Evaluating the risk of endometriosis based on patients’ self-assessment questionnaires

Background Endometriosis is a condition that significantly affects the quality of life of about 10 % of reproduc- tive-aged women. It is characterized by the presence of tissue similar to the uterine lining (endometrium) out- side the uterus, which can lead lead scarring, adhesions, pain, and fertility issues. While numerous factors associated with endometriosis are documented, a wide range of symptoms may still be undiscovered.

In this study, we employed machine learning algorithms to predict endometriosis based on the patient symptoms extracted from 13,933 questionnaires. We compared the results of feature selection obtained from vari- ous algorithms (i.e., Boruta algorithm, Recursive Feature Selection) with experts’ decisions. As a benchmark model architecture, we utilized a LightGBM algorithm, along with Multivariate Imputation by Chained Equations (MICE) and k-nearest neighbors (KNN), for missing data imputation. Our primary objective was to assess the model’s perfor- mance and feature importance compared to existing studies.

We identified the top 20 predictors of endometriosis, uncovering previously overlooked features such as Cesarean section, ovarian cysts, and hernia. Notably, the model’s performance metrics were maximized when utilizing a combination of multiple feature selection methods. Specifically, the final model achieved an area under the receiver operator characteristic curve (AUC) of 0.85 on the training dataset and an AUC of 0.82 on the test- ing dataset.

The application of machine learning in diagnosing endometriosis has the potential to significantly impact clinical practice, streamlining the diagnostic process and enhancing efficiency. Our questionnaire-based prediction approach empowers individuals with endometriosis to proactively identify potential symptoms, facilitating informed discussions with healthcare professionals about diagnosis and treatment options.

Endometriosis, Questionnaire, Machine learning, Symptom-based prediction, Fertility

Endometriosis is a medical condition characterized by the presence of the endometrial tissue (the mucous mem- brane of the uterus) outside the uterine cavity. It is esti - mated that about 1 in 10 women of reproductive age, or approximately 200 million women worldwide, may suffer from endometriosis, making its prevalence significant [1, 2]. The condition can persist for decades, starting as early as a woman’s first period and continuing beyond menopause [3]. Endometriosis is a heterogeneous dis - ease with symptoms including menstrual pain, chronic pelvic pain, dyspareunia, and infertility. The severity of Open Access © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecom- mons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Reproductive Biology and Endocrinology *Correspondence: Krystian Zieliński [email protected] Anna Kloska [email protected] 1 INVICTA, Research and Development Center, Sopot, Poland 2 Department of Biomedical Engineering, Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Gdańsk, Poland 3 Department of Medical Biology and Genetics, Faculty of Biology, University of Gdańsk, Gdańsk, Poland Page 2 of 13Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 the disease is determined by the number and depth of endometrial lesions and often presents with comorbidi - ties like migraines, irritable bowel syndrome, and chronic fatigue syndrome. The implications of endometriosis are multifaceted and can vary depending on individual expe - riences. It negatively impacts various aspects of quality of life and takes a toll on mental health [1]. Chronic pelvic pain can significantly disrupt daily activities, necessitat - ing pain management strategies such as medications and lifestyle adjustments. Individuals may also experience stress, anxiety, depression, and frustration due to the unpredictability of symptoms and challenges in obtaining an accurate diagnosis and effective treatment [4]. Endometriosis is a common cause of infertility in women, often leading to adhesions and scar tissue that disrupt fallopian tube and ovarian function. This often necessitates fertility treatments like in  vitro fertiliza - tion (IVF) for conception. Given a woman’s biologically limited reproductive timeframe, a quick diagnosis of endometriosis can significantly impact her chances of conceiving [5]. Currently, the typical diagnostic methods for endometriosis include patient interviews and ultra - sound imaging (USG). However, USG may not always provide a complete and accurate diagnosis, especially in cases involving endometriosis in the uterus or ovaries. Often, confirmation of the diagnosis requires invasive and costly procedures such as laparoscopy or, in the case of extraperitoneal endometriosis, magnetic resonance imaging (MRI) [6]. Consequently, treatment decisions, including those related to IVF, often rely primarily on the patient’s medical history. Numerous medical factors correlate with the likelihood of developing endometriosis, although a wide range of symptoms may still be undiscovered. For instance, early menarche [7–9] and shorter menstrual cycles [10] have been associated with a higher risk of endometriosis. Con- versely, the use of oral contraceptive pills has been linked to a reduced risk [11]. Additionally, a consistent inverse correlation between body mass index (BMI) and endo - metriosis has been observed, possibly due to hormonal variations among women with different body weights [7]. However, the relationship between oral contracep - tive pills and endometriosis risk is complex. Some stud - ies indicate a decreased risk among current users but an increased risk among past users. Despite this, oral contraceptive pills are frequently prescribed to alleviate endometriosis-related pain, suggesting their effectiveness in suppressing symptoms of the condition [12]. Despite recent advancements in identifying risk fac - tors for endometriosis, the field still faces the constraint of requiring surgical diagnosis to confirm the disease. During patient examinations, doctors gather a wealth of information, some of which may lead to conflicting

