A consequence of using a parametric frailty model with nonparametric baseline hazard for analyzing clustered time-to-event data is that its regression coefficient estimates could be sensitive to the underlying frailty distribution. Recently, there has been a proposal for specifying both the baseline hazard and the frailty distribution nonparametrically, and estimating the unknown parameters by the maximum penalized likelihood method. Instead, in this paper, we propose the nonparametric maximum likelihood method for a general class of nonparametric frailty models, i.e. models where the frailty distribution is completely unspecified but the baseline hazard can be either parametric or nonparametric. The implementation of the estimation procedure can be based on a combination of either the Broyden-Fletcher-Goldfarb-Shanno or expectation-maximization algorithm and the constrained Newton algorithm with multiple support point inclusion. Simulation studies to investigate the performance of estimation of a regression coefficient by several different model-fitting methods were conducted. The simulation results show that our proposed regression coefficient estimator generally gives a reasonable bias reduction when the number of clusters is increased under various frailty distributions. Our proposed method is also illustrated with two data examples.
Background As point-of-care ultrasound (POCUS) has gained popularity, some educational guidelines have been developed. However, in Vietnam, no training course in pediatric POCUS has yet been developed. This was challenging, especially during the COVID-19 pandemic. Objectives This study aimed to implement a three-month hybrid training course for pediatric POCUS training in Vietnam using both online and face-to-face hands-on sessions and to assess participants' self-efficacy level and change in their attitudes towards pediatric POCUS. Methods A hybrid training course in pediatric POCUS was implemented at a children's hospital in Vietnam. This study developed a standardized training course, including online learning, live lectures, hands-on sessions, and skill assessment based on the POCUS consensus educational guidelines. Physicians interested in pediatric POCUS were recruited for participation. They completed a self-evaluation survey before and after the course using a Likert score to assess their background, self-efficacy in performing POCUS, overall satisfaction with the course, and change in their attitudes towards POCUS three months after the course. Results A total of 19 physicians participated in the course. The mean post-training self-efficacy score was significantly higher than the pre-course assessment score: 73.1 (standard deviation (SD): 7.2) vs. 48.9 (SD: 12.5) (p <0.05). The efficacy level was retained three months after the course. Furthermore, overall satisfaction with the course was high at 9.5 (SD: 0.6). After the course, almost all participants strongly agreed to increase the use of POCUS in their clinical practice. Conclusion A hybrid training course in pediatric POCUS was successfully implemented in Vietnam and found the participants' self-efficacy level to be significantly higher after the course and the effect to be retained after the course. The training course could positively affect the participants' attitudes towards POCUS, encouraging them to use POCUS more frequently in their clinical practice.