Systems and methods for personalized insulin titration - Patents.com

Abstract

A computing system for providing titration dose guidance to a subject for treating diabetes, the system comprising one or more processors and a memory, the memory including instructions for executing, by the one or more processors, (i) a representative predictive algorithm for the subject adapted to calculate a mean and variance of resulting fasting blood glucose values ​​(FBG) for the subject as a function of an injected dose size of insulin, the predictive algorithm adapting in response to acquired FBG and insulin dose size data for the subject, and (ii) a probabilistic algorithm adapted to calculate a probability of hypoglycemia for the subject as a function of insulin dose size based on the predicted mean and variance FBG values, and the FBG target range.

Description

[Technical field]

[0001] The present disclosure relates generally to systems and methods for assisting patients and healthcare professionals in managing insulin therapy for diabetes. In certain aspects, the present invention relates to systems and methods suitable for use in diabetes management systems that provide optimized individualized basal insulin titration regimens. [Background technology]

[0002] Diabetes mellitus (DM) is an insulin secretory disorder leading to hyperglycemia and various degrees of peripheral insulin resistance. Type 2 diabetes mellitus is characterized by a progressive disruption of normal physiological insulin secretion. In healthy individuals, basal insulin secretion by pancreatic β cells occurs continuously to maintain steady glucose levels for extended periods between meals. In healthy individuals, insulin is rapidly released in response to a meal with an initial first-phase spike, followed by a prolonged insulin secretion that returns to basal levels 2-3 hours later, with a meal-induced secretion. Poorly controlled hyperglycemia over many years can lead to multiple health complications. Diabetes mellitus is one of the leading causes of premature morbidity and mortality worldwide.

[0003] Effective control of blood / plasma glucose can prevent or delay many of these complications, but may not be able to reverse them once established. Thus, achieving good glycemic control in an effort to prevent diabetic complications is a major goal in the treatment of type 1 and type 2 diabetes. Smart titrators using adjustable step sizes, as well as physiological parameter estimates and predefined fasting blood glucose target values, have been developed to administer insulin drug treatment regimens.

[0004] Many non-insulin treatment options exist for diabetes, but as the disease progresses, the most promising response is usually with insulin. Notably, diabetes is associated with progressive beta-cell loss, and many patients, especially those with long-standing disease, will eventually need to transition to insulin because the degree of hyperglycemia (e.g., HbA1c ≥ 8.5%) makes it unlikely that another agent will provide sufficient benefit.

[0005] An ideal insulin regimen aims to mimic as closely as possible the physiological profile of insulin secretion, which has two major components: continuous basal secretion and a postprandial spike. Basal secretion controls overnight and fasting glucose, while the postprandial spike controls postprandial hyperglycemia.

[0006] Based on onset and duration of action, injectable formulations are broadly classified as basal (long-acting analogues [e.g., insulin detemir and insulin glargine] and very long-acting analogues [e.g., insulin degludec (for once-daily administration) and insulin icodec (for once-weekly administration)], and intermediate-acting insulins [e.g., isophane insulins, etc.], and prandial (rapid-acting analogues [e.g., insulin aspart, insulin glulisine, and insulin lispro]). Premixed insulin preparations incorporate both basal and prandial insulin components.

[0007] Basal insulin is typically the only (initial) insulin treatment for type 2 diabetes, whereas for type 1 diabetes, basal insulin can be used in combination with fast-acting insulin before meals.

[0008] Generally, to determine the optimal basal insulin dose for a given patient, the patient is titrated starting with an initial safe recommended low dose of basal insulin (typically 10 U / day) and then increased until fasting plasma glucose (FPG) is within the target range, generally 80-130 mg / dL with a dose of typically 40-70 U / day for type 2 diabetes. Alternatively, fasting blood glucose (FBG) values ​​are used; BG and PG are often used interchangeably. Dose adjustments should be more modest and less frequent as the target is approached, and tapering is recommended if hypoglycemia occurs.

[0009] However, there are significant barriers not only to initiating insulin-based therapy, but also to optimizing doses and intensifying regimens, all of which are necessary steps to tailor treatment to individual needs and maintain glycemic control.

[0010] Inter-patient variability: Different types of diabetes, different stages of each type, duration of diabetes, age, different lifestyle habits, and individual physiological differences all contribute to the complex optimization and intensification of treatment regimens.

[0011] Intra-patient variability: Additionally, the overall pathogenesis of diabetes can vary within each patient over time. This is particularly true for type 2 diabetes, where muscle and liver cells accumulate insulin resistance over time, leading to the progressive nature of type 2 diabetes. The complex pathophysiology and progressive nature of T2D means that good glycemic control becomes increasingly difficult over time, and treatment augmentation is often required.