about an endometriosis diagnosis. Conse - quently, there is a pressing need for a unified method that accounts for valid factors and calculates the likelihood of having endometriosis. The scientific community has demonstrated a growing interest in developing methods for diagnosing endome - triosis [13]. There is an increasing reliance on modern statistical methods, such as machine learning, to enhance this process. The development of a predictive model for endometriosis diagnosis could enable healthcare provid - ers to identify the condition earlier and more accurately, thereby improving patient outcomes and optimizing the use of healthcare resources. However, the development of such a predictive tool presents several challenges, includ - ing the availability of suitable training data. In this study, we administered a custom question - naire, meticulously crafted by experienced reproduc - tive medicine specialists, to patients before their initial visit to an infertility treatment clinic. We analyzed the data collected from these questionnaires to identify the most crucial features for predicting endometriosis. Both gynecologists and machine learning techniques were employed to identify these key features. The primary goal of our research was twofold: first, to assess the feasibil - ity of training a predictive model for endometriosis, and second, to compare the significance of these features to those identified in existing studies. Finally, we provided clinicians with a model that predicts the likelihood of endometriosis, complete with an explanation.

Ethics and consent to participate The study is a retrospective study based on anonymized datasets and therefore does not require the consent of the ethical committee or the patients. Dataset The study utilized retrospective data from the Invicta database, which maintains comprehensive patient records. The study group comprised patients diagnosed with endometriosis by medical professionals at Invicta clinics, in accordance with the standards set by the European Society of Human Reproduction and Embry - ology (ESHRE). The control group included both infer - tility patients not diagnosed with endometriosis and egg donors without known fertility issues. Relevant attributes considered potentially valuable predictors were extracted and merged into a single dataset. The dataset was lim - ited to self-assessment questionnaire responses collected from June 2018 to August 2022 and included attributes characterizing patients, visits, questionnaire questions, and responses. A total of 13,933 questionnaires were pro- cessed. The questionnaire contained 272 patient-related Page 3 of 13 Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 questions, 134 of which were selected for further analy - sis; the rejected questions pertained to information such as e.g., eye color or hair shape. To process the data, questionnaire answers were cat - egorized into groups for which processing functions were developed. Each function converted the question - naire answers into a table where columns represented questions and answers. For questions with n possible answer options, n columns were generated. The answer formats in the questionnaire data included single-select, binary, multi-select, date, numeric, and mixed. Quantita - tive variables were bounded by minimum and maximum thresholds determined by experts to eliminate extreme values. Categorical variables were transformed into a dichotomous form, and ordinal coding was used for ordi- nal variables. Attributes conveying equivalent informa - tion from different questionnaire questions or answers were merged. The resulting data frame consisted of 204 columns and 11,819 rows, with the visit ID serving as the index. Note that the number of columns exceeds the number of questions because some questions were of the multi-select type; thus, the number of features increased after one-hot encoding. The target feature in this study was the diagnosis of endometriosis, obtained either from the patient’s medical history or the qualifying questionnaire routinely admin - istered at the outset of assisted reproductive technology procedures at Invicta clinics. Using regular expression matching operations, we scoured the database for instances of endometriosis diagnosis and subsequently integrated these findings with the responses from the qualification questionnaire. This resulted in a target fea - ture consisting of 910 labels denoting an endometriosis diagnosis. Comprehensive statistics characterizing the study population are presented in Table 1. Feature selection Feature selection is a critical step in machine learning because it enhances model performance, reduces compu- tational complexity during training, and improves result interpretability. The quality of the features used to train a model can significantly affect its performance. Choos - ing the most informative features not only improves the model’s accuracy but also minimizes overfitting and prevents the model from learning irrelevant or noisy patterns in the data. Moreover, it considerably reduces the computational complexity of the training process, thereby expediting training faster, especially for large datasets with numerous features [14]. Table 1 Basic statistics describing the study population. For features with binary responses, 0 indicates a negative answer, while 1 indicates an affirmative response to a questionnaire question Feature % of affirmative or Mean Data available Min Max Patient age (years) 34.69 11819 20 55 Appendectomy 21.27% 4433 0 1 Caesarean section 4.85% 4433 0 1 Drainage fallopian tubes 9.42% 11363 0 1 Infertility diagnosis 20.39% 11446 0 1 Hernia 3.16% 4433 0 1 Pelvic inflammatory disease (PID) 1.42% 11456 0 1 Few months of trying to get pregnant 29.87% 11819 0 1 Less than 3 years of trying to get pregnant 63.39% 11819 0 1 Over 3 years of trying to get pregnant 3.87% 11819 0 1 Ovarian cysts 11.69% 11287 0 1 No periPelvic pain 11.52% 11819 0 1 Moderately severe periPelvic pain 45.84% 11819 0 1 Very strong periPelvic pain 16.45% 11819 0 1 Recurrent vaginitis 13.53% 11456 0 1 Reduction of sex drive 8.10% 11150 0 1 Removal of ovarian cysts 3.54% 11284 0 1 Average menstrual cycle length (days) 28.66 10659 18 40 Body mass index (BMI) 23.50 10874 15.9 46.9 Number of pregnancies 0.62 4321 0 7 Number of miscarriages 1.11 4321 0 10 Endometriosis 10.46% 11819 0 1 Page 4 of 13Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 In our study, we conducted experiments using the complete dataset and applied three different feature selection methods, complemented by experts’ decisions and statistical analysis. A key strategy was multistage feature selection to ensure that the trained models were not overfitting due to the inclusion of non-informative features. We also took additional measures, including specific hyperparameter settings and 5-fold cross-val - idation, and performed 25 replications of the process using different seeds to split the data into 5 folds, in order to evaluate overfitting. Furthermore, the features selected via statistical methods enabled us to compare existing knowledge with potential endometriosis pre - dictors that might not have been previously identified. The process of feature