing a trajectory of exemplary observations (HR and RR) of one simulated patient for whom the change occurs after one day, according to some embodiments of the present invention;

FIGs. 4A and 4B present detection time and false alarms in a premature infant systemic infection simulation made according to some embodiments of the present invention;

FIG. 5 is a graph showing week-length trajectory of heart rate (HR) and respiratory rate (RR) in a simulation made according to some embodiments of the present invention; and

FIG. 6 is a graph showing analysis of the glucose data for ARL2FA of 200, 400, and 800 according to some embodiments of the present invention. DETAILED DESCRIPTION

The present invention, in some embodiments thereof, relates to change-point detection tools and, more specifically, but not exclusively, to systems and method for change -point detection for treating patients in real time.

The methods and systems described herein allow implementing change-point detection (CPD) based on real time analysis of measurements of one or more sensors. The detection allows generating treatment notifications for implementing dynamic treatment regimes. Exemplary detections may be of sepsis in preterm infants in an intensive care unit and/or detection of a change in glucose levels of a diabetic patient.

According to some embodiments of the present invention there are provided methods and systems for change -point detection (CPD) and treatment for implementing a dynamic treatment regime with a very large number of stages (e.g., hundreds or thousands), see R. D. Vincent, J. Pineau, N. Ybarra, and I. E. Naqa. Practical reinforcement learning in dynamic treatment regimes. In M. R. Kosorok and E. E. M. Moodie, editors, Adaptive Treatment Strategies in Practice, pages 263-296. Society for Industrial and Applied Mathematics, 2015, which is incorporated herein by reference.

In one example, the DTR is for a Premature Infant Late-Onset Neonatal Sepsis

(LONS). LONS is one of the major causes of mortality of premature infants is systemic infection, which leads to multi-organ systemic inflammatory response syndrome and sepsis, which is a life-threatening condition that arises due to infection. Preterm infants, born before gestational age of 37 weeks, are at greater risk for morbidity and mortality in the neonatal period. In preterm infants, the spectrum of symptoms of sepsis includes increase in heart rate, respiratory distress that ranges from mild tachypnea to respiratory failure, increase in ventilatory support in the mechanically ventilated patient, and temperature instability (see M. P. Griffin, D. E. Lake, T. M. O'Shea, and J. R. Moorman. Heart rate characteristics and clinical signs in neonatal sepsis. Pediatric Research, 61(2):222-227, 2007 and J. Bekhof, J. B. Reitsma, J. H. Kok, and I. H. Van Straaten. Clinical signs to identify late-onset sepsis in preterm infants. European Journal of Pediatrics, 172(4):501-508, 2013 which are incorporated herein by reference). Because the signs and symptoms of sepsis can be subtle and nonspecific, any deviation from an infant's usual pattern of activity or feeding should be regarded as a possible indication of systemic bacterial infection, see A. Maayan-Metzger, N. Linder, D. Marom, T. Vishne, S. Ashkenazi, and L. Sirota. Clinical and laboratory impact of coagulase-negative staphylococci bacteremia in preterm infants. Acta Paediatrica, 89(6):690-693, 200 which is incorporated herein by reference. In practice, the isolation of a pathogenic bacterium from a blood culture is the only method to truly confirm the diagnosis of neonatal sepsis. However, there is a significant time lag before blood culture results are available in V. Nizet and J. O. Klein. Bacterial sepsis and meningitis. Infectious Diseases of the Fetus and Newborn, 2011 and I. Kurlat, B. J. Stoll, and J. E. McGowan. Time to positivity for detection of bacteremia in neonates. Journal of Clinical Microbiology, 27(5): 1068-1071, 1989, which are incorporated herein by reference. As a result, clinical assessment and laboratory tests are used to identify neonates at significant risk for sepsis so that antibiotic treatment may be initiated while awaiting blood culture results. The clinical assessment for sepsis is done based on various physiological measures (e.g., heart rate, respiratory rate, saturation, blood pressure, temperature) taken just before the assessment time. Historical data of the infant is not currently used systematically, and is strongly based on the physicians' recall, despite the fact that infants in neonatal intensive-care unit are constantly monitored. The systems and methods described herein may provide a DTR that uses up- to-date data of an infant, aiming to detect sepsis as early as possible.

In another example, the DTR is fasting glucose level monitoring (FGLM). Blood glucose monitoring is the main tool for diabetic patients to check their diabetes control and their response to their diabetic care plan. Keeping a log of the glucose results is considered vital. Therefore, to help keep track of diabetic patients' levels, there are free online tools that help diabetic patients usage track and analyze their blood glucose readings (such as Diabetes 24/7, see for example www(dot)diabetes(dot)org/. The systems and methods described herein may use records of blood-glucose measurements of a diabetic patient taken by the patient with the use of a glucometer for the detection of a glucose level change. Such measurements may have been taken for example in mornings, at least eight hours after ingesting food, on an average of about twice a week, for instance over a period of several years. Such a DTR may be used for fast detection of a change from the target blood-glucose distribution. When such a change is detected, an alert for intervention such as a clinical visit may be presented to the user and/or sent to the physician.