[0012] Treatment adherence: The inability to initiate, optimize, and intensify basal insulin therapy is also caused by clinical inertia that leads to treatment adherence, which is typically related to forgetfulness, perceived need for medication, fear of hypoglycemia, and lack of confidence or uncertainty regarding insulin titration.

[0013] To address some of the above problems, several titration concepts and algorithms have been proposed, for example as disclosed in US Pat. Nos. 5,393,633, 5,496,923, 5,597,103, 5,641,362, and 5,713,626.

[0014] However, there is still a need for a basal insulin titration algorithm that can better take into account the differences in patient populations and therefore help patients reach treatment goals faster.The algorithm should also provide glycemic control over time, thus managing diabetes progression over time.Ideally, it should predict the dose required to reach glycemic goals early in treatment, thus providing HCPs as well as patients with insights that allow meaningful titration, as well as providing an estimate of the risk of hypoglycemia, thus reducing the fear of hypoglycemia when gradually increasing dose size to reach goals. [Prior art documents] [Patent documents]

[0015] [Patent Document 1] U.S. Patent Publication No. 2019 / 0147999 [Patent Document 2] U.S. Patent Publication No. 2020 / 0227170 [Patent Document 3] U.S. Patent Publication No. 2019 / 0272912 [Patent Document 4] U.S. Patent Publication No. 2017 / 213009 Summary of the Invention

[0016] In the present disclosure, embodiments and aspects are described that address one or more of the above objectives or that address objectives that are apparent from the following disclosure as well as the description of exemplary embodiments. In the context of the present invention, the terms FBG and FPG, respectively, of BG and FG, are used interchangeably when not used in combination with a specific value. Accordingly, in the present disclosure and claims, the term FBG stands for FBG as well as FPG.

[0017] In summary, the present invention is based on the recognition that a titration algorithm personalized to each individual patient is better suited to achieve the goal of an effective titration process. Thus, a data-driven basal insulin titration algorithm is provided that provides personalized decision support to guide dose adjustments to find the optimal insulin dose.

[0018] Accordingly, in a first aspect of the present invention, a computing system for providing a titration dose guidance recommendation to a query subject for treating diabetes mellitus is provided, the system comprising one or more processors and a memory. The memory includes instructions for executing, by the one or more processors, (i) a representative prediction algorithm for the subject adapted to calculate the mean and variance of the resulting fasting blood glucose value (FBG) for the subject as a function of the size of an injected dose of insulin, the prediction algorithm adapting in response to the acquired FBG and corresponding insulin dose size data for the subject, (ii) a probability algorithm adapted to calculate the probability of hypoglycemia, hyperglycemia, respectively, for the subject as a function of insulin dose size based on the predicted mean and variance FBG values ​​and a predefined FBG target range, and (iii) a policy algorithm adapted to calculate the probability for a corresponding policy target as a function of insulin dose size based on the calculated probabilities of hypoglycemia, hyperglycemia, respectively. The memory further includes instructions that, when executed by the one or more processors, perform a method in response to receiving a dose guidance request (DGR), the method including: (a) obtaining, for the subject, an FBG target to be used as a predetermined FBG target range for the probabilistic algorithm; (b) obtaining from the subject an updated dataset including latest FBG values ​​and corresponding insulin dose sizes; (c) using a predictive algorithm, calculating the mean and variance of the resulting FBG for the subject as a function of the size of an injected dose of insulin based on the updated dataset; (d) using a probabilistic algorithm, calculating the probability of hypoglycemia, hyperglycemia, respectively, for the subject as a function of insulin dose size; (e) using a policy algorithm, calculating the probability of a policy target as a function of insulin dose size; and (f) determining an insulin dose size having the highest calculated probability for meeting the policy target, wherein the determined dose size represents a recommendation for the requested dose size.

[0019] In this way, a data-driven insulin titration algorithm is provided that ensures a high degree of personalized decision support to guide dose adjustments to find the optimal insulin dose based on a given policy and corresponding target.

[0020] The predictive algorithm may be in the form of a probabilistic model with mean μ(x) and variance σ(x) as outputs, where μ(x) is the mean of the predicted FBG as a function of insulin dose x and σ(x) is its variance.

[0021] The probabilistic algorithm may be in the following form:

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number

[0022] The titration process may start "from scratch" with no historical data of the patient, which will then be accumulated during the process. That is, the initial update data set may include only the latest FBG value and the corresponding insulin dose size, which may be zero. Alternatively, the titration process may start based on multiple historical data sets for the subject. For each update, a new update data set is created by combining the latest data values ​​with the historical data values.