selection is visualized in Fig. 1 . The first step in feature selection involved the appli - cation of the Boruta algorithm [15– 17] to the dataset. Originally based on the Random Forest machine learn - ing model, the algorithm compares the importance of each feature in the original dataset with the importance of that same feature when randomly shuffled. To begin, the original dataset was duplicated and appended with randomly shuffled copies of each feature. A Random Forest model was then trained on this augmented data - set. This model assigned an importance score to each feature based on how well it separated the target vari - able. The algorithm compared the importance score of each feature with the scores of its shuffled counterparts. If a feature’s importance score significantly exceeded that of its shuffled copies, it was deemed significant. Features not classified as significant were removed, and the process was repeated until only significant features remained. The Boruta algorithm is particularly useful for iden - tifying relevant features in high-dimensional datasets, where the number of features greatly exceeds the number of observations. It can identify complex feature interac - tions and select features that are relevant for predicting the target variable. Furthermore, the Boruta algorithm is resistant to noisy or redundant features, making it a robust method for feature selection. In the next step, all original variables, along with their Boruta rankings as additional information, were pre - sented to three experts. Their task was to evaluate the relevance of these attributes for predicting endometriosis based on their expertise. The experts used a fixed map - ping system to label each variable. Variables were marked with ‘-1’ when experts were certain that they did not cor- relate with endometriosis. Attributes marked with ‘0’ were considered to possibly affect prediction, while those marked with ‘1’ were highly recommended for prediction. A set of variables, consisting of those marked with ‘0’ and ‘1’ , was then used to determine feature importance. Addi- tionally, this expert classification allowed us to compare attributes identified by experts and those that were top- ranked by machine-learning algorithms. Another technique used in the study to determine the most important factors for endometriosis was Recur - sive Feature Selection (RFE) [18, 19]. The RFE algorithm recursively eliminates features from the dataset and ranks the remaining ones based on their importance. The rationale behind RFE is that by removing the least Fig. 1 Diagram of feature selection process incorporated in the study Page 5 of 13 Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 important features, the model’s performance will either remain unchanged or improve, as it will focus on the most significant features. As differences between single model runs may vary, the process of RFE in the study can be described in the fol - lowing steps: 1. It first trains a model on the entire set of features and calculates the importance of each one. 2. Features are ordered according to their Boruta score. The least important feature as identified by the Boruta algorithm, is removed. A model is then trained 25 times using different initial random states. 3. At each step, the model’s performance is evaluated using the area under the receiver operator character - istic curve (AUC-ROC score). 4. Using statistical test (Kolmogorov-Smirnov) [20], the distribution of AUC-ROC scores for the model trained on the current subset is compared with that of the model trained in the previous step 5. If the test shows that there are no statistical differ - ences between model scores, a feature is removed from the training set. 6. The algorithm stops when all of the features have been tested. Model As a benchmark model architecture, a gradient boosting technique [21] was applied. We selected the LightGBM [22] implementation of the algorithm because it is char - acterized by high performance and has built-in capabili - ties for handling missing data. In the context of medical questionnaires, handling missing data is a major concern. LightGBM can manage missing values by treating them as separate categorical values. When building decision trees, the algorithm creates a separate branch for missing values and assigns weights to them based on their rela - tive importance to the target variable. Training the algo - rithm is an iterative process that begins by initializing the model with a single decision tree that has a single root node containing the mean value of the target variable. The algorithm then iteratively trains a series of decision trees. Each new tree is trained to correct the errors made by its predecessors. During each iteration, the algorithm calculates the gradients and Hessians of the loss func - tion with respect to the predicted values and updates the model accordingly. To determine splits in each tree, the algorithm searches for the best-split point that maxi - mizes the reduction in the loss function. To prevent overfitting, various regularization methods [23] were incorporated. These include feature bagging, data bagging, l1 and l2 regularization on weights. To assure weak learners, the maximum depth and the maxi - mum number of leaves for each tree were set. The hyperparameters of the model were determined using random grid hyperparameter optimization [24]. This technique allows for the identification of the best hyperparameters for a machine-learning model by ran - domly sampling values from a predefined range of hyper- parameters. This method was used in conjunction with cross-validation to find the hyperparameters that pro - duced the highest cross-validation score. Random grid samples are combinations of parameters drawn from a defined parameter space. In each iteration, the selected hyperparameters were used to train and evaluate the model using cross-validation. The performance of the model was evaluated based on the AUC score. The random grid search method can efficiently explore the hyperparameter space and find a suitable set of hyperparameters for the model without the need for an exhaustive search across the entire space. This approach is particularly useful for high-dimensional search spaces where an exhaustive search is computationally infeasible. Listing 1 Hyperparameter space used in the studyMissing data imputation To test other types of model architectures, missing values in the dataset had to be imputed. The task was exception- ally complex due to various potential reasons for miss - ing values, e.g., patients may have opted not to disclose certain information for personal reasons, some ques - tions were dependent on other answers (e.g., a patient who never took a particular medication wouldn’t answer dosage-related questions), or certain questions were not available in specific versions of the questionnaire. To handle this, we compared the results of imputation meth- ods using the mean and median with iterative methods such as the Multivariate Imputation by Chained Equa - tions (MICE) [25] and k-nearest neighbors (KNN) algo - rithm [26]. For the MICE algorithm, we used the IterativeImputer implementation available in sklearn [27]. This iterative

