# Comparative Analysis of Local Differential Privacy Schemes in Healthcare Datasets
## 1 Introduction  
In the ever-evolving realm of healthcare technology, the implementation of robust privacy safeguards has become indispensable. A pivotal approach in this regard is the utilization of local differential privacy, a technique devised to safeguard individual-level data while simultaneously facilitating the extraction of valuable insights from aggregated datasets. As the healthcare industry increasingly embraces digital solutions and data-driven decision-making, the necessity to strike a balance between innovation and the protection of sensitive patient information has become more pressing than ever. Nowadays, our data are multidimensional, making it possible to extract vast amounts of information. For instance, a healthcare institution with a dataset tracking patient activities can glean valuable insights. A patient's interactions within a hospital environment, treated as high-dimensional data, can be analyzed to uncover patterns such as patient admission and discharge times, the duration of medical procedures, staff interactions, and preferred modes of transportation within the hospital premises, among other relevant metrics. In recent years, safeguarding personal data privacy has gained heightened significance, driven by the expanding array of industries, not limited to healthcare, that actively collect and store our information. A significant privacy concern revolves around data publishing, and one approach to tackle this issue is through Central Differential Privacy (CDP) [1]. This method facilitates the release of sensitive data, permitting statistical analysis while preserving individual privacy. However, it is important to note that in CDP, users are required to share their original information with a central server. In contrast, LDP aims to address this limitation. Unlike CDP, users in LDP do not need to place trust in the communication channel or central server. Instead, they encode their data and introduce random noise before transmitting it to the central server. This process effectively protects users' privacy while still enabling the central server to compute the distribution of user statistics. [PERSON] et al. [2] and [PERSON] et al. [3] provide overviews of LDP technology, summarizing and analyzing state-of-the-art research in the field. [PERSON] [3] provides an overview of existing works that serves as a foundational resource for exploring emerging challenges in the future. These challenges include the relaxation of LDP, privacy amplification, and the development of solutions tailored for small populations. Meanwhile, [PERSON] [2] investigates the impact of collecting multiple sensitive attributes under LDP on fairness. They experiment with several LDP approaches, including Generalized Randomized Response (GRR), Binary Local Hashing (BLH), Optimal Local Hashing (OLH), RAPPOR, Optimal Unary Encoding (OUE), Subset Selection (SS), and Thresholding with Histogram Encoding (THE) to train Machine Learning (ML) models. The models are then evaluated using several metrics, including the F1-score, area under the receiver operating characteristic curve (AUC), Disparate Impact (DI), Statistical Parity Difference (SPD), Equal Opportunity Difference (EOD), and Overall Accuracy Difference (OAD). The differences between [PERSON] [2] and our work are presented in Table 1.  
RAPPOR [4] is one of the most well-known LDP approaches; it was developed by Google as an extension of Google Chrome, which collects process names and homepages from users using an LDP algorithm. Furthermore, Apple has incorporated an LDP application into their devices [5], intended for identifying popular emojs and detecting high energy and memory usage in their devices. These examples represent just a few instances of the diverse applications of LDP in practice. Nevertheless, the application of LDP schemes faces challenges when dealing with multi-dimensional data, primarily stemming from dimensionality issues like the curse of dimensionality.