[0023] In an exemplary embodiment, the computing system comprises a smartphone having a display, the display being controlled to display the determined dose size representative of the requested recommended dose size.

[0024] In a second aspect of the present invention, a computing system for providing titration dose guidance recommendations to a query subject for treating diabetes mellitus is provided, the system comprising one or more processors and a memory. The memory includes instructions for executing, by the one or more processors, (i) a representative prediction algorithm for the subject adapted to calculate a mean and variance of resulting fasting blood glucose values ​​(FBG) for the subject as a function of an injected dose size of insulin, the prediction algorithm adapting in response to acquired FBG and corresponding insulin dose size data for the subject, and (ii) a policy algorithm adapted to calculate a probability of a corresponding policy target as a function of insulin dose size based on the predicted mean and variance FBG values. The memory further includes instructions that, when executed by the one or more processors, perform a method in response to receiving an administration guidance request (DGR), the method including: (a) obtaining, for the subject, an FBG target to be used as a policy target for the probabilistic algorithm; (b) obtaining from the subject an updated dataset including latest FBG values ​​and corresponding insulin dose sizes; (c) using a predictive algorithm to calculate, for the subject, the mean and variance of the resulting FBG for the subject as a function of the size of an injected dose of insulin based on the updated dataset; (d) using a policy algorithm to calculate the probability of the policy target as a function of insulin dose size; and (e) determining an insulin dose size having the highest calculated probability for meeting the policy target, wherein the determined dose size represents a recommendation for the requested dose size.

[0025] In a further aspect of the present invention, there is provided a corresponding method for providing titration dose guidance recommendations to a query subject for treating diabetes mellitus, the method comprising the steps of (i) obtaining, for the subject, FBG targets to be used as predefined FBG target ranges for the probabilistic algorithm, and (ii) obtaining from the subject an updated dataset comprising the latest FBG values ​​and corresponding insulin dose sizes. The method includes the further steps of (iii) calculating, for the subject, the mean and variance of the resulting FBG for the subject as a function of the size of the injected dose of insulin based on the updated dataset using a representative adaptive prediction algorithm for the subject; (iv) calculating, for the subject, the probabilities of hypoglycemia, hyperglycemia, respectively, as a function of insulin dose size based on the predicted mean and variance FBG values ​​and the predetermined FBG target range using a probability algorithm; (v) calculating, for the subject, the probabilities for the corresponding policy target as a function of insulin dose size based on the calculated probabilities of hypoglycemia, respectively, using a policy algorithm; and (vi) determining an insulin dose size having the highest calculated probability for meeting the policy target, wherein the determined dose size represents a dose size recommendation.

[0026] In yet a further aspect of the present invention, a computing system is provided for providing a titration dose guidance recommendation to a query subject for treating diabetes mellitus. The system comprises one or more processors and a memory. The memory includes instructions for executing, by the one or more processors, (i) a representative prediction algorithm for the subject adapted to calculate the mean and variance of the resulting fasting blood glucose value (FBG) for the subject as a function of the size of an injected dose of insulin, the prediction algorithm adapting in response to the acquired FBG and corresponding insulin dose size data for the subject, and (ii) a probabilistic algorithm adapted to calculate the probability of hypoglycemia for the subject as a function of insulin dose size based on the predicted mean and variance FBG values ​​and a hypoglycemic target value. The memory further includes instructions that, when executed by the one or more processors, perform a method in response to receiving a dose guidance request (DGR), the method including: (a) obtaining an updated dataset from the subject, the updated dataset including an latest FBG value and a proposed insulin dose size; (b) obtaining a threshold acceptable probability for hypoglycemia for the subject; (c) using a predictive algorithm to calculate the mean and variance of the resulting FBG for the subject as a function of the size of an injected dose of insulin based on the updated dataset for the subject; (d) using a probabilistic algorithm to calculate the probability of hypoglycemia for the subject for the proposed insulin dose size; (e) determining whether the proposed insulin dose size is above or below the threshold acceptable probability; and (f) communicating to the subject whether the proposed insulin dose size is acceptable or should be reduced.

[0027] In this way, a data-driven insulin algorithm is provided that can be used to verify that any titration algorithm or given dose suggested by an HCP is safe to a desired level of confidence.