imputes missing values in a dataset by modeling each feature with missing values as a function of the other features in that dataset. The algorithm starts by initializ - ing the missing values with an initial value, such as the Page 6 of 13Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 mean or median of the feature. It then iteratively imputes the missing values by modeling each feature with miss - ing values as a function of the other features. The imputa- tion is done round-robin, where each feature is imputed in turn. For each feature with missing values, a regression model is trained using the other features in the dataset as predictors. The model is used to predict the missing values for that feature. While in the original MICE paper, the algorithm used linear regression to determine miss - ing values, IterativeImputer allows the use of other archi- tectures. In this study, we opted for the Bayesian Ridge algorithm [28] due to its reduced computational time. The algorithm repeats the feature model training and imputation steps for a predefined number of iterations or until the imputed values converge. The KNN algorithm can also be used for missing data imputation. It identifies the nearest neighbors for each observation with missing values and uses the feature val - ues of those neighbors to determine the missing value. The algorithm identifies the k-nearest neighbors for each observation based on a selected distance metric. Next, it imputes the missing value by taking the average (for continuous variables) or the mode (for categorical vari - ables) of the values of k-nearest neighbors. This process is repeated for each missing value in the dataset. One of the advantages of using the KNN algorithm for missing data imputation is its ability to handle both categorical and continuous variables. Additionally, KNN works well for datasets with nonlinear relationships between features. Software This study was conducted on the Ubuntu 20.04.5 LTS version of the operating system, with an 11th Gen Intel®Core™ i7-11800H @ 2.30GHz × 16 processor and a GPU GeForce RTX 3050 Ti Mobile. Python version 2.7.18 was used for the study.

Results of feature selection Out of 258 initial features, 20 were selected by the Boruta algorithm, 67were chosen by experts, and 165 were picked using the RFE algorithm. Interestingly, three fea - tures selected by Boruta-namely frequent urination, headaches, and reduction of sex drive-were not chosen by RFE. Additionally, experts did not select 12 features that were picked using the Boruta algorithm and 13 features considered important by the experts were not selected by any of the feature selection methods; these included ovarian cysts, hysteroscopy, appendectomy, hernia, fallopian tube drainage, disturbing symptoms related to the urogenital system, feeling overall healthy, spooning, cytomegaly, Caesarean section, and tonsils. A full list of selected features by each method is available at Additional file 1. To optimize the parameters of the LightGBM classifica- tion model, a random grid search was run for each subset of features. The algorithm generated 1,000 different ver - sions of the model. The best parameters were then cho - sen based on a 3-fold cross validation AUC score. Using the selected hyperparameters shown in Table  2, models were trained using 5-fold cross-validation. The performance metrics are shown in Table 3. To ensure the robustness of the results, experiments were repeated 25 times, each with a different random seed for cross-vali - dation split. Based on the model’s results, the best error metrics were obtained using the subset of features selected by RFE, with an average AUC above 0.81. In contrast, the Table 2 Model hyperparameters selected for models trained on a subset of features selected by a given method

colsample bytree learning rate max bin max depth num leaves reg alpha reg lambda subsample subsample freq Boruta 0.50 0.10 39 3 31 0.20 0.20 0.30 51 Experts’ decisions 0.29 0.03 46 6 20 0.05 0.07 0.76 48 Recursive selection 0.28 0.05 53 5 9 0.10 0.07 0.75 47 Table 3 Metrics obtained by models trained on a subset of features selected by a given method

