Sampling designs and statistical methods for incomplete data analysis

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Many studies involve incomplete data which may arise due to the study design under consideration, or missingness by happenstance. For example, budgetary constraints may prevent measuring expensive covariates for all individuals in a cohort which leads us to consider appropriate sampling designs and to have incomplete data as a result of the sampling design. The main goal of this research proposal is to identify efficient sampling designs under such a situation in different data type settings, and develop, evaluate and apply statistical methods for incomplete data analysis. To limit sample size for obtaining values of expensive covariates while giving adequate