A gamma pass prediction conformal risk control method

Abstract

The application discloses a kind of gamma passage rate prediction conformal risk control methods, which comprises the following steps: S1: data acquisition, and pretreatment is carried out;S2: schedule form mode and image mode feature are input into multimodal depth network to obtain quantile feature;S3: quantile feature is carried out dose difference quantile decoding to obtain dose difference matrix quantile and gamma passage rate quantile;S4: conformal prediction is carried out, and dose difference is carried out conformal risk control.The safety of the prediction of the application is higher, and the consistency of uncertainty estimation is higher.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of machine learning, in particular to a gamma pass rate prediction conformal risk control method. BACKGROUND

[0002] Existing gamma pass rate prediction mostly only pays attention to global performance, and does not pay enough attention to the safety of prediction. Machine learning methods based on statistical learning usually have a generally large prediction variance on some data, but the current machine learning-based gamma pass rate prediction algorithm does not measure this uncertainty.

[0003] Most existing uncertainty measurement algorithms usually only use symmetric probability modeling and do not pay attention to asymmetric risk, but using probability alone is insufficient in gamma pass rate prediction applications, because predicting a qualified plan as unqualified only requires redesigning the plan, while predicting an unqualified plan as qualified has the risk of medical accidents.

[0004] Most existing deep learning-based uncertainty algorithms usually have the problem of overestimating confidence and statistically inconsistent with actual test results when measuring uncertainty. SUMMARY

[0005] In view of the above technical features, the present application provides a gamma pass rate prediction conformal risk control method, comprising the following steps:

[0006] S1: data acquisition and preprocessing;

[0007] S2: inputting the plan table modal and image modal features into a multi-modal deep network to obtain quantile features;

[0008] S3: dose difference quantile decoding the quantile features to obtain dose difference quantile and gamma pass rate quantile;

[0009] S4: conformal prediction and conformal risk control of dose difference.

[0010] Further, step S1 comprises the following sub-steps:

[0011] S11: obtaining 2D dose image data;

[0012] S12: resampling the 2D dose image data to obtain images with consistent spatial resolution;

[0013] S13: cutting and removing redundant background;

[0014] S14: performing normalization processing;

[0015] S15: performing feature extraction and feature conversion to obtain basic features Zgpr.

[0016] Further, step S2 includes the following sub-steps:

[0017] S21: input the base feature Zgpr into the GPR quantile decoder, predict three quantiles Yddp using the regression model;

[0018] S22: input the base feature Zddp into the dose difference quantile decoder, predict the dose difference using the U-Net decoder, convert the channels to one through three convolutional layers for regression;

[0019] S23: the GPR quantile decoder outputs three quantiles qα low , q1 / 2 and qα up of the gamma passing rate, and the dose difference quantile decoder outputs the dose difference segmentation result and the corresponding uncertainty quantification.

[0020] Further, step S3 includes the following sub-steps:

[0021] S31: establish a multi-granularity prior network architecture, which allows simultaneous training of DDP and GPR prediction tasks;

[0022] S32: use quantile regression of Pinball loss, the calculation method is:

[0023]

[0024] Further, step S4 includes the following sub-steps:

[0025] S41: based on segmentation conformal prediction:

[0026] P(Y n+1 ∈C α (X n+1 ))≥1-α

[0027]

[0028] Further, step S4 also includes the following sub-steps:

[0029] S42: perform conformal risk control:

[0030]

[0031] Further, step S4 also includes the following sub-steps:

[0032] S43: perform conformal risk control of dose difference:

[0033]

[0034] wherein, a is a user-set risk, and λ is a calibration factor; the calibration factor is calculated by the following method:

[0035] First formula of a:

[0036]

[0037] Second formula of a, definition of λ set:

[0038]

[0039] Third formula of a, formula of the last used calibration factor λ, after obtaining the calibration factor λ, the calibration factor λ is substituted into T λ Calibration:

[0040]

[0041] a is a user-set risk, and λ is a calibration factor; the calibration factor is calculated by the following method: w is a weighted quantile converted into a.

[0042] The present application has the advantages that the safety of the prediction is high, and the consistency of the uncertainty estimation is high. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings described below are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained according to the structures shown in the drawings without creative labor.

[0044] Figure 1 Flowchart of the present application. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the following will combine the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, not all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations.

[0046] It should be noted that: similar labels and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0047] Some embodiments of the present application will be described in detail with reference to the drawings. The following embodiments and features of the embodiments described below can be combined with each other in the case of no conflict.