Precision Recall Specificity Accuracy F1 weighted Test AUC Train AUC Matthew’s coefficient Boruta 0.26 0.69 0.77 0.76 0.80 0.80 0.81 0.32 Experts’ decisions 0.23 0.69 0.73 0.72 0.77 0.78 0.85 0.28 Recursive selection 0.25 0.74 0.73 0.73 0.78 0.81 0.85 0.31 Page 7 of 13 Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 model trained on features selected by experts achieved the worst error metrics, with an AUC below 0.78. These error metrics are shown in Table   3. Although the Boruta algorithm selected only 20 important col - umns, the model trained on this subset achieved an AUC of 0.8, comparable to that obtained for recur - sive feature selection. The model trained on features selected by experts had the lowest evaluation metrics. The model trained with RFE-selected features had the highest recall, while the model trained with Boruta- selected features achieved the highest Matthew’s coef - ficient. Additionally, a comparison of the AUC metrics obtained for the train and test subsets shows that the model trained with Boruta-selected columns is the most robust. The difference between the AUCs calcu - lated on the train and test subsets was only 0.01. In con - trast, the overfit was 0.07 and 0.04 for models based on expert-selected and RFE-selected features, respectively. While higher, these levels of overfit are still acceptable. Using different random seeds did not impact the AUC metrics for any of these models; the difference between the first and third quantiles of the results was below 0.005, confirming the method’s stability. Imputation techniques and final model The study demonstrated that the choice of feature sub - sets significantly affects the performance of the models. To fully understand the impact that different imputation techniques might have on the modeling, experiments were conducted separately for each column subset identi- fied in previous steps. Three different imputation meth - ods were used: KNN, mean, and MICE, and each was applied to all feature subsets. The results, presented in Fig.  2, reveal very low variability in the models’ perfor - mance depending on the imputation method used. Most differences in performance occur due to varying feature sets. Using KNN and MICE resulted in a slight decrease in AUC for feature subsets selected by the Boruta and expert decision methods, as compared to models that did not employ any imputation. Imputing average val - ues into each feature did not impact the models perfor - mance. Overall, the findings suggest that imputation does not always improve model performance. However, using these techniques allows researchers take advantage of different models that are otherwise unable to handle missing values. Since the optimal column subset selection was dis - puted, an additional model was trained to supplement Fig. 2 Boxplot of the area under the curve (AUC) values for different cross-validation splits after imputation with different methods. The difference between Q1 and Q3 for most cases is less than 0.01; therefore, the model’s training process can be evaluated as stable. There is a much bigger difference between methods of feature selection than between imputation techniques. In each case, the recursive selection was superior compared to Boruta. Experts’ decisions appear to be the least effective method of feature selection Page 8 of 13Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 the initial results. The final feature subset included all features selected by the Boruta algorithm, as well as the top 20 features ranked by SHAP values in other models but not included in the Boruta subset of features. Nine of the newly added features had been selected by experts. These were: BMI, patient age, longest menstrual cycle length, shortest menstrual cycle length, average men - strual cycle length, number of pregnancies, number of miscarriages, length of trying to get pregnant, oral con - traceptive pills. Additionally, featrues that were highly ranked in the model trained on the RFE feature subset were included, i.e., Pelvic inflammatory disease (PID) and First menarche. The new feature subset comprised 30 columns. For this selected subset of features, the following GBM parameters were chosen: { "colsample_bytree": 0.49, "learning_rate": 0.03, "max_ bin": 41, "max_depth": 4, "num_leaves": 25, "reg_alpha": 0.2, "reg_lambda": 0.2, "subsample": 0.83, "subsample_ freq": 42 }. Models were trained 25 times using different seeds in 5-fold cross-validation to ensure the stability of the results. For each run and each split, evaluation metrics were calculated for both the training and testing sub - sets. This resulted in 5 train evaluation metrics and 5 test evaluation metrics for each of the 25 runs. Next, the error metrics from each run were averaged. The selected model was explained using Shapley additive explanations (SHAP) values to assess the impact of each feature on the model’s output (Fig. 3). To further analyze the impact of the features, a correlation matrix was calculated. For features on interval and ratio scales, Spearman’s corre - lation coefficient was used, while Matthew’s correlation coefficient was used for binary features (Supplementary Table 1). The highest correlation was noticed for frequent urination, reduction of sex drive, and urinary-genital system symptoms. Among features on the ratio scale, the strongest correlation was found between the average menstrual cycle length and the shortest/longest men - strual cycle length. The model achieved the highest performance met - rics among all experiments (Table   4) demonstrating the advantages of using a combination of multiple methods for feature selection. Features with the highest posi - tive correlation with endometriosis included ovarian cysts, diagnosed infertility, high pelvic pain, disturbing Fig. 3 The 20 most important features are sorted by the magnitude of the SHapley Additive exPlanations (SHAP) values. Plots display the SHAP values for each feature of a given observation in a horizontal orientation. Each dot on the plot represents an individual observation and the position of the dot on the x-axis represents the magnitude of the SHAP value. The color of the dot represents the value of the corresponding feature for that observation, with red indicating high feature values and blue indicating low feature values Page 9 of 13 Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 symptoms related to the urogenital system, and reduc - tion of the sex drive. Features that negatively correlated with endometriosis included appendectomy, high BMI, tonsils, hernia, Caesarean section, and shorter menstrual cycle. The impact of patient age on endometriosis diag - nosis appears to be non-monotonic and may depend on other features.

