UC Riverside

In a randomized clinical trial (RCT) with a control group vs. treatment group design, mixture models (Lindsay, 1995; G. McLachlan and Peel, 2000) can be a good choice for the treatment group response distribution in anticipation that there might be a sub-population of the treated population whose responses have the same distribution as the control group. It is well known that such sub-populations of ‘non-responding’ treated patients exist in oncology trials (Spear et al., 2001; Manegold et al., 2016). Although it would be ideal to identify a-priori the features that characterize individuals who will respond (a ‘responder’) to the treatment and those who will not (a ‘non-responder’), this dissertation considers inference when such information has yet to be ascertained. Post-hoc sub-group analyses are known to lead to an inflated rate of false discoveries (Lagakos et al., 2006). Assessing the existence of subgroups with mixture model inference before proceeding with identifying subgroups based upon biomarkers can decrease the false discovery rate among sub-group analyses. Jeske and Yao (2020) demonstrated that ignoring the heterogeneity of treatment effects could result in an under-powered experiment and have the risk of missing some useful treatments. When heterogeneity is indeed present and treatment effects are sub-population specific, the average treatment effect obtained by the standard methods can lead to incorrect conclusions. Hence, the use of mixture models to represent the response distribution within the treatment group is compelling and it is desirable to describe the nature of this sub-population specific effect via inference on the corresponding parameters from the mixture distribution. This dissertation explores four methods of point estimation for the parameters. Two of the methods are also used to construct confidence bounds (both intervals and regions) for the parameters. Simulation is used to assess the performances of the various methods and make a recommendation. The recommended methods are illustrated on an example blood pressure data set.