[0028] Hereinafter, the following embodiments of the present invention will be described with reference to the drawings. [Brief description of the drawings]

[0029] [Figure 1] Figure 1 illustrates graphically the basic concepts of Gaussian process regression. [Diagram 2] FIG. 2 illustrates generally how the probability of hypoglycemia and hyperglycemia as a function of insulin dose can be determined. [Diagram 3] FIG. 3 illustrates the different components of the Bayesian modeling framework and the titration concept based on the policy function. [Figure 4] FIG. 4 shows the in silico results for once-daily insulin using the proposed Bayesian approach for the first policy function. [Diagram 5] FIG. 5 shows the in silico results for once-daily insulin using the proposed Bayesian approach for the second policy function. [Figure 6] FIG. 6 shows the in silico results for once-daily insulin using the proposed Bayesian approach for the third policy function. [Figure 7] FIG. 7 shows in silico results for once-daily insulin using the proposed Bayesian approach for the fourth policy function. [Figure 8] FIG. 8 shows the different components of a Bayesian modeling framework adapted to validate whether a given titration algorithm or a given dose suggested by an HCP is safe. [Figure 9] FIG. 9 shows a titration lookup table. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0030] Overall, a diabetes dosing guidance system is provided that helps patients with diabetes by generating recommended insulin doses. Such a system uses a given algorithm to generate recommended insulin doses and treatment advice for diabetic patients based on BG and insulin dosing history.

[0031] Essentially, such a system includes a back-end engine ("Engine"), which is a primary aspect of the present invention, used in combination with interacting systems in the form of clients and operating systems.

[0032] The client is the software component that requests dosing guidance from the perspective of the engine. The client gathers the necessary data (e.g., CGM data, insulin dosage data, patient parameters) and requests dosing guidance from the engine. The client then receives a response from the engine.

[0033] On a small local scale, the engine may run directly as an app on a given user's smartphone and thus be a self-contained application including both client and engine. Alternatively, the system setup may be designed to be implemented as a back-end engine adapted to be used as part of a larger cloud-based diabetes management system. Such a cloud-based system allows the engine to be always up to date (as opposed to an app-based system running entirely on, for example, the patient's smartphone), to implement advanced methods such as machine learning and artificial intelligence, or to use the data in combination with other services in a larger "digital health" setting. Such a cloud-based system would ideally handle a large volume of patient requests for dosage recommendations.

[0034] While a "full" engine may be designed to take care of all computing aspects, it may be desirable to split the engine into a local and cloud version so that a near-patient dosing guidance system can run independent of a dependency on cloud computing. For example, when a user makes a request for dosing guidance via the client app, the request is sent to the cloud engine, which returns a dose recommendation. If cloud access is not available, the client app performs the dose recommendation calculation using the current local algorithm. Depending on the user's app settings, the user may or may not be notified.

[0035] In an exemplary embodiment of the present invention, a Bayesian optimization approach is implemented in which a sequential design strategy for global optimization of black-box functions that does not assume any functional form is used.

[0036] BG data for a given patient may be provided, for example, as self-measured blood glucose measurements (SMBG) measured under fasting conditions (FBG) or as BG data from a continuous glucose monitor (CGM). Using the BG and insulin dosage data, a data-driven probabilistic model can be developed that captures the effect of insulin on blood glucose.

[0037] A Bayesian modeling framework is used to predict blood glucose as a function of insulin and to provide confidence in the predicted function. The confidence in the prediction function is an important variable, which is then used to predict:

[0038] 1. Probability of hypoglycemia (BG<=4mmol / L) 2. Probability of reaching the target (4<=BG<=7mmol / L) 3. Probability of hyperglycemia (BG>=7mmol / L) More precisely, the mean and variance are modeled using appropriate black-box surrogate functions such as Gaussian process models or random forest models, i.e., for any given insulin dose, the model will predict the mean and variance of fasting blood glucose.

[0039] The model is updated for each patient using insulin doses and fasting glucose measurements. Each time a new data point becomes available (i.e., dose from the previous period (e.g., last week or day), and FBG obtained after the dose was given), the mean and variance of the black-box model are updated by conditioning it to the data. The basic idea of ​​Gaussian process regression is shown diagrammatically in Figure 1.

[0040] More specifically, the true unknown function is shown as a dashed line. The solid dots represent old data points and the black circles indicate new data points. A Gaussian Process (GP) model is used as a surrogate to model the true unknown function. The mean of the GP model is shown as a full line and the variance is shown in the boxed area. At every time step t, when new data points are available, the mean and variance of the GP model are updated by conditioning the data points.

[0041] First, the use of a Bayesian modeling framework is based on patient data, which allows the decision support tool to be personalized for each individual patient: since the model is tuned to the patient data, the predicted mean and variance are individualized for each patient.