[0048] Referring to Figure 1 A gamma pass rate prediction conformal risk control method comprises the following steps:

[0049] S1: data acquisition and preprocessing;

[0050] S2: input the planning table modal and image modal features into the multi-modal deep network to obtain quantile features;

[0051] S3: dose difference quantile decoding is performed on the quantile features to obtain dose difference matrix quantile and gamma pass rate quantile;

[0052] S4: conformal prediction and dose difference conformal risk control.

[0053] In this embodiment, the dose image obtained in step S1 shows different spatial resolutions and sizes, so several preprocessing steps are needed. First, the 2D dose image is resampled to a consistent spatial resolution of 1mm x 1mm, and then cropped to 512 x 512 pixels to remove redundant background. Finally, before inputting the network, the pixel values of the input image are rescaled to [0, 1] by Min-Max normalization to ensure the consistency of the input data.

[0054] Each sample contains two modal data: image modal and table data. Specifically, the image modal is a 512 x 512 matrix representing the image modal. All element values are between 0 and 1, representing the relative dose intensity; the table data is a 33-dimensional vector, all elements are complexity indicators representing the table modal. The specific target variable of the GPR prediction task is a three-dimensional vector, corresponding to the three common standards in clinical practice. GPR represents the gamma pass rate. The specific target variable of the DDP task is a 512 x 512 matrix, which is the same as the image modal input. DDP represents the dose difference. These definitions enable us to effectively model the PSQA (deep learning automated plan quality assurance) task and perform corresponding prediction and verification.

[0055] Then, feature extraction is performed through network flow: input data, image modal data (such as dose planning array) is processed by image encoder (such as ResNet) to extract features. The table modal data (such as complexity indicators) is processed by the table encoder to extract features.

[0056] Feature extraction, the image encoder converts the image modality data into a feature vector of dimension Nc x W x H. The table encoder converts the table modality data into a feature vector of dimension Nt x W x H (where W and H are the last two dimensions of the image modality).

[0057] Feature transformation, the extracted image features and table features are concatenated from different paths to form a Zgpr of dimension Nc + Nt. The table modality features, shaped as Batch x (Nt x W x H), are reshaped to Batch x Nt x W x H and then concatenated with the image modality data. The quantile feature fusioner merges these features into a unified base feature Zddp.

[0058] Step S2 is specifically: decoding by the dose difference quantile decoder, in order to handle asymmetric risk, several quantile forms are set, including distributed and non-distributed quantiles, inputting the base feature Zgpr into the GPR quantile decoder, using a regression model to predict three quantiles Yddp; inputting the base feature Zddp into the dose difference quantile decoder, using a U-Net decoder to predict the dose difference. Three convolutional layers convert the channels to one for regression; the GPR quantile decoder outputs three quantiles of the Gamma passing rate {qαlow, q1 / 2, qαup}. The dose difference quantile decoder outputs the dose difference segmentation result and the corresponding uncertainty quantification.

[0059] Step S3 is specifically: calculating by the multi-granularity regression prior network architecture, which is optimized for multi-task learning, allowing simultaneous training of DDP and GPR prediction tasks. And using quantile regression of Pinball loss, since in the radiotherapy plan verification task, the data is extremely imbalanced, most samples are passing, and only a small number of samples are not passing, and we have an asymmetric risk preference, while most uncertainty methods are symmetrically distributed modeling (some references), so we take a non-distribution assumption quantile regression model to evaluate uncertainty.

[0060] The purpose of quantile regression is to estimate a given quantile level τ of the target variable Y under the condition that the feature variable X takes the value x. That is, we are interested in building a model The approximate conditional quantile distribution function y = Q τ (Y|X). One strategy to estimate such a model is to minimize the Pinball loss:

[0061]

[0062] To demonstrate this, we write down the expectation of the loss:

[0063]

[0064] Differentiate the above expression:

[0065]

[0066] Setting the above expression to zero gives the minimum loss at quantile The absolute loss corresponds to which is related to the median of the estimated condition, corresponding to the MAE loss. This model applies the pinball loss to output lower, median, and upper quantiles to quantify asymmetric uncertainty, typically with up α low > α

[0067] Step S4 is specifically: performing conformal prediction:

[0068] Individual deep quantile regression cannot achieve strict uncertainty quantification. Simply optimizing a loss function that incorporates uncertainty measures often leads to overestimation or underestimation problems. This method can only be used as a heuristic measure of uncertainty, severely limiting the application of deep learning in clinical practice. On the other hand, due to the complexity of the situation, doctors sometimes need quantile values that the model has not been trained on. Although some work attempts to input quantiles into the model to obtain the output of any quantile, many studies show that this method cannot produce satisfactory quantile estimates. Unlike the deep uncertainty measurement algorithm used during training described above, conformal learning uses post-calibration, which can provide model-independent finite sample guarantees for the predictions of machine learning models and is considered to achieve strict uncertainty quantification.

