# Comparative Analysis of Local Differential Privacy Schemes in Healthcare Datasets
## 1 Introduction
This study also encompasses several experiments on datasets with different characteristics, including variations in size, attribute composition, and correlation from various industries. Among these datasets are well-known sets commonly used to evaluate LDP or CDP approaches. Healthcare takes center stage in this collection of datasets. This evaluation is made because datasets in the healthcare domain often exhibit high correlations among attributes. For instance, the risk of developing various diseases tends to increase with age, encompassing conditions such as heart disease, stroke, cancer, and Alzheimer's disease. This phenomenon arises from multiple factors, including changes in cell function, the accrual of damage over time, and the decline of the immune system. Certain diseases also exhibit age-related prevalence, with childhood cancer being more common in children and prostate cancer being more prevalent in older men. Another solution to apply LDP into medical datasets was proposed by [PERSON] et al. [16]. They normalized all data to a range between \(-1\) and \(1\), and they applied the bounded Laplacian method to prevent the generation of out-of-bound values following the application of the differential privacy algorithm. To preserve the cardinality of categorical variables, postprocessing via discretization was conducted. The efficacy of the algorithm was assessed using both synthetic and real-world data sourced from the eICU Collaborative Research Database. Evaluation involved comparing the original and perturbed data using misclassification rates for categorical data and the mean squared error for continuous data on ML models. Furthermore, the researchers compared the performance of classification models predicting in-hospital mortality using real-world data. The differences between this work and ours is presented in Table 1.  
We assess the performance of LOPUB [6], LOCOP [10], and BRR using three metrics: average variant distance (AVD), \(R\)-squared, and the average absolute Pearson correlation coefficient (AAR). AVD is employed to quantify the difference between the probabilities of two joint probability distributions--the original and those computed by the LDP approaches. Subsequently, we propose using \(R\)-squared, a metric that gauges the performance of LASSO and Bayesian Ridge Regression algorithms applied to LDP approaches. Finally, we evaluate how the performance of LDP approaches is affected by the correlation between elements in a dataset using AAR. With a privacy budget set to \(\epsilon=0.1\) per attribute and \(k=5\), after conducting one hundred experiments, our work achieves a 57% reduction in the average variant distance compared to that of LOPUB. The contributions of this paper are summarized as follows:  
1. We propose a new LDP schema using BRR for joint probability estimation and the baseline algorithm LOPUB [6]. 2. We propose two metrics, \(R\)-squared and AAR, for evaluation of the performance. 3. We show in this document the experimental results using six open datasets that demonstrates the superiority of estimation accuracy and the robustness across diverse characteristics including numbers of users, attributes, and AARs. The subsequent sections of the paper are organized as follows: Section 2 provides the preliminaries, while Section 3 details our proposed approach. The paper concludes with the sections Experiments and Conclusions.