[0042] Secondly, by predicting the probability of hypoglycemia as a function of insulin dose for a particular patient, this can be used to verify whether the proposed dose is safe. For example, the dose can be suggested by the HCP, a standard treatment titration algorithm, or any other dosing guidance algorithm. If the predicted probability of hypoglycemia at the proposed insulin dose is lower than some acceptable value, the proposed dose can be administered. Predicting the risk of hypoglycemia also reduces the fear of hypoglycemia and improves the patient's confidence in increasing the insulin dose until the target is reached. Figure 2 shows a schematic of how the probability of hypoglycemia and hyperglycemia as a function of insulin dose can be determined.

[0043] Third, the updated surrogate model (such as a Gaussian process model) can be used to directly titrate the insulin dose. This can be done by constructing a "policy" (also known as an acquisition function in the computer science domain) that will suggest what the next insulin dose should be. The decision-making policy is based on the calculated probability of hypoglycemia and the probability of hyperglycemia. For example, one decision-making policy may be based on the probability of reaching the target zone. This provides a predicted target dose, i.e., the insulin dose at which the patient is expected to reach the glycemic target. The predicted target dose can then be used to directly titrate the insulin dose, which can help the patient reach the target faster.

[0044] Predicting the probability of hypoglycemia and the probability of targeting as a function of insulin dose also provides useful insight to patients and HCPs.

[0045] Exemplary embodiments The above approach can be used for basal insulin titration in type 1 or type 2 diabetes.

[0046] Note that the dose calculation, i.e. the proposed dose, is done using a probabilistic model with mean μ(x) and variance σ(x), where μ(x) is the mean of the predicted FPG as a function of insulin dose x and σ(x) is its variance.

[0047] New data sets are used to update the models that form the basis of the dose calculations, but the calculations themselves are based on probabilistic models, so the significance of the calculations does not depend on the amount of data available.

[0048] The probabilistic model can be any that models a phenomenon as well as its uncertainty distribution, i.e., at any query point, the probabilistic model returns the value of the function and its confidence binding.

[0049] The algorithm has a default one-size-fits-all model, which may be referred to as the "prioritized mean function." For a given insulin analog, some information is known about the effect of insulin on blood glucose. Typically, the more insulin injected, the lower the resulting blood glucose. The default one-size-fits-all model will be based on this design. One example is a linear function: [Number 3] BG=mx+c In the absence of data, a decision will be calculated based on this default model. Of course, this model is not optimal because it is not individualized to the individual. Therefore, it is overly conservative, but as more data is collected, the default model can be updated and therefore adapted to a given individual. Alternatively, a more advanced model may be used, just as a given model may be optimized for a given demographic characteristic.

[0050] The dataset consists of (insulin dose size, FPG) pairs; more precisely, the already injected dose, and its corresponding or resulting FPG. That is, the patient injects insulin on day 1 and measures the corresponding FBG on the morning of day 2. In this way, we can observe the effect that insulin had on the patient. This observation is what is needed to update the probabilistic model.

[0051] Thus, starting with an initial dataset D={(0, FPG0)} on day 0, where FPG0 is the patient's starting blood glucose value, i.e., untreated FPG, since no insulin has been administered before. This can also be referred to as an updated dataset, since there are no datasets prior to the first dataset.

[0052] Day 0: The patient receives the initial dose of I1 (eg, I1=10 U).

[0053] Day 1: Patient measures FPG. The updated dataset now has D={(0, FPG0), (I1, FPG1)}.

[0054] The probability model is updated using D={(0, FPG0), (I1, FPG1)}, i.e., using Bayes' rule from classical elementary statistics.

[0055] The algorithm then uses the model to calculate a new insulin dose I2. Policies 1, 2, 3, or 4 (see below) can be used for this. These policies are based on the mean and variance of the updated model. The patient takes insulin I2

[0056] Day 2: The patient has their FPG measured.

[0057] The updated data set now has D={(0,FPG0),(I1,FPG1),(I2,FPG2)}.

[0058] Update the probabilistic model using D={(0,FPG0),(I1,FPG1),(I2,FPG2)}.

[0059] The algorithm then uses the model to calculate a new insulin dose, I3. The patient takes insulin I3.

[0060] From the third day onwards, repeat the above procedure.

[0061] Day N: D = {(0, FPG0), (I1, FPG1), (I2, FPG2)...., (I N ,FPGN)}.

[0062] For once-weekly insulin, Week 1, Week 2, ... are used instead of Day 1, Day 2, ...