In this study, we demonstrated that a preliminary diagno- sis of endometriosis can be made based on a simple ques- tionnaire containing specific questions. We identified the top 20 predictors of endometriosis, including some previously overlooked features like Cesarean section, ovarian cysts, and hernias. We also confirmed a strong correlation between menstrual pains and the likelihood of having endometriosis. Additionally, our approach of multi-step feature selection improved the models robustness. The delayed diagnosis of endometriosis underscores the need for a simple and reliable screening tool to iden - tify women at higher risk. Previous studies have used questionnaires completed by patients as initial screen - ing tools for endometriosis [29]. These questionnaires often included detailed inquiries about factors such as the age of menarche, cycle duration, dysmenorrhea, pain descriptors, dyschezia, urinary symptoms, ovarian cysts, diagnosed infertility, appendectomy, and pelvic pain diar- rhea [30–34]. Although several studies have attempted to develop mathematical models based on self-administered or preoperative questionnaires to predict endometriosis [35, 36], some of them were complex or required addi - tional diagnostic parameters (e.g., ultrasound and pelvic examination), making them impractical for patient self- completion. Additionally, certain measures were limited to specific populations (e.g., women with site-specific endometriosis or deep-infiltrating endometriosis) or had lower accuracy rates for early-stage endometriosis. In our study, similar features were confirmed to have high pre - dictive value. Furthermore, our findings revealed addi - tional symptoms such as Cesarean section, ovarian cysts, and hernia, which had not been previously considered predictors. The primary challenge for applying machine learning algorithms in healthcare is the need for large amounts of high-quality data. For a relatively rare condition such as endometriosis, a prediction model relies on accurate and representative patient data. A prediction model must be rigorously tested and validated in a variety of patient populations to ensure that it is accurate and reli - able. Obtaining this requires access to large and diverse patient populations. Datasets from questionnaires can be challenging for several reasons - missing data, inconsist - encies, and quality issues. Missing data can be caused by questionnaire non-responses or invalid responses. Ques - tionnaires may also have inconsistencies in the data, such as duplicate responses or responses that do not match the question, while quality issues can arise from ques - tionnaire design, respondent bias, or other factors. To ensure the reliability and validity of the data, it is essen - tial to identify and correct these issues. Additionally, the whole process of training the model using multiple fea - ture selection methods and hyperparameter optimization can have a high time complexity. It is crucial to emphasize endometriosis’s diverse trajec- tory throughout a woman’s life. This diversity is reflected in the wide range of symptoms, disease progression, and treatment responses that women with endometriosis experience [37]. To effectively track the complex longitu- dinal changes in endometriosis features, it is important to leverage machine learning models tailored for longi - tudinal data, such as recurrent neural networks (RNNs) or specific survival analysis models. These models can capture the dynamic relationships between features over time and identify patterns that may be difficult to detect using traditional statistical methods. In the feature stud - ies by leveraging machine learning models, researchers can gain a deeper understanding of the inherently diverse trajectory of endometriosis and develop more personal - ized and effective treatment strategies. The results of our study were compared with a simi - lar study predicting endometriosis based on data from the UK Biobank [38]. It should be noted that this study included a more comprehensive range of patient medical and genetic data; therefore, comparing the two studies at the feature level could be biased. Of the top 20 features identified in the study based on the UK Biobank data, only seven were also included in the top 20 of the features of both studies (Table   5). In our dataset, eight features that were indicated as important in other studies were Table 4 Metrics obtained by the final model Subset Precision Recall Specificity Accuracy F1 weighted AUC Matthew’s coefficient Train 0.29 0.76 0.78 0.78 0.82 0.85 0.37 Test 0.26 0.73 0.76 0.76 0.80 0.82 0.33 Page 10 of 13Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 not available for the current study. Additionally, five fea - tures were excluded during the feature selection process. Compared to the study [38], the length of the menstrual cycle, the number of live births, and pelvic inflammatory disease were noticeably less important for prediction in our study. On the other hand, diagnosed infertility had a higher impact on the model’s output. The study based on the UK Biobank data showed a low impact of the BMI on the prediction, whereas the model trained on Invicta data this feature was ranked higher. Neither study identified The age of menarche as a strong predictor of endome - triosis. When comparing AUCs, the model trained with INVICTA data performaned slightly better, with an AUC of 0.82 against the 0.79 for the UK Biobank data. Comparison of other metrics, as shown in Table  6, highlights the different approaches in both studies for selecting the optimal threshold between labels “sick” and “not sick” . In the current study, the optimal thresh - old was selected as the point closest to (0,1) on the ROC curve. Higher recall scores mean fewer false nega - tive predictions, i.e., fewer