According to some embodiments of the present invention there are provided a system for analyzing sensor data that includes input interface(s) adapted to receive from sensor(s) measurements of biological parameter(s) of a target patient in real time (e.g. vital signs) during a period of one hour or more, for example every minute or an hour during any hospitalization period. The system includes processor(s) and a code, stored in memory coupled to the processor. When the code is executed by the processer(s), measurements are recorded as sequence(s) in the memory, for example trajectories. This allows calculating model(s) according to a first portion of each one of the sequence(s), for example historical data and a similarity value by placing a second portion of the sequence(s) the model, for instance the last n observations or a portion thereof. This allows performing a check the similarity value against thresholds to detect a presence or an absence of a suspicious change. The thresholds may be adapted by an operator of the system to achieve a desired level of false positive detection and/or detection time. The system further includes an output interface adapted to output indication(s) of the presence of the suspicious change based on an outcome of the check as described below.

The systems and methods described herein are used for identifying changes at unknown times and estimating, for example, the location of changes in a stochastic process namely solving change-point detection (CPD) problem.

According to some embodiments of the present invention, a Shiryaev-Roberts CPD procedure is used for generating alerts for treating LONS. In such embodiments, a code executing the procedure may analyze one or more measures received in real time from Neonatal Incubator Sensors such as heart rate Sensors, respiratory rate Sensors, saturation Sensors, blood pressure Sensors, and/or temperature Sensors. The code may then output instructions for generating an alert for a physician to check for sepsis and/or for starting a sepsis treatment. The Shiryaev-Roberts CPD procedure may adaptively learn from the patient's past observations as described below.

According to some embodiments of the present invention, a Shiryaev-Roberts CPD procedure is used for generating alerts for treating FGLM. In such embodiments, a code executing the procedure may analyze one or more measures received from Sensors such as a glucometer. The code may then output instructions for generating an alert for a physician to check for diabetic deterioration and/or for starting a diabetic deterioration treatment. The Shiryaev-Roberts CPD procedure may adaptively learn from the patient's past observations as described below.

Unlike procedures executed in the methods and systems described herein, much of the literature on DTRs considers a small finite set of stages. At each stage, based on past history for example historical measurements of the patient, a decision on treatment is taken. Techniques such as g-estimation of optimal regime structural nested mean models (SNMMs) (e.g. see J. M. Robins. Optimal structural nested models for optimal sequential decisions. In D. Y. Lin and P. J. Heagerty, editors, Proceedings of the Second Seattle Symposium in Biostatistics, Lecture Notes in Statistics, pages 189-32 and Springer New York, 2004. 9. J. Robins, L. Orellana, and A. Rotnitzky. Estimation and extrapolation of optimal treatment and testing strategies. Statistics in Medicine, 27(23):4678-4721, 2008 which are incorporated herein by reference) and Q-learning (see R. S. Sutton and A. G. Barto. Reinforcement Learning: An Introduction. MIT Press, 1998. 11. S. A. Murphy. A generalization error for Q-learning. Journal of Machine Learning Research, 6: 1073-1097, 2005, I. Nahum-Shani, M. Qian, D. Almirall, W. E. Pelham, B. Gnagy, G. A. Fabiano, J. G. Waxmonsky, J. Yu, and S. A. Murphy. Q-learning: a data analysis method for constructing adaptive interventions. Psychological Methods, 17(4):478-494, 2012 and M. S. Kramer E. E. M. Moodie, B. Chakraborty. Q-learning for estimating optimal dynamic treatment rules from observational data. The Canadian Journal of Statistics, 40(4): 629-645, 2012 which are incorporated herein by reference) use backward recursion to find a DTR. These algorithms are useful in both the design of sequential multiple assignment randomized trials (S. A. Murphy. An experimental design for the development of adaptive treatment strategies. Statistics in Medicine, 24(10): 1455-1481, 2005 which is incorporated herein by reference) and analysis of observational data (J. Robins, L. Orellana, and A. Rotnitzky. Estimation and extrapolation of optimal treatment and testing strategies. Statistics in Medicine, 27(23):4678-4721, 2008; Su. Rosthoj, C. Fullwood, R. Henderson, and S. Stewart. Estimation of optimal dynamic anticoagulation regimes from observational data: a regret-based approach. Statistics in Medicine, 25(24):4197- 4215, 2006 which are incorporated herein by reference). However, these algorithms require detailed modeling and are computationally very expensive, which limits their applicability when the number of decision points is large (J. Robins, L. Orellana, and A. Rotnitzky. Estimation and extrapolation of optimal treatment and testing strategies. Statistics in Medicine, 27(23):4678-4721, 2008; A. Ertefaie, Constructing dynamic treatment regimes in infinite -horizon settings. arXiv: 1406.0764 [stat], 2014, which are incorporated herein by reference). Dynamic marginal structural models (MSM) provide a different approach for finding dynamic treatment regimes (L. Orellana, A. Rotnitzky, and J. M. Robins. Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, Part I: Main content. The International Journal of Biostatistics, 6(2): Article 8, 2010, which is incorporated herein by reference). These techniques estimate the best time to initiate a treatment based on a risk score. In this setting, the available decision rules consist of risk- score values. Treatment is initiated after a specific risk-score value is crossed. These policies are indeed DTRs, as the actual time of initiating a treatment depends on the dynamic patient state at each decision point. MSMs use inverse probability weighting in their estimation. This can be problematic when the number of stages is large, as the weights in the denominator can become very small. Discussion on MSMs and comparison to SNMMs can be found in J.

Robins, L. Orellana, and A. Rotnitzky. Estimation and extrapolation of optimal treatment and testing strategies. Statistics in Medicine,

2008 which is incorporated herein by reference.

According to some embodiments, a model that describes dynamics is used, optionally, with control algorithms such as dynamic programming or constrained optimization algorithms (e.g. see D. E. Rivera, M. D. Pew, and L. M. Collins. Using engineering control principles to inform the design of adaptive interventions: A conceptual introduction, Drug and Alcohol Dependence, 88:S31-S40, 2007; H. T.