[0063] As shown, the dataset is a table with two columns: insulin dose size, and measured FPG. Every day (or week), a new row is added, thereby updating the dataset. Fasting blood glucose can be measured using any glucose sensing device, either interstitial, blood, or urinary. ---

[0064] The mean and variance of fasting blood glucose are modeled as a function of insulin dose x. [Number 4] BG(x)~GP(μ(x),σ(x)) where x is the insulin dose [U], BG is blood glucose in [mmol / L], μ(x) is the mean blood glucose and σ(x) is the variance.

[0065] Using the updated mean and variance, the probability of being on target and the probability of hypoglycemia as a function of insulin dose can be calculated by using the cumulative distribution function denoted by Φ(·).

number

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[0066] target low =4 and target high For =7,

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[0067] As a first example, the Kanderain model modified for T2D (Aradottir et al. 2019) is used as a virtual patient. Note that no model information is used by the algorithm. In this example, basal insulin titration is shown. The target dose can be updated daily, once every n days, or weekly. The patient can also be titrated to the proposed target dose in smaller steps.

[0068] To titrate insulin dose directly, a policy function needs to be constructed that guides the insulin dose update. Any policy function constructed using the probabilities of hypoglycemia and hyperglycemia can be used.

[0069] FIG. 3 shows the different components of the concept described above.

[0070] Examples of three decision-making policies that can be used to suggest the next dose are described below.

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[0071] The first policy is based on calculating the probability of being within a predefined target range of 4 and 7 mmol / L, i.e. the target is a range. As shown, the first policy does not optimize the probability of reaching a particular target value, e.g. the average of the range, but in contrast only optimizes the probability that the achieved BG is within a pre-set range (which may be, e.g., 4.1 or 6.9 mmol / L), and thus the probability of being within the target range. The same considerations apply to the second and third policies.

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[0072] The second policy is based on aggregating the probabilities of constraint feasibility (in this case the lower and upper bounds on the BG values).

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[0073] The third policy is based on a trade-off between the probabilities of hypoglycemia and hyperglycemia, ie, choosing the point where the probabilities of hypoglycemia and hyperglycemia cross over.

[0074] Further policy functions can potentially be constructed based on the probabilities of hypoglycemia and hyperglycemia. Any such meaningful policy can be used.

[0075] Additionally, the policy function may also be based on the average of a Gaussian process model. [Number 12] Policy 4(x) = -(μ(x) - target) 2 where μ(x) is the mean of the Gaussian process model. As shown, in the fourth policy, the target is a single value, not a range.

[0076] To incorporate information about the probability of hypoglycemia and hyperglycemia in policy 4, it can also be scaled with the probability of feasibility, i.e., by multiplying policy 4 by policy 2.

[0077] Once the policy function is selected, the suggested dose is given by the insulin value that maximizes the policy function.

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[0078] The following implementations of different policies are illustrated using a series of plots.

[0079] In all plots, the bottom subplot (a) shows the Bayesian model updated with only a few past data points prior in the titration procedure. Using a Gaussian process model, the probability of hypoglycemia and hyperglycemia as a function of insulin dose is also calculated (in this case every 3 days) as shown in the top subplot (a). As the titration process continues, more data points are obtained and the Gaussian process model is updated with each new data point. The bottom subplot (b) shows the updated GP model with more data points after a few weeks, and the corresponding probabilities of hypoglycemia and hyperglycemia are shown in the top subplot (b). Subplot (c) shows the SMBG measurements and the insulin dose administered daily using the proposed Bayesian titration approach. The Bayesian titration approach is started on day 20, which can be seen to help individualize the titration to a particular patient and thus reach glycemic targets more quickly.

[0080] Figure 4 shows the in silico results of policy 1 for once-daily insulin using the proposed Bayesian approach on two different days, one at an early stage of the titration procedure (a) and one at a later stage of the titration procedure (b). As more data points become available, the Gaussian process captures the insulin-glucose effect more accurately and therefore suggests a more appropriate target dose, as shown in (c).

[0081] FIG. 5 shows Policy 2, which corresponds to the in silico results for once-daily insulin using the proposed Bayesian approach on two different days.

[0082] FIG. 6 shows Policy 3 corresponding to the in silico results for once-daily insulin using the proposed Bayesian approach on two different days.

[0083] FIG. 7 shows Policy 4 corresponding to the in silico results for once-daily insulin using the proposed Bayesian approach on two different days.

[0084] The examples given above show that estimates of the probability of hypoglycemia give HCPs and patients meaningful insights regarding the risk of hypoglycemia for a proposed dose. These can be used to construct policies that can be used to guide insulin titration.

