We reviewed 215 citations from PubMed and 118 were included in our final sample to develop these methodological guidelines (Fig. 1). Sixteen additional studies (i.e., inspiring examples from European countries) identified from InfAct project were also included to the final sample. The final sample included 134 studies using linked data and/or machine learning techniques to address various research questions either to describe or estimate health indicators in the field of health status monitoring or the evaluation of certain treatments in medical/health care. Among these citations, some guidelines were also identified to adopt the appropriate format of methodological guidelines [7, 8]. We reviewed the methodologies applied in the selected studies and developed a check-list of various steps that could be adopted systematically to calculate health indicators using linked data and/or ML-techniques.
We have developed a checklist of key methodological steps that are recommended to adopt systematically while calculating population-based health indicators and include the following items as methodological guidelines with examples of studies:
The seventh step is the data analysis that may include variable selection, application of different statistical techniques, sensitivity/uncertainty analysis and some potential issues that may encounter during the data analysis.
A. Variables selection: First, all variables with a variance equal to zero are removed. Then the ReliefF exp method could be applied (i.e., is a noise tolerant method and is not affected by features interactions) to estimate the score based on the relevance of each variable to the outcome of interest and to minimize the collinearity effect . All variables are ranked according to the ReliefF exp score and for continuous variables the score ranges from 0 to 1. For example, the cutoff score could be selected based on the visual inspection of the ordered plot of ReliefF values for all variables, called “elbow plot” approach (e.g., 0.01). In this case, the variables that had a ReliefF exp score equal or more than 0.01 could be included to train different models and the variables less than 0.01 could be excluded.
B. Statistical techniques: There are several statistical techniques that are applied to linked data either using classical statistical techniques or with ML-techniques. The former may be used for regression and later for classification purposes. In general, both of these techniques could be used to estimate, classify and predict the population health indicators or to evaluate the health care interventions according to the available linked datasets. The brief description of different techniques is reported in additional file 2.
i. Classical statistical techniques: Several classical statistical techniques were identified in the selected studies to analyze the linked data set. Following are the most commonly used techniques: linear and logistic regression, Linear Discriminant Analysis (LDA) model [12, 13], multilevel linear regression , multivariate logistic regression , multivariable hierarchical modified Poisson regression , Cox regression models , LASSO regression [18, 19], Generalized Estimating Equation (GEE) models , inverse probability weighting methods , Blinder-Oaxaca decomposition method  and Markov modelling .
ii. ML-techniques: Several ML-techniques are applied, which focused on health care research. These techniques could be adopted to population health studies. Following are the most commonly used supervised ML-techniques: linear and logistic regression, Linear Discriminant Analysis (LDA) model [12, 13], partial least square discriminant analysis model , decision tree , random forest  and Gradient Boosting Classifier [GBC] [27, 28], k-nearest neighbours/k-means , support vector machine [SVM] , neural networks , convolutional neural networks, hierarchical clustering  and XGBoost .
To develop and apply ML-techniques, following three main steps are used to train and select the final model:
a. Training various models: Some commonly used models are linear discriminant analysis, logistic regression, flexible discriminant analysis and decision trees that are applied to the training data set. The performance of each model is compared in terms of area under the receiver operating characteristic (AUC) curve. AUC curve is an evaluation metric for binary classification problems. It is a probability curve that plots TPR (true positive rates) or sensitivity against FPR (false positive rates) or I – Specificity at various threshold values and essential separates the ‘signal’ from the ‘noise’. The AUC is the measure of the ability of a classifier to distinguish between classes . The higher the AUC, the better the performance of the model at distinguishing between positive and negative classes.
b. Model validation techniques: To validate the model, k-fold cross-validation is commonly used technique. Using this technique, the given data set is split into a K number of sections/folds where each fold is used as a testing set at some point. For example, 5-fold cross validation (K = 5) where the data set is split into 5 folds. In the first iteration, the first fold is used to test the model and the rest are used to train the model. In the second iteration, 2nd fold is used as the testing set while the rest serve as the training set. This process is repeated until each fold of the 5 folds have been used as the testing set . This technique allows to estimate the performance or accuracy of the model using data not utilized during training of the model.
After the first validation of the models using k-fold cross-validation on training data set, the model performances are assessed using the test data set.
c. Selection of final model: After the model validation, the algorithm selection process is automated by giving the computer a specific metrics including sensitivity, specificity, positive predictive value, negative predictive value, F1-score and kappa. Finally, a single model is retained based on its performance, computational parsimony and its transferability to other databases.
C. Sensitivity/uncertainty analysis: After the selection of final model, sensitivity analysis is performed. This analysis refers to identifying the most influential assumptions or parameters for a given output of a mathematical computer model (i.e., the sensitivity of output by changing the inputs) or to evaluate the effect of uncertainty in each uncertain computer input variable on a particular model output . It helps to understand the relationship between input and output variables and the robustness of the results of a computing model . The most common methods are: variance-based method , elementary effects method  and regression analysis.