Banks and T. Jang. Feedback control of HIV antiviral therapy with long measurement time. International Journal of Pure and Applied Mathematics, 66(4):461-485, 2011; S.

Deshpande, N. N. Nandola, D. E. Rivera, and J. W. Younger; Optimized treatment of Fibromyalgia using system identification and hybrid model predictive control. Control

Engineering Practice, 33:161-173, 2014 which are incorporated herein by reference).

Optionally, the CPD procedure described herein does not attempt to estimate the treatment effect. Hence, no model for the treatment effect is assumed. This is in contrast to MSMs, which model the intervention effect in order to find an optimal treatment. Optionally and unlike MSM procedure, no general risk-score level that applies to all patients is used. Instead, a risk-score level may be dynamically adapted per patient based on past observations.

Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not necessarily limited in its application to the details of construction and the arrangement of the components and/or methods set forth in the following description and/or illustrated in the drawings and/or the Examples. The invention is capable of other embodiments or of being practiced or carried out in various ways.

The present invention may be a system, a method, and/or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention. The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing.

Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network.

The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions.

The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

Reference is now made to FIG. 1 which is a method for real time detection of suspicious events based on a CPD procedure such as a Shiryaev -Roberts CPD procedure that optionally adaptively learn from patient's past observations, according to some embodiments of the present invention. Reference is also made to FIG. 2 which is an exemplary system 200 that executes a code for CPD procedure such as a Shiryaev - Roberts CPD procedure according to some embodiments of the present invention. The system 200 comprises one or more processor(s) 201 and a memory 202 adapted to store a detection code 203. The system 200 further comprises interfaces 204 for receiving data, optionally real time data, from one or more sources, for instance sensors 207 such as a plurality of Neonatal Incubator Sensors and/or a glucometer as described below. The outputs of the sensors may be received directly and/or via a network 205, either via a wire or wirelessly. The system 200 further comprises an output 210 for outputting instructions for displaying or otherwise presenting alerts or treatment instructions, for example on a display 212 a physician client 211 which may be for example a smartphone, a laptop, a tablet and/or a desktop. The system 200 may be implemented using one or more servers and/or by a processor based device connected one or more incubators. Alternatively, the system 200 may be a mobile device such as a smartphone, executing the code for processing measurements of sensors of the mobile device and/or sensors connected to the mobile device in real time.

The methods and systems described herein may be used for applying CPD procedures for DTRs under infinite horizon settings. For example, the CPD may be implemented in real time on preterm infant data to detect sepsis. The detection is performed automatically at least as well as the physician as exemplified below. It should be noted that the methods and systems perform continuous monitoring, an action that cannot be performed by physicians who do not have the time for systematic analysis of the infant trajectories on a regular basis. By using the systems and methods for executing the CPD, clinically-observed physiological changes can be observed before systemic inflammation is spread.

By using the systems and methods described herein, an additional safety net may be deployed in neonatal intensive care units (NICUs) and/or other intensive care units for generating notifications when suspicious changes are detected and for drawing the attention of neonatologists to an infant at an earlier stage, when treatment might prevent complications. Since the proposed methods are feasible computationally, and the measurements are already recorded, integration of these methods in practice are simple to carry out. The methods and systems described herein may also be used for mobile- health (mHealth), where patients are monitored remotely using smartphones or other mobile devices (see C. L. Ventola. Mobile devices and apps for health care professionals: Uses and benefits. Pharmacy and Therapeutics, 39(5):356-364, 2014 and references therein). Clearly, our proposed methodology can be easily integrated into mobile applications, thereby improving the clinical decision process.

In this application it is assumed that observations are normally distributed before and after the change point and the data are independent. Deviating from the normality assumption raises both theoretical and computational challenges though some CPD methods can be applied to non-normal data (see L. Gordon and M. Pollak. A robust surveillance scheme for stochastically ordered alternatives. The Annals of Statistics, 23(4): 1350-1375, 1995 for nonparametric version of SR). The assumption that the observations are independent can be relaxed, for example, by assuming that the data follow an auto-regression model, see M. Shauly-Aharonov, M. Pollak, and Y. Plakht. A method for detecting life-threatening signals in serum potassium level after myocardial infarction. arXiv preprint arXiv: 1602.06717, 2016. The procedure used herein uses historical data. For example, in some applications, measurements over a day old or more than a week old may be used for predicting a current status of a monitored patient and including such measurements burdens both the ability to detect a change and the computation time. As shown at 101, measurements, also referred to herein as observations, are received via the interfaces. The observations are sampled by a sensor such as a neonatal incubator sensor every, second, minute, hour, day, week and/or any intermediate period. The observations may be received as a sub sequence of a continuous sequence of observations.

For example, a setting in which random observations is collected

sequentially. These observations may represent, for example, heart rate measures of an infant that are sequentially recorded every minute. The sequence is the to have a change -point at time, denoted herein as v, when observations X are generated

from a distribution function with a density denoted herein as f_Q, and observations

are generated from a different distribution with a density denoted herein as

As further described below, a number of sequences may be received simultaneously from different sensors which are monitoring simultaneously a common target, such as a baby, either synchronically or asynchronically.

Now, as shown at 102, the received sequence(s) is sequentially observed and analyzed using a CPD procedure, such as a Shiryaev-Roberts CPD procedure.