[0069] Deep conformal learning is generally based on split conformal prediction. Split conformal prediction requires a calibration dataset independent of the training, validation, and test datasets, and an acceptable significance level α ∈ (0, 1) set by the user. Split conformal prediction (Split CP) first needs to define the inconsistency score S(x, y) (usually a measure of prediction error) and construct the prediction set Cα(Xn+1) for the new test sample Xn+1. Its mathematical form is:

[0070] P(Y n+1 ∈ C α (X n+1 )) ≥ 1-α

[0071]

[0072] The only assumption is that the calibration and test datasets form an exchangeable set of random variables (a weaker condition than independent and identically distributed), and both are independent of the training dataset.

[0073] Conformal risk control, while conformal prediction has achieved a strict uncertainty measure, it does not take into account the highly asymmetric risks in radiotherapy plan verification. Misclassifying an effective plan as ineffective usually only requires additional computational resources to redesign the plan, while misclassifying an ineffective plan as effective can lead to potential medical malpractice and threaten patient lives. Moreover, the IMRT plan data distribution is highly imbalanced, with most plans being effective and only a few being ineffective. In this case, deep learning models tend to predict effectiveness. Therefore, more sophisticated inconsistency measures are needed to better meet clinical needs. Conformal risk control (CRC) generalizes the idea of conformal prediction to this setting, ensuring that the prediction set keeps the expected risk below a user-predefined level a. Mathematically, it is defined as:

[0074]

[0075] Unlike the training loss function that compares the true value and the point prediction, CRC l considers the loss function that compares the true value and the set prediction. If l is defined as a non-covering indicator function (binary loss), it equals 1 when the non-covering condition is met, otherwise it equals 0:

[0076]

[0077] Then CRC reduces to the definition of CP because the expected value of an indicator function of an event equals the probability of that event occurring. Therefore, CP can be considered as a special case of CRC. The probabilistic guarantee of CRC is based on the minimal assumption that the test dataset DE and the calibration dataset DC samples are independently and identically distributed, and the training dataset DT is independent of the test dataset DE and the calibration dataset DC.

[0078] CRC requires the user to set the loss function l according to the application needs, which mathematically represents the risk or error, and then set the maximum tolerable risk a. The loss function l is not used as a training loss, which means that applying CRC will not directly affect the model training or prediction algorithm. Instead, the loss function l allows the user to “encode the concept of error” in their predictions. For clarity, the loss function l will be referred to as the conformalized loss. With the preserved calibration data, one can estimate Finite-sample, model-independent, and marginal guarantees are obtained for CRC.

[0079] Finally, conformal risk control of dose difference is performed, for the DDP quantile model that generates pixel scores for the matrix regression predictor, for input X we have:

[0080] q(X) = (qk(X))ij, ij ∈ [1,..H] x [1,..W], k ∈ [alow, 1 / 2, aup]} ;

[0081] where ij corresponds to the position of a dose point in the planning matrix, k corresponds to the three quantiles. Given λ and quantiles We define the calibration interval C λ (X) and the calibration function T λ (q(X)) as follows:

[0082]

[0083] It is important to note that in the DDP task, are matrices. In this context, we keep the above definitions and λ as scalars, where the operations between matrices use matrix addition and subtraction, and the operations between a matrix and the scalar λ use scalar multiplication on the matrix. Finally, we use to denote the pixel interval in the corresponding index of the plan array.

