Most of the personal information nowadays exist in the form of digital data which includes sensitive information such as medical records, credit card information, private instant messages, etc. In this research, we aim to investigate the data privacy problem in collecting and mining user sensitive information. We focus our research on: (i) data privacy in survival analysis which uses medical records to learn useful survival models in medical research; and (ii) data privacy in collecting user data which is the current practice of many corporations and governments. We use differential privacy, which is the golden standard in privacy protection, to address the data privacy problem in survival analysis and user data collection. To this end, we aim to achieve the following: • Guaranteeing privacy for survival analysis models which include (i) parametric and nonparametric survival models; and (ii) continuous-time and discrete-time survival regression models. • Guaranteeing privacy for users whose data is collected by corporations and governments. The main contributions of this thesis are given as follows: • For nonparametric survival models, we have proposed a private mechanism for two popular nonparametric estimators, namely Kaplan-Meier estimator and Nelson-Aalen estimator. For parametric survival models, we have proposed a simple private mechanism for accurately estimating the parameter of the exponential distribution. In addition, we have also proposed a private mechanism based on the local sensitivity concept for estimating the parameters of the Weibull distribution. • For estimating uncertainty in parametric survival models, we have proposed a private framework which allows learning the posterior function. Moreover, we have applied the proposed framework to parametric models with Weibull distribution and flexible parametric models. • We have proposed three private approaches for estimating the discrete-time survival regression model, namely extended output perturbation approach, extended objective perturbation approach, and posterior sampling approach. • We have proposed a posterior sampling approach for continuous-time survival regression model. In addition, we have also proposed a posterior perturbing approach which supports a relaxation of differential privacy for scenarios in which differential privacy is impractical. • For user data collection, we have proposed mechanisms which allow each user to publish a randomized vector of categorical data and numerical data. The proposed mechanisms are asymptotically optimal in both accuracy and run-time. Moreover, we have applied the proposed mechanisms to supervised learning problems under the empirical risk minimization framework. Doctor of Philosophy