For example, as shown at 102A a similarity value, such as a similarity ratio (SR) statistic, is calculated by placing the sequence of real time observations of the patient in a model generated based on historical observations of the patient. The model is calculated based on historical observations of the monitored patient (e.g. 10,000, 100,000, 1,000,000 or any intermediate or larger number of observations for each sequence of observations). The observations are recorded over a period of few hours, few days, few years, and/or few years.

Then, as shown by 102B, the calculated similarity value is check against one or more thresholds to detect a suspicious change. For example, the check is for whether the similarity value is higher than the one or more thresholds as described below.

As shown at 102C, this process is repeated for each observation (taking into account previous n-1 observations) to detect an absence or a presence of a suspicious change which may be indicative of a pathology such as a sepsis or a diabetic event.

In use, after each observation

a presence or an absence of a change in a distribution within the sequence

is determined. Optionally, the Shiryaev- Roberts CPD procedure is applied, (see A. N. Shiryaev, On optimum methods in quickest detection problems, Theory of Probability & Its Applications, 8(l):22-46, 1963 and S. W. Roberts. A comparison of some control chart procedures. Technometrics, 8(3):411-430, 1966, which are incorporated herein by reference) and its generalizations (see in M. Pollak and D. Siegmund, Sequential detection of a change in a normal mean when the initial value is unknown, The Annals of Statistics, 19:394-416, 1991 and L. Gordon and M. Pollak, A robust surveillance scheme for stochastically ordered alternatives. The Annals of Statistics, 23(4): 1350-1375, 1995 which are incorporated herein by reference). This allows detecting a true change relatively quickly as demonstrated below while rarely raising false alarms. There are various procedures for CPD, see Shewhart charts W. A. Shewhart. Economic control of quality of manufactured product. ASQ Quality Press, 1931. which is incorporated herein by reference), E. S. Page. Continuous inspection schemes. Biometrika, 41(1/2): 100-115, 1954 and C. S. van Dobben De Bruyn. Cumulative sum tests: theory and practice. Griffin, 1968 which are incorporated herein by reference. The Shiryaev-Roberts (SR) procedure and its generalizations have asymptotic properties in terms of speed of detection (see M. Pollak. Optimal detection of a change in distribution. The Annals of Statistics, 13:206-227, 1985 and M. Pollak and A. G. Tartakovsky. Optimality properties of the shiryaev-roberts procedure. Statistica Sinica, 19: 1729-1739, 2009 which are incorporated herein by reference) and have success in simulations (see S. W. Roberts. A comparison of some control chart procedures. Technometrics, 8(3):411-430, 1966 which is incorporated herein by reference) and their ability to handle dependent data relatively easily.

Reference is now made to a mathematical description of the appliance of the SR CPD procedure (e.g. 102A-102C). At time n, given the sequence X

a likelihood ratio that a suspicious change occurred at time v, for some

that no change in the distribution occurred, is given by:

where denotes a joint density of the observations when no change ever takes

place and is a joint density of observations when v=k and the first observations are distributed as they would be under a regime dictated by f_∞. At each time-point n, a value, such as a similarity ratio (SR) statistic, is calculated as follows:

This allows detecting a suspicious change when R_n is sufficiently large; for example, this detection may occur when the SR statistic value is larger than a threshold, optionally pre-specified, denoted herein as A:

Equation 1:

for example, when the observations are independent, with (marginal) densities pre-change (denoted f and post-change (denoted f then:

Equation 2:

The detection timing and false alarm prevalence depends on the threshold A. Optionally, two measures which are used to measure a success of a CPD procedure are taken into account when setting A. One measure of interest is the expected time to false alarm when no change in the distribution takes place. Formally, this is E[N], given v = ∞; this is usually referred to as the Average Run Length to False Alarm (ARL2FA). The other measure of interest is the expected delay, the expected time from a change in the distribution to its detection. Optionally, the threshold is automatically calculated based on measures when the measures are set using a user interface by a user, for instance a user using a user client connected to the system 200. Formally, when the change occurs at time v, a quantity of interest is E[N - v\N > v] . For a given density fo and a given threshold A, assuming that no distribution change takes place, ARL2FA > A and ARL2FA w A x constant, where the constant can be computed, see M. Pollak. Average run lengths of an optimal method of detecting a change in distribution. The Annals of Statistics, 15(2):749-779, 1987 which is incorporated herein by reference.

Optionally, threshold A is an outcome of a function of a desirable ARL2FA that may be set by a user, for example an operator of the system 200. Comparison between different CPD procedures may be done by comparing the expected delay, assuming all procedures have the same ARL2FA.

In some embodiments of the present invention, R_n is calculated based on a pre- change density value fo and a post-change density value /; when one of these densities or both are unknown. In such embodiments, a normal distribution in a sequence of observations is modeled (e.g. for detecting LONS or FGLM) and use for detecting a change in a mean of the normal distribution. The mean changes by δ standard deviations when

before the change and X

after the change where all the observations are independent.

Optionally, Model 1 is used. In Model 1 fo is known but /; is unknown, for example when a long trajectory is calculated from observations (e.g. last n observations) without a distribution change. In this case, the parameters μο and σ of fo may be estimated and fo is treated as known. As δ parameter of /; is unknown, a reasonable value for δ is assumed_, for example calculated as described in M. Pollak and D. Siegmund, Sequential detection of a change in a normal mean when the initial value is unknown, The Annals of Statistics, 19:394-416, 1991 which is incorporated herein by reference.