[0084]

[0085] For the GPR task, we calibrate three criteria separately, so C λ All operations of (X) are scalar operations, and the larger λ is, the larger the interval represents:

[0086] Let Consider the loss function We assume that l takes values in a bounded interval (-∞, B], where We define:

[0087]

[0088] We consider a sequence of IMRT plans and their corresponding predicted target values (X i , Y i )i=1 n+1 The first n samples constitute our calibration set D C , and the (n+1)th sample is considered as a test sample. We denote L i (λ) = (Cλ(X i ), Y i ),

[0089] The calibration set aims to estimate the correct value and ensure that the risk remains below the maximum tolerable risk level. Given the maximum tolerable risk level We define:

[0090]

[0091] Since / is usually a proportionality or an indicator function, the upper limit B of / is usually 1. In implementation, we rearrange the terms of the above equation to obtain the following form:

[0092]

[0093] For clarity, we define Thus the expression can be written as:

[0094]

[0095] Let L i (λ) be non-increasing, right-continuous, and bounded by B < +∞. Let λmaxexist such that Li(λmax)≤α. Further let L1(λ),...,LN+1(λ) form a commutative sequence, then we have:

[0096] Since L i (λ) is monotonic in λ, can be found by an exponential search on the parameter λ, with the error range defined by the user as ∈; it is calculated by the following method:

[0097] First formula in order:

[0098]

[0099] Second formula in order, definition of the set of λ:

[0100]

[0101] Third formula in order, formula for the last used calibration coefficient λ, after obtaining the calibration coefficient λ, the calibration coefficient λ is substituted into T λ Calibration:

[0102]

[0103] α w is the weighted quantile converted to the original distribution.

[0104] For the foregoing embodiments, for the sake of simple description, they are all expressed as a series of action combinations, but those skilled in the art should know that the application is not limited by the order of the described actions, because according to the application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should know that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily necessary for the application.

[0105] In the above embodiments, the basic principles and main features of the present application and the advantages of the present application are described. It should be understood by those skilled in the art that the present application is not limited to the above embodiments, and the above embodiments and descriptions in the specification are only to illustrate the principles of the present application. Any modifications and changes made by those skilled in the art without departing from the spirit and scope of the present application shall be within the protection scope of the claims of the present application.

Claims

1. A gamma pass rate prediction conformal risk control method, characterized in that, Comprising the following steps: S1: data acquisition and preprocessing: Each sample contains two kinds of modal data: image modal and table data, specifically, all element values of the image modal are between 0 and 1, representing the relative dose intensity; all elements of the table data are the complexity indicators of the table modal; the planned table modal and image modal features are input into the multi-modal deep network to obtain the quantile features; the image encoder converts the image modal data into a feature vector with dimensions Nc×W×H, and the table encoder converts the table modal data into a feature vector with dimensions Nt•W•H; feature conversion: the extracted image features and table features are connected from different paths to form Nc+Nt-dimensional basic features Zgpr; the table modal features with the shape of Batch×(Nt•W•H) are reshaped to Batch×Nt×W×H, and then connected with the image modal data, and the quantile feature fusioner combines these features into unified basic features Zddp; Step S2 comprises the following sub-steps: S21: input the basic features Zgpr into the GPR quantile decoder, and use the regression model to predict three quantiles Yddp; S22: input the basic features Zddp into the dose difference quantile decoder, and use the U-Net decoder to predict the dose difference, and convert the channels to one through three convolutional layers for regression; S23: GPR fractional quantile decoder outputs three fractional quantiles of the gamma pass rate , and a dose difference fractional quantile decoder outputs dose difference quantile results and corresponding uncertainty quantification; S3: establish a multi-granularity prior network architecture, which allows simultaneous training of dose difference DDP and gamma pass rate GPR prediction tasks; S4: conformal prediction and conformal risk control of dose difference; step S4 comprises the following sub-steps: S41: segmentation-based conformal prediction: wherein a is an acceptable level of saliency set by the user, C α (X n+1 ) is the new test sample X n+1 constructed prediction set; Step S4 further comprises the following sub-steps: S42: conformal risk control: ； ； Step S4 further comprises the following sub-steps: S43: conformal risk control of dose difference: ； wherein, ; a is a user-set risk, and l is a calibration factor; which is calculated by the following method: The first formula in sequence: ； The second formula in sequence, the formula for using the calibration coefficient λ, after obtaining the calibration coefficient λ, the calibration coefficient λ is substituted into Tλ for calibration: ； for calibrating the interval, for calibrating the function; The third formula in sequence: ； α w is the weighted quantile transformed into.

2. A gamma pass prediction conformal risk control method as claimed in claim 1, wherein, Step S1 comprises the following sub-steps: S11: obtain 2D dose image data; S12: resample the 2D dose image data to obtain images with consistent spatial resolution; S13: cut and remove the redundant background; S14: perform normalization processing; S15: perform feature extraction and feature conversion to obtain basic features.

3. A gamma pass prediction conformal risk control method as claimed in claim 1, wherein, Step S3 further comprises the following sub-steps: Quantile regression using Pinball loss, the calculation method is: ； ； 。

Images