D. Potential issues during data analysis: During the data analysis, following are some common issues, which may encounter: missing data, imbalanced datasets and bias-variance tradeoff.
i. Missing data: In datasets (small or big), missing values are often the main issue that can introduce a substantial amount of bias, make handling and data analysis harder and strongly influence the model performance.
There are three types of missing data : 1. Missing Completely At Random (MCAR): if subjects who have missing data are a random subset of the complete sample of subjects, 2. Missing Not At Random (MNAR): if the probability that an observation is missing depends on information that is not observed, like the value of the observation itself is missing, and 3. Missing At Random (MAR): the probability that an observation is missing commonly depends on information for that subject that is present i.e., the reason for missing data is based on other observed patient characteristics.
Imputations of missing values: Imputation is a process of replacing missing values in a dataset. Following are some common approaches, which could be applied to both type of studies using classical statistical methods and ML-techniques
a. For classical statistical methods: There are three most commonly used techniques i.e., 1. listwise/complete case deletion, 2. single imputation and 3. multiple imputations. Simple/single imputation techniques (e.g. linear regression) for handling missing data (such as complete case analysis, overall mean/mode/median imputation, and the missing-indicator method) are more feasible to apply but may produce biased results. Multivariate Imputation by Chained Equation (MICE) is a multiple imputation techniques and does not avoid all bias but may be less prone to bias and does not help with MNAR [40, 41].
b. For ML-studies: There are eight most common ways to replace the missing values, which could be applied in both non-ML and ML-models: 1. rows/listwise/complete case deletion, 2. replacing with mean/median/mode, 3. assigning a unique category, 4. using most frequent or zero/constant values, 5. predicting the missing values using linear regression, 6. using algorithms which support missing values, 7. Multivariate Imputation by Chained Equation (MICE) and 8. deep learning (DataWig) [42, 43]. These techniques are also robust to MAR data.
Instead of data imputation, a novel method based on additive least square support vector machine (LS-SVM) is potentially a promising technique for tackling missing data in epidemiological studies and community health research .
II. Imbalanced datasets: Second issue is the imbalanced dataset (i.e., the number of positive and negative targets/cases/values are unequal.) that can skew in class distribution and may bias ML-algorithms. Many ML-techniques, such as neural networks, make more reliable predictions from being trained with balanced data . There are two commonly used approaches to create a balanced data set, first is the down sampling and the second one is over sampling [45, 46].
III. Bias and variance tradeoff: The third issue is the bias and variance tradeoff. The concept of bias and variance and their relationship with each other is fundamental to the true performance of supervised ML models . Bias refers to the error in the ML-model due to wrong assumptions. A high-bias model will underfit the training data. Variance refers to problems caused due to overfitting. This is a result of the over-sensitivity of the model to small variations in the training data. A model with many degrees of freedom (such as a high-degree polynomial model) is likely to have high variance and thus overfit the training data. Increasing a model’s complexity will reduce its bias and increase its variance. This is also the rational for cross-validation approaches. This balance is key to finding the most generalizable model .
Model tuning/hyperparameter tuning: It is an important step to improve the model performance and accuracy. Robust model tuning provides insight on how model structure and hyperparameters influence the model performance . Hyperparameters are adjustable parameters that must be tuned in order to obtain a model with optimal performance. There are some techniques, which are commonly used to tune the hyperparameters : grid search, random search and Bayesian optimization .
9. Study limitations: Study limitations are important and should be reported to addressing various issues for further research. Different studies using data linkage and/or ML-techniques reported some common study limitations related to data sources (linkage, quality, access and privacy), study design and statistical methods. Following are some limitations, which may influence the quality of research studies: Data linkage (e.g., different data collection methods in different areas make it difficult to link and to compare the data, lack of standard methods for data collection or inability to link some cases due to incorrect identifier); Data quality (e.g., lacking completeness of information for some routinely collected data sources, unavailability of certain information to improve the results of some analyses, lacking information on secondary cause of death, exclusion of some groups for whom no linkage could be done due to lack of identifier); Access/availability of certain data sources (e.g., readily unavailability/inaccessibility of data related to employment, education, occupation and socioeconomic status, lack of data on health inequalities at local levels); Data privacy (e.g., certain variables cannot be explored due to privacy or confidentiality issues, legal interoperability issues to link various data sources); Study design (e.g., causality, misclassification of exposure outcome, bias, age of study sample, use of isotropic model of exposure); Study methods (e.g., appropriate choice of a time window to code the variables to estimate the incidence, overfit or underfit of the model used in ML-studies, boosted algorithm may require a high computational capacity).