Alternatively, a more flexible solution is to assume a prior on the unknown parameter δ. For example, when is greater than μ a one-sided prior is

assumed for δ The exact form of prior plays a secondary role in an expected delay a prior that facilitates the calculation may be selected, see M. Pollak. Optimality and almost optimality of mixture stopping rules. The Annals of Statistics, 6(4):910-916, 1978. A convenient form is Equation 3:

where TruncN(r,

denotes a positive truncated-at-zero normal distribution with mean τ and variance with density

where

denote a standard normal density and a cumulative distribution functions, respectively. For Model 1:

E uation 4:

where

^ire the standardized variables.

When a direction of the change is unknown, a two-sided prior is assumed, for instance:

Equation 5:

The R_n statistic for the two-sided prior is the average of Equation 4 applied to

Alternatively, a Model 2 is applied. In this model both μθ and μΐ are unknown but σ is known. In these embodiments sequence of standardized recursive residuals (e.g. see R. Brown, J. Durbin, and J. Evans. Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society: Series B (Methodological), 37(2): 149-192, 1975) is:

As ¾ are independent normal, then Y_k are normal, and are independent by construction. The distribution of Y_k is not depended on μο or μι but only on the difference. Thus, one can look for a distribution change using sequence Y₂, Y3, . . .. Priors for δ may be used as described in Equation 3 and Equation 5. Here, the obtained statistic for the one-sided prior is when

For a two-sided prior, the statistic may be computed in a similar way to that of Equation 5.

Alternatively, Model 3 is used. In this model μο, <τ, and δ are unknown and

and define

In this model, the distribution of Z

is not depended on μο and σ and a distribution change may be calculated using

2, ₃ .. Derivation of the statistic for Model 3 for a one-sided prior of the form

optionally calculated as described in A endix A. The statistic for the two-sided prior

^{'1' "}

is the average of the aforementioned statistic for Model 3 applied to

and to

. Derivation of the statistics for Models 1 and 2 follow the same line of proof and thus are omitted from the description of model 3.

Now, as shown at 103, when a presence of a suspicious change is determined or detected, a notification or alert is outputted, for example for presentation to a user or a physician.

It should be noted that the above models assumed that the observed trajectory Xi, X2, is one-dimensional. In some embodiments, for example when a number of observations are received from a number of sensors, observations at each time-point are multi-dimensional. For example, when a plurality of outputs of a plurality of Neonatal Incubator Sensors are received, for instance heart rate and respiratory rate, multidimensional observations are analyzed to determine a suspicious change. In practice, the densities are usually unknown and modeling and estimation in this setting has high computational complexity (see T. L. Lai and H. Xing. Sequential change-point detection when the pre- and post-change parameters are unknown. Sequential Analysis, 29(2): 162-175, 2010). Various methods may be considered for combining the up-to- date p series of observations (e.g. see P. Wessman. Some principles for surveillance adopted for multivariate processes with a common change point. Communications in Statistics - Theory and Methods, 27(5): 1143-1161, 1998). Optionally, a notification or alert is generated when a change is detected in one of the sequences of observations. Alternatively, a notification or alert is generated at the first time a change is declared by one or more of the sequences. Alternatively, a notification or alert is generated based on a combination, such as a linear combination, of the sequences that often can be provided by an investigator, as described below.

As indicated above, when analyzing the sequences of the observations, one of models 1-3 is used. The performance of the three models by simulations is described below. When the observations are outputs of Neonatal Incubator Sensors, trajectories of multiple infants are recorded. These trajectories allows estimating a mean process over time of heart rate and respiratory rate as a function the covariates birth week and birth weight and optionally also the respective variances. In practice, the mean processes vary considerably between infants and therefore the estimators have large variance. When the variance processes are more stable Model 2 for which the pre-change mean is unknown may be used (the variance is known). In addition, since for a sepsis one expects a rise in the mean level of the measurements, a one-sided prior (e.g. as described with reference to Equation 3) is used for the post-change distribution.

Optionally, the observations are Glucose Level values of a single patient. In such an embodiment, both mean and variance are considered to be unknown hence Model 3 may be used. Since the direction of the change is unknown, a two-sided prior (e.g. as described with reference to Equation 5) is used for the post-change distribution. EXAMPLES

Reference is now made to the following examples, which together with the above descriptions; illustrate the invention in a non limiting fashion. Two simulation settings, corresponding to the two examples, premature infants and glucose level monitoring, which are analyzed below.

First, Premature Infant Late-Onset Neonatal Sepsis is simulated. For each simulated premature infant trajectory, a birth week is drawn uniformly between weeks 25 to 34. Gender is drawn with equal probabilities. Weight at birth was drawn according to I. E. Olsen, S. A. Groveman, M. L. Lawson, R. H. Clark, and B. S. Zemel. New intrauterine growth curves based on United States data. Pediatrics, 125(2):e214-e224, 2010 as a function of the birth week and gender. Heart rate (HR) and respiratory rate (RR) were drawn from the normal distribution every 15 minutes for a period of two weeks. The mean functions of HR and RR change over time and are based on interpolation of the means reported in P. G. Katona and J. R. Egbert. Heart rate and respiratory rate differences between preterm and full-term infants during quiet sleep: possible implications for sudden infant death syndrome. Pediatrics, 62(l):91-95, 1978, and a weighted linear combination of the birth week and the birth weight. The standard deviation and correlation were calculated from the data and were taken as time independent. When infection occurs, there is typically an increase of both HR and RR, see M. P. Griffin, D. E. Lake, T. M. O'Shea, and J. R. Moorman, Heart rate characteristics and clinical signs in neonatal sepsis, Pediatric Research, 61(2): 222-227, 2007 which is incorporated herein by reference. An infection is simulated by a gradual linear increment of the mean that starts at a given time -point and stabilizes after 8 hours. The level after 8 hours is the previous rate plus 25 beats -per-minute for HR, and plus 8 breaths-per-minute for RR. A change is simulated in the distribution after one, three, or seven days. FIG. 3 shows a trajectory of one simulated patient for whom the change occurs after one day. The three models discussed above are considered, namely: mean and standard deviation are known, mean is unknown but standard deviation is known, and both mean and standard deviation are unknown. These models are executed with four different levels of sensitivity for changes, corresponding to approximately 100, 200, 400, and 800 average run lengths to false alarm (ARL2FA). Four different methods are considered to detect the change: HR only, RR only, the minimum between the two (denoted by Min), and a linear combination of 75% HR and 25% RR (denoted by Combined). The weights for the combined method were proposed by a neonatologist. Finally, for the change in the mean, we use the one-sided prior Equation 3 with mean _ = 1.25 and standard error = 0.5. For each combination of change-point location (1, 3, and 7 days), model (known, unknown mean, and unknown mean and standard deviation), ARL2FA (100, 200, 400, and 800), and method (HR, RR, Min, and Combined) are repeated the simulation 100 times. Two outcomes are recorded detection time and the actual number of false alarms (per week). The results appear in the following tables:

In the above table premature infant systemic infection is analyzed: Average detection time (in hours) from change-point. Change point occurs after 1, 3, and 7 days; assuming Model 1 (both mean and standard deviation are known, denoted

M-1), Model 2 (mean is unknown, denoted M-2), and Model 3 (both mean and standard deviation are unknown, denoted M-3).

In the above table premature infant systemic infection is analyzed: Average number of false alarms per week. Change point occurs after 1, 3, and 7 days; assuming Model 1 (both mean and standard deviation are known, denoted M-l), Model 2 (mean is unknown, denoted M-2), and Model 3 (both mean and standard deviation are unknown, denoted M-3).

FIGs. 4A and 4B present the results for ARL2FA of 200 (in each chart arranged from left to right are Min, HR, RR and combined). In FIG. 4A detection time (in hours) from change -point for ARL2FA of 200 are presented. The Change point occurs after 1, 3, and 7 days; assuming Model 1 (both mean and standard deviation are known, denoted Known), Model 2 (Mean is unknown), and Model 3 (both mean and standard deviation are unknown, denoted Unknown. In FIG. 4B False alarms per week for ARL2FA of 200 are presented. Change point occurs after 1, 3, and 7 days; assuming Model 1 (both mean and standard deviation are known, denoted Known), Model 2 (Mean is unknown), and Model 3 (both mean and standard deviation are unknown, denoted Unknown).

Based on the simulation results, the following may be deduced:

(i) The methods HR, Min, and Combined are comparable in detection time. The Combined method is typically better when either the distribution is known or the standard deviation is known, while the Min method is better when both mean

and standard deviation are unknown. (ii) The Combined method has fewer actual false alarms in almost FIG. 3.

Simulated trajectory of two days of heart rate (HR) and respiratory rate (RR).

The mean begins to change gradually after one day (at 00:00+ Id). The change stops after 8 hours (at 08:00+ Id) and the mean remains at the obtained level thereafter.

All categories compared to HR and Min.

(iii) The method RR is slower to detect the changes, but has the fewest actual false alarms.

(iv) Comparing the results for the change after 1, 3, and 7 days, there is not much of a difference in the detection time between the three models, despite the fact that additional information is gathered.

(v) There is no significant difference between the three models regarding the detection time, however, the unknown distribution has a significantly higher rate of actual false alarms compared to the other two algorithms.

In conclusion, for the data analysis the unknown mean algorithm is used which performs as well as the known distribution and is more appropriate to the simulated application.

Second, Glucose Level Monitoring is simulated. The simulated trajectories are of glucose levels. For simplicity, each time-point represents a week. The glucose levels before the change-point are independent, normally distributed with mean 135 and standard deviation 20. After the change-point, the mean decreases gradually by 0.25 in mg/dL (milligrams per deciliter) units per time -point for 100 weeks and stabilizes at glucose level of 110 mg/dL thereafter. The standard deviation does not change. The above models are considered namely, mean and standard deviation are known, mean is unknown, and both mean and standard deviation are unknown. The corresponding algorithms are executed with four different levels of sensitivity for changes corresponding to approximately 100, 200, 400, and 800 ARL2FA. Finally, for the change in the mean, we used the two-sided prior Equation 5 with mean τ = 1.25 and standard error = 0.5. The change-points that occur at week 50, 100, and 200 are considered. For each combination of change-point, algorithm, and sensitivity level, we repeated the simulation 100 times. The following outcomes have been recorded: detection time and actual false alarm (per 100 weeks).

The results appear in the following table:

where detection time and average number of false alarms per 100 weeks when change occurs after 50, 100, and 200 weeks and where Model 1 (both mean and standard deviation are known, denoted M-1), Model 2 (mean is unknown, denoted M- 2), and Model 3 (both mean and standard deviation are unknown, denoted M-3) are assumed. The results are similar to premature-infant-systemic-infection results:

(i) Higher ARL2FAs lead to slower detection time but fewer actual false alarms.

(ii) There is no significant difference between the three models in both detection time and number of false alarms.

(iii) Comparing the results for change-point at 50, 100, and 200 weeks, there is not much of a difference in the detection time between the three models, despite the fact that additional information is gathered.