[0085] This approach requires choosing an initial prior mean function to capture the effect of insulin on blood glucose. This can be chosen appropriately using domain knowledge. For example, for a given insulin analogue, some information is available about the effect of insulin on blood glucose. Typically, the more insulin, the lower the blood glucose. So a linear function can be heuristically chosen. [Number 14] BG=mx+c where m is the slope and c is the intercept.

[0086] The model selected can be a one-size-fits-all model that captures the effect of insulin on blood glucose. This initial one-size-fits-all prior model can then be individualized to the patient as new data points become available.

[0087] As more data points become available, the previous slopes and intercepts should ideally also be updated, so that when data points are unavailable the previous ones can be extrapolated in a more meaningful way.

[0088] This approach can be used with once-daily insulin analogues, or once-weekly insulin analogues.

[0089] Table 1 below shows a numerical example using the Bayesian approach combined with policy 3 (noise-free) described above. [Table 1]

[0090] In the illustrated model example, the actual dose taken by the patient corresponds exactly to the dose suggested by the algorithm, e.g., 25.35 U. In a real-world scenario, the dose would be rounded to an integer-sized dose. The point is "time splitting," so the suggested dose in row x matches the SMBG in row x+1.

[0091] In a second exemplary embodiment, a Bayesian modeling framework is used to validate whether a given dose suggested by some titration algorithm or HCP is safe, as shown in FIG. 8. With each new data point, a Gaussian process model can be updated to develop an individualized model that predicts the mean and variance of blood glucose as a function of insulin dose. This probabilistic model can predict the probability of hypoglycemia as described above. The predicted probability of hypoglycemia can be used to validate whether a proposed dose increase is safe. The dose updates can come from either the HCP or any given titration algorithm.

[0092] The above approach was tested using insulin icodec (a long-acting basal insulin analogue intended for once-weekly treatment being developed by Novo Nordisk A / S for the treatment of type 1 and type 2 diabetes) clinical trial data from the NN4465 trial, where titration was performed according to a lookup table. An example of such a lookup table is shown in FIG. 9.

[0093] A numerical example using a simple titration algorithm combined with a Bayesian approach is given in Table 2 below. Note that the example starts at week 14 because the uncertainty measures are more reliable after a few weeks. [Table 2]

[0094] The first four columns are numerical examples using a conventional titration algorithm, here the 14-0-14 algorithm. Column 2 shows the SMBG for the actual day of the week and the SMBG for the past two weeks, where the titration value is calculated as the average of the three measurements. A Bayesian approach is used as an additional level of protection to predict the probability of hypoglycemia for a 14-0-14 based dose. Accordingly, a Bayesian approach can be used to "reject" dose increases due to large increases in the probability of hypoglycemia. As shown, if a dose increase reduces SMBG, the probability of hypoglycemia tends to increase.

[0095] Comparing Tables 1 and 2, it can be seen that the predicted probability of hypoglycemia is much higher in Table 2 than in Table 1. This is partly based on the fact that the algorithm behind Table 1 is optimized to minimize these values ​​(and also minimize the probability of hyperglycemia), whereas the algorithm behind Table 2 is not optimized either. The probabilities also depend on the specific hyperparameters chosen to describe the uncertainty bands for the individual algorithms, and also on the specific kernels chosen. These parameters are not identical for the two algorithms, in part because the algorithm in Table 1 is designed for use with once-daily insulin, e.g., insulin degludec, whereas the algorithm in Table 2 is designed for use with once-weekly insulin, e.g., insulin icodec.

Claims

1. 1. A computing system for providing titration dosage guidance recommendations to a query subject for treating diabetes mellitus, the system comprising: one or more processors; and a memory, the memory comprising: A) by said one or more processors, - a representative predictive algorithm for the subject adapted to calculate the mean and variance of resulting fasting blood glucose values ​​(FBG) for the subject as a function of the size of an injected dose of insulin, said predictive algorithm adapting in response to acquired FBG and corresponding insulin dose size data for the subject; - a probabilistic algorithm adapted to calculate the probability of hypoglycemia, hyperglycemia, respectively, for said subject as a function of insulin dose size based on the predicted mean and variance FBG values ​​and a predefined FBG target range; - a policy algorithm adapted to calculate, based on the calculated probabilities of hypoglycemia and hyperglycemia, probabilities for a corresponding policy target as a function of insulin dose size; B) instructions that, when executed by the one or more processors, perform a method in response to receiving a dose guidance request (DGR), the method comprising: - obtaining, for said subject, FBG targets to be used as said predefined FBG target ranges of said probabilistic algorithm; - obtaining an updated data set from said subject comprising the most recent FBG values ​​and corresponding insulin dose sizes; - calculating, for the subject, the mean and the variance of the resulting FBG as a function of the size of an injection dose of insulin based on the updated data set using the prediction algorithm; - calculating the probability of hypoglycemia and hyperglycemia, respectively, for said subject as a function of insulin dose size using said probabilistic algorithm; - calculating the probability of the policy target as a function of insulin dose size using the policy algorithm; determining the insulin dose size having the highest calculated probability of meeting the policy target, the determined dose size representing a recommendation for a requested dose size.

