Academic

Likelihood method is a key technique in the realm of statistical inference, particularly when dealing with intricate models that encompass multiple parameters. When faced with complex datasets, likelihood method together with other statistical tools can be a creative trial for building accurate models.

In my work, we study two topics in statistical research. In the first topic, we propose an EM-based maximum binomial likelihood to estimate the unknown cumulative distribution functions (CDFs) and the mixture parameter in a compound mixture model. In the field of nonparametric statistics, there is often a requirement to efficiently estimate a cumulative distribution function (CDF) using data drawn from unidentified distributions. Yet, when there is a need to concurrently estimate two independent distributions, and we are unaware of the specific distribution to which a portion of the observations belong, the standard empirical estimator does not fully make use of the available sample. In response to this challenge, our approach treats the identifiers of these observations as unobserved data. We then use isotonic regression in conjunction with the Expectation-Maximization (EM) algorithm to obtain maximum binomial likelihood estimators for the CDFs and the mixture parameter. The accuracy of this method is corroborated by simulation studies, particularly when applied to data with such characteristics.

In our second topic, we propose a binomial likelihood technique designed for the management of healthcare datasets. Quality-Adjusted Life Years (QALYs) present an effective way to present the effects of a disease or its treatment on a person’s health and overall quality of life. This medical dataset is consist of two parts: cTTO data and DCE data. The cTTO data involves participants assigning numerical values to assumed health statuses, while the DCE data involves participants making preference decisions between pairs of health statuses. One of the approaches to derive utilities from the EQ-5D is the likelihood method. This method operates under the premise that individuals opt for the health state that amplifies their expected utility. In this study, we offer a detailed review of this approach. The likelihood-based strategy, striving to integrate data reminiscent of composite Time Trade-Off (cTTO) and Discrete Choice Experiment (DCE) as a singular entity. Simulation studies are carried out to prove the effectiveness of our recommended method along with other potential alternatives.