Reference is now made to an exemplary implementation of the detection process wherein premature infant late-onset neonatal sepsis (LONS) is monitored for detection. The data of 14 premature infants that were admitted to the neonatal intensive care unit (NICU) at Tel-Aviv Medical Center (Ichilov) between 2013 and 2015 is analyzed. Nine of the infants suffered from systemic infection and five were taken as controls. The data to which the method was applied is a portion of a large neonatal dataset that is currently being collected at Tel- Aviv Medical Center.

For each infant, we looked at a single week taken from the first or second week of their hospitalization in the NICU. The focus is on the following sequences of observations: heart rate (HR) and respiratory rate (RR) which are registered every 1 minute. In order to decrease noise and auto-correlation, averages of 15-minute intervals are used. Normality and auto-correlation were assessed on day-length trajectories of infants that did not suffer from LONS. Normality is checked using the Shapiro-Wilk test and seems to hold for RR and to partially hold for HR (46% of the trajectories). Durbin-Watson test for auto-correlation was significant for most trajectories. For simplicity, in this analysis the auto-correlation by decreasing

the sensitivity level (see M. Shauly-Aharonov, M. Pollak, and Y. Plakht. A method for detecting life-threatening signals in serum potassium level after myocardial infarction. arXiv preprint arXiv: 1602.06717, 2016 for a time-series approach) is accounted for. The diagnosis of a neonatologist is compared to that performed by the generalized SR CPD algorithm.

All 14 blinded trajectories have been presented to a neonatologist who marked points on each trajectory in which a change-point was suspected, see dashed line in FIG. 5 where a week-length trajectory of heart rate (HR) and respiratory rate (RR) observations are presented. The automated SR-type CPD is also performed, see dot- dashed line in FIG. 5 that represents the time of an alarm made by the SR algorithm. The black solid line represents the time that blood culture was taken. The dashed line represents the time that sepsis was suspected by the neonatologist.

Based on the simulation results, Model 2 is used with unknown mean but known standard deviation that was calculated from the data. The linear combination approach is used with weights of 0.75 for HR and 0.25 for RR. For the change, it is assumed that truncated normal prior as described with reference to Equation 3 with mean τ = 2 and a standard deviation = 0.5. The chosen sensitivity level was approximately ARL2FA = 4000 (the results were not very sensitive to this value). Then both neonatologist and algorithm results are compared to the hospital records of when blood cultures were taken, due to suspicion of systemic infection (black solid line in FIG. 5). The results are given in the following table:

where the detection time of each infant who suffered from systemic infection belongs to one of the following categories: the detection occurred before blood culture was taken (Before Test), after the blood culture was taken (After Test), or no change was detected (No Detection). The n/N columns represent the number of infants in each category out of the total number of infants. The Time columns represent the average difference in hours between detection and the time the blood culture was taken. The False Alarm column represents the number of infants with no systemic infection for whom a false alarm was raised. As can be seen from this table, the neonatologist and the SR algorithm perform comparably. On this dataset, on average the SR algorithm detects the change earlier, but has one more false alarm compared to the neonatologist. The advantage of the SR algorithm is that it can check automatically and constantly for a change in the distribution, unlike the neonatologist. The method may also take into account some or all of the history of the monitored patient, which is not always done in practice by physicians.

Moreover, in this analysis only the combined data of heart and respiratory rates are considered. The simulation results suggest that using measurements such as body temperature and saturation, both which are collected on a regular basis for every infant in the NICU may reduce the number of false alarms. Finally, a larger cohort of patients should enable fine tuning of the algorithm parameters resulting in faster detection and fewer false alarms.

Reference is now made to an exemplary implementation of glucose level monitoring. The data of this example consist of more than 400 blood glucose measurements of a diabetic patient, in mg/dL, made by the patient with the use of a glucometer. The measurements were taken in the morning, after at least eight hours since ingesting food, on the average of about twice a week, over a period of several years during the last decade. A post-facto check suggests that before change the data are normally distributed with no significant auto -correlation. The variability of the measurements is composed of two factors: that of the measuring instrument and that due to personal characteristics of the patient. Whereas in principle the former factor could be obtained from the manufacturer of the glucometer, the latter is not known in advance of surveillance. Therefore, the standard deviation of the observations is regarded as unknown. At onset of surveillance, the mean is unknown. Previous measurements that led to using a glucometer are not available, and even had they been obtainable they would not have been numerous enough to enable a claim of knowing the mean, especially since they may have caused the patient to be more careful with adherence to a diet. Therefore, the data is analyzed using an SR procedure for independent normally distributed observations with unknown initial mean and variance (Model 3). For the post-change distribution, the two-sided prior of Equation 5 with mean τ = 1.25 and standard deviation = 0.5 was used. The he algorithm is executed with 200, 400, and 800 ARL2FA. The results appear in FIG. 6 which is a set of graphs depicting an analysis of the glucose data for ARL2FA of 200, 400, and 800. The dashed lines represent the time of an alarm raised by the SR algorithm. As can be seen from FIG. 6, when using smaller ARL2FAs, the detection is faster (256 time-points for 200 ARL2FA compared to 271 for 400 ARL2FA, and 270 for 800 ARL2FA). On the other hand, lower ARL2FAs result in more actual false alarms. We also checked for ARL2FAs of 1600, 3200 and 6400, which yield exactly the same results as ARL2FA of 800.

Appendix A: Detecting a change of a normal mean with unknown baseline

Note that

so

Clearly, one cannot differentiate between v = 1 and v = oo. Therfore, Λ

Note that a prior on δ yields a closed form for

which again has a quadratic form (in δ) in the exponent. Letting b and

and so the final form is

The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein. It is expected that during the life of a patent maturing from this application many relevant methods and systems will be developed and the scope of the term a processor, a sensor, and a system is intended to include all such new technologies a priori.