2. The computing system of claim 1 , wherein the memory includes a historical data set for the subject.

3. 3. The computing system of claim 1 or 2, comprising a smartphone having a display, the display being controlled to display a determined dose size representative of a recommendation for the requested dose size.

4. 1. A computing system for providing titration dosage guidance recommendations to a query subject for treating diabetes mellitus, the system comprising: one or more processors; and a memory, the memory comprising: A) by said one or more processors, - a representative predictive algorithm for the subject adapted to calculate the mean and variance of resulting fasting blood glucose values ​​(FBG) for the subject as a function of the size of an injected dose of insulin, said predictive algorithm adapting in response to acquired FBG and corresponding insulin dose size data for the subject; - a policy algorithm adapted to calculate the probability of a corresponding policy target as a function of insulin dose size based on the predicted mean and variance FBG values; B) instructions that, when executed by the one or more processors, perform a method in response to receiving a dose guidance request (DGR), the method comprising: - obtaining, for said subject, an FBG target to be used as the policy target of a probabilistic algorithm; - obtaining an updated data set from said subject comprising the most recent FBG values ​​and corresponding insulin dose sizes; - calculating, for the subject, the mean and the variance of the resulting FBG as a function of the size of an injection dose of insulin based on the updated data set using the prediction algorithm; - calculating the probability of the policy target as a function of insulin dose size using the policy algorithm; determining the insulin dose size having the highest calculated probability of meeting the policy target, the determined dose size representing a recommendation for a requested dose size.

5. 1. A method for providing titration dose guidance recommendations to a query subject for treating diabetes mellitus, the method comprising: - obtaining, for said subject, FBG targets to be used as predefined FBG target ranges for a probabilistic algorithm; - obtaining an updated data set from said subject comprising the most recent FBG values ​​and corresponding insulin dose sizes; - using a representative adaptive prediction algorithm for said subject, calculating, for the subject, the mean and variance of the resulting FBG for the subject as a function of the size of an injected dose of insulin based on the updated data set; - calculating, using a probabilistic algorithm, the probability of hypoglycemia, hyperglycemia, respectively, for said subject based on predicted mean and variance FBG values ​​and said predefined FBG target range as a function of insulin dose size; - calculating, using a policy algorithm, a probability for a corresponding policy target based on said calculated probabilities of hypoglycemia and hyperglycemia, as a function of insulin dose size; - determining the insulin dose size having the highest calculated probability for meeting the policy target, the determined dose size representing a dose size recommendation.

6. 6. The method of claim 5, wherein the updated dataset is obtained using a historical dataset for the subject, and a most recent FBG value and corresponding insulin dose size for the subject.

7. 1. A computing system for providing titration dosage guidance recommendations to a query subject for treating diabetes mellitus, the system comprising: one or more processors; and a memory, the memory comprising: A) by said one or more processors, - a representative predictive algorithm for the subject adapted to calculate the mean and variance of resulting fasting blood glucose values ​​(FBG) for the subject as a function of the size of an injected dose of insulin, said predictive algorithm adapting in response to acquired FBG and corresponding insulin dose size data for the subject; - a probabilistic algorithm adapted to calculate the probability of hypoglycemia for said subject as a function of insulin dose size based on the predicted mean and variance FBG values ​​and the hypoglycemic target value; B) instructions that, when executed by the one or more processors, perform a method in response to receiving a dose guidance request (DGR), the method comprising: - obtaining an updated data set from said subject, said data set including a most recent FBG value and a suggested insulin dose size; - obtaining a threshold acceptable probability of hypoglycemia for said subject; - calculating, for the subject, the mean and the variance of the resulting FBG as a function of the size of an injection dose of insulin based on the updated data set using the prediction algorithm; - calculating the probability of hypoglycemia for the subject for the proposed insulin dose size using the probabilistic algorithm; - determining whether the proposed insulin dose size is above or below the threshold acceptable probability; - communicating to the subject whether the proposed insulin dose size is acceptable or should be reduced.

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