sick patients misclassified as patients without endometriosis. If the model is to be used as a screening tool, this approach would be benefi - cial for patients with the lowest probabilities of having endometriosis, as additional medical exams would not be necessary. Additionally, patients with a higher prob - ability of having endometriosis could undergo further examination to confirm or exclude the diagnosis. Based on discussions with practitioners, it is advised to pro - vide both the probability of diagnosis and the percent - age of patients who had the same or lower probability of endometriosis. This generally makes the interpreta - tion of scores easier for gynecologists. Table 5 Feature comparison between models based on data from the UK Biobank and INVICTA questionaries. It should be noted that certain features are absent in the INVICTA dataset due to their non-inclusion in the patient questionnaire, either in the specified format or any other form that would enable a direct match with corresponding features in the UK Biobank data Feature UK Biobank INVICTA length of menstrual cycle 0 12 age at first live birth 1 Not available in the data n92 - excessive, frequent and irregular menstruation 2 Not selected to the modelling number of live births 3 16 n83 - noninflammatory disorders of ovary, fallopian tube and broad ligament 4 Not available in the data stomach/abdominal pain for 3+ months 5 Not selected to the modelling source of report of k58 (irritable bowel syndrome) 6 Not available in the data UK Biobank assessment centre 7 Not available in the data pelvic inflammatory first 8 <20 n94 - pain and other conditions associated with female genital organs and menstrual cycle 9 4 degree bothered by menstrual cramps 10 4 year of birth 11 15 estrogen exposure 12 Not available in the data n97 - female infertility 13 3 n81 - female genital prolapse 14 Not available in the data irregular cycle 15 Not selected to the modelling n84 - polyp of female genital tract 16 Not selected to the modelling n73 - other female pelvic inflammatory diseases 17 <20 o70 - perineal laceration during delivery 18 Not available in the data n85 - other noninflammatory disorders of uterus except cervix 19 Not available in the data body mass index (BMI) 20 6 Table 6 Metrics obtained by the final model Study dataset Precision Recall Accuracy F1 AUC % of endometriosis UK Biobank 0.50 0.30 0.92 0.37 0.78 0.04 Invicta 0.26 0.73 0.76 0.38 0.82 0.10 Page 11 of 13 Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 In the fields of medical research and healthcare, the availability of diverse datasets from various medical cent - ers offers valuable opportunities for developing predic - tive models and extracting meaningful insights. However, comparing the results of modeling across these data - sets presents several challenges resulting from varia - tions in data collection protocols, patient demographics, and healthcare practices. Such differences can intro - duce inconsistencies in model performance and hinder the generalizability of findings. Therefore comparing the results of the two studies can result in misleading conclusions. Our study has several limitations. The first is the use of a non-validated questionnaire; however, its reliability and validity as a data collection tool is guaranteed by its long-term use in the clinical setting. Over 15 years of use and feedback from gynecologists working with it suggest that the tool is robust and has been refined over time for clinical relevance. The questionnaire covers a wide range of topics relevant to infertility, including phenotypic fea - tures, treatment history, general health (including men - strual cycle, drugs, and lifestyle), and genetic factors, and it includes a statement for patients to confirm the truth - fulness of their answers adding a level of accountability to the data. It has to be filled out using a patient’s online account and the system has built-in forms of data vali - dation. The questionnaire is integrated into the clinics’ hospital information system, making it accessible to the treating physician and ensuring it is part of the patient’s medical record. As each medical center may follow its procedures for data gathering, including variations in data formats, missing data handling, and feature engineering tech - niques the differences resulting from those aspects can introduce bias and make direct comparisons challenging. To address this issue, it is crucial to establish standard - ized protocols for data collection across medical centers. Standardization should include the selection and defi - nition of variables, data preprocessing techniques, and handling of missing data. By adopting standardized pro - cedures, the comparability of datasets can be improved, enabling more meaningful comparisons of modeling results. Additionally, this would enable researchers to use transfer learning in the larger spectrum of domains. Another limitation of our study is its reliance on ret - rospective data and diagnoses provided by medical professionals. Although these diagnoses adhere to the guidelines of the European Society of Human Reproduc - tion and Embryology (ESHRE), it should be noted that not all might have been based on histological findings, traditionally considered the gold standard for diagnosing endometriosis; unfortunately, these data were not avail - able in our dataset. However, current ESHRE guidelines indicate that advances in imaging technologies have necessitated a reevaluation of this gold standard [39, 40]. In this light, it is possible that not all of those diagnoses were based on histological findings as it is a standard that requires a serious medical intervention whose risks often outweigh the risks of starting treatment, and hence in a clinical setting it is not always employed. Due to these