As used herein the term "about" refers to ± 10 %.

The terms "comprises", "comprising", "includes", "including", "having" and their conjugates mean "including but not limited to". This term encompasses the terms "consisting of" and "consisting essentially of".

The phrase "consisting essentially of" means that the composition or method may include additional ingredients and/or steps, but only if the additional ingredients and/or steps do not materially alter the basic and novel characteristics of the claimed composition or method.

As used herein, the singular form "a", "an" and "the" include plural references unless the context clearly dictates otherwise. For example, the term "a compound" or "at least one compound" may include a plurality of compounds, including mixtures thereof.

The word "exemplary" is used herein to mean "serving as an example, instance or illustration". Any embodiment described as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments and/or to exclude the incorporation of features from other embodiments.

The word "optionally" is used herein to mean "is provided in some embodiments and not provided in other embodiments". Any particular embodiment of the invention may include a plurality of "optional" features unless such features conflict.

Throughout this application, various embodiments of this invention may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range. Whenever a numerical range is indicated herein, it is meant to include any cited numeral (fractional or integral) within the indicated range. The phrases "ranging/ranges between" a first indicate number and a second indicate number and "ranging/ranges from" a first indicate number "to" a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween.

It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination or as suitable in any other described embodiment of the invention. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment is inoperative without those elements.

All publications, patents and patent applications mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention. To the extent that section headings are used, they should not be construed as necessarily limiting.

Claims

WHAT IS CLAIMED IS:

1. A system for analyzing sensor data comprising:

at least one input interface adapted to receive from at least one sensor a plurality of measurements of at least one biological parameter of a target patient in real time during a period of at least an hour;

a processor;

a code, stored in memory coupled to the processor, wherein when the code is executed by the processer:

recording the plurality of measurements as at least one sequence in the memory,

calculating a model according to a first portion of the at least one sequence,

calculating a similarity value by placing a second portion of the at least one sequence the model, and

performing a check the similarity value against at least one threshold to detect a presence or an absence of a suspicious change; and

an output interface adapted to output an indication of the presence of the suspicious change based on an outcome of the check.

2. The system of claim 1, wherein the period is of at least one week.

3. The system of claim 1, wherein the model is generated using a Shiryaev -Roberts formulation.

4. The system of claim 1, wherein the model is generated by calculating a pre- change density value and a post-change density value when one of these densities is estimated and another is deduced from the first portion.

5. The system of claim 1, wherein the model is generated according a mean extracted from a plurality of sequences of measurements of the at least one biological parameter of a plurality of other patients which are different from the target patient.

6. The system of claim 1, wherein the model is generated using a cumulative distribution function.

7. The system of claim 1, wherein the model is generated by calculating a joint density of at least some of the measurements of the first portion when no change takes place and a second joint density of at least some of the measurements of the second portion

8. The system of claim 1, the plurality of measurements are sequentially taken in a rate of at least once a minute.

9. The system of claim 1, wherein the at least one sensor comprises a Neonatal Incubator Sensor; wherein the indication is of a Late-Onset Neonatal Sepsis.

10. The system of claim 9, wherein the Neonatal Incubator Sensor comprises a member of a group consisting of a heart rate sensor, a respiratory rate sensor, a saturation sensor, a blood pressure sensor, and a temperature.

11. The system of claim 1, wherein the at least one sensor comprises a glucometer wherein the indication is a glucose level change.

12. The system of claim 1, wherein the at least one threshold is set according to a combination of an Average Run Length to False Alarm (ARL2FA) an expected time from an appearance of the change in the at least one sequence and a detection thereof.

13. The system of claim 1, wherein the similarity value is at least one similarity ratio (SR) statistic value.

14. The system of claim 1, wherein the at least one input interface is adapted to receive the plurality of measurements from each of a plurality of sensors in real time during a period of at least an hour; wherein when the code is executed by the processer the plurality of measurements are recorded as a plurality of sequences in the memory; wherein the calculating a mode, the calculating a similarity value, and the performing a check are performed for each one of the plurality of sequences.

15. The system of claim 13, wherein the output interface is adapted to output the indication based on the outcome of the respective check.

16. The system of claim 13, wherein the output interface is adapted to output the indication based on a combination of a number of checks each of a different sequence from the plurality of sequences.

17. A method for analyzing sensor data comprising:

receiving from at least one sensor a plurality of measurements of at least one biological parameter of a target patient in real time during a period of at least an hour; recording the plurality of measurements as at least one sequence in the memory; calculating a model according to a first portion of the at least one sequence; calculating a similarity value by placing a second portion of the at least one sequence the model;

performing a check the similarity value against at least one threshold to detect a presence or an absence of a suspicious change; and

outputting an indication of the presence of the suspicious change based on an outcome of the check.

18. A computer program product for analyzing sensor data, the computer program product comprising:

one or more non-transitory computer-readable storage mediums, and program instructions stored on at least one of the one or more storage mediums, the program instructions comprising:

program instructions for receiving from at least one sensor a plurality of measurements of at least one biological parameter of a target patient in real time during a period of at least an hour; program instructions for recording the plurality of measurements as at least one sequence in the memory;

program instructions for calculating a model according to a first portion of the at least one sequence;

program instructions for calculating a similarity value by placing a second portion of the at least one sequence the model;

program instructions for performing a check the similarity value against at least one threshold to detect a presence or an absence of a suspicious change; and

program instructions for outputting an indication of the presence of the suspicious change based on an outcome of the check.