# Evaluating Cluster-Based Synthetic Data Generation for Blood-Transfusion Analysis
## 1 Introduction  
Health care research often is a collaborative, or even international effort. This may require exchange of data, so that an analyst can combine or compare data from different sources. When these data contain personal and sensitive information, privacy regulations and concerns may restrict data sharing, which can limit research opportunities. An increasingly popular privacy-enhancing solution is to share a synthetic version of the original data [1]. By analyzing artificial data instead of the original health care records, the privacy of the included individuals can be protected [2]. Synthetic data can be generated for a variety of purposes, such as machine learning, software testing, education, and data retention (see [3, 4] for an overview of use cases). Typically, synthetic data generation involves creating a _model_ of the data, which describes the associations and patterns that should be reproduced with artificial individuals. These individuals are generated by sampling records from the model. Multiple approaches have been proposed; frequently used methods include Conditional Tabular Generative Adversarial Networks (CTGAN) [5], Synthpop [6], and PrivBayes [7] (see [8] for an overview). Most synthetic data approaches have been evaluated using publicly available, real data (such as data from the UCI Machine Learning repository [9]) and several have been applied to use cases as well [10]. For example, [11] demonstrate the data quality (_utility_) of synthetic COVID-19 data generated with sequential trees. Although some of these applications show that analyses can be reproduced, it remains challenging to gain insight into privacy risks [3]. Assessing the magnitude of these risks is critical because synthetic data methods can leak sensitive information with the generated data [12]. Differential privacy [13] is a frequently used approach in addressing this topic, which has been implemented in combination with synthetic data generators (e.g., [14, 15]). The differential privacy framework can be used to bound the impact that one individual has on the outcome distribution of the model (i.e., synthetic data) by introducing noise. As a result, strong privacy guarantees can be made, which is one of the reasons that the approach has gained considerable popularity [16]. It remains up for debate, however, how much noise is sufficient to preserve privacy [17]. Although setting an appropriate threshold is a common challenge for privacy frameworks, this is a particular complication for differential privacy, because the parameters are known to be difficult to interpret [18]. In addition, several articles (e.g., [19, 20]) show that differential private noise can result in detrimental effects on synthetic data quality or may not succeed in avoiding privacy inference attacks. Methods without differential privacy do not impose explicit privacy-preserving techniques onto the model; synthetic data are expected to preserve more privacy because they do not consist of real people. Empirical privacy metrics can be used to quantify any remaining risks, such as attribute inference and membership inference [19, 21, 22]. These types of privacy measures do not directly assess whether the model has memorized specific, personal information, but make an approximation by considering the generated data. As a result, the outcome is subject to randomness in the synthetic data and there is a risk of misestimating privacy leakage. Recently, Cluster-Based Synthetic Data Generation (CBSDG) has been introduced, which sets itself apart from other available approaches by (1) incorporating interpretable privacy-preserving techniques into the model and (2) generating a tractable model with which privacy risks can be measured [23]. CBSDG creates clusters of similar individuals, typically containing 25 individuals, and removes all the relations between the variables within these clusters.