of our retrospective data, we were unable to categorize endometriosis by type and stage in the study group to explore the sensitivity of the final model in response to endometriosis type. However, we acknowl - edge that this would be a valuable direction for future research. The use of convenience-based data integration for parameter selection excluding some traits such as eye color can also be recognized as a limitation of the study. Recent findings found an association between certain pigmentation traits, such as green eyes and blonde/light brown hair [41] or blue eyes [42] and endometriosis risk potentially hinting at genetic or environmental factors contributing to endometriosis development. Exploring these traits may also have implications for understanding the disease’s pathogenesis. A limitation also lies in the use of experts’ knowledge to identify a list of features important for predicting endo - metriosis. Such data should be approached with caution. Experts’ decisions can be subjective and may vary among individuals. Errors in judgment or personal biases can affect their assessments.

The use of patient-completed questionnaires as screen - ing tools for endometriosis holds the potential to iden - tify individuals at increased risk. Patient-based screening tools combined with ML can lead to empowering patients to self-identify symptoms and consult their symptoms with healthcare professionals. Our study demonstrates that research is still required to determine clinical factors associated with endometriosis, not only to investigate the common, medically-confirmed factors but also to pinpoint new ones. Ongoing validation and research are essential to establish an effective and accurate screening tool for endometriosis. Abbreviations AUC-ROC Area under the receiver operator characteristic curve BMI Body mass index IVF In vitro fertilization RFE Recursive Feature Selection KNN K-nearest neighbors MICE Multivariate imputation by chained equations MRI Magnetic resonance imaging PCOS Polycystic ovary syndrome PID Pelvic inflammatory disease SHAP SHapley Additive exPlanations Page 12 of 13Zieliński et al. Reproductive Biology and Endocrinology (2023) 21:102 USG Ultrasound imaging Supplementary Information The online version contains supplementary material available at https:// doi. org/ 10. 1186/ s12958- 023- 01156-9. Additional file 1. Supporting information. Additional file 2. Supplementary Table 1. Correlation matrix.

None. Authors’ contributions Conceptualization: K.Z., J.R., D.Drz.; Data curation: K.Z., D.Dra.; Formal analysis: K.Z., D.Dra.; Investigation: K.Z.; Methodology: K.Z., J.R.; Project administration: D.Drz.; Software: K.Z.; Supervision: J.R., M.K.; Validation: K.Z.; Visualization: K.Z., D.Dra.; Writing-original draft: K.Z., D.Dra., A.K.; Writing-review & editing: K.Z., A.K. All authors read and approved the final manuscript. Authors’ information None. Funding The research was co-financed by the National Center for Research and Development as part of the project: an AI-based software platform aiding the diagnosis and treatment of infertility issues. Co-financing agreement No. POIR.01.01.01-00-0390/21-00. The funders had no role in study design, data collection or analysis, the decision to publish, or the preparation of the manuscript. Availability of data and materials INVICTA Fertility Clinics do not allow public disclosure of patient data used in this study. In case of additional questions, please contact the authors or INVICTA Research and Development Center([email protected]). The source code is available at the GitHub repository (https:// github. com/ CBR- Invic ta/ Endom etrio sis)-notebooks contain results and plots generated using the dataset. Declarations Ethics approval and consent to participate Conducted as a retrospective study, our research adhered to the Declaration of Helsinki’s principles. We secured written informed consent from all partici- pants. To ensure privacy, all personal data were de-identified. Consent for publication Not applicable. Competing interests The authors of this manuscript have the following competing interests: K.Z., D.Dra., M.K., D.Drz, and A.K. are employees of INVICTA, clinics and medical laboratories for infertility treatment. The affiliation does not affect the authors’ impartiality, adherence to journal standards and policies, or availability of data. Received: 6 September 2023 Accepted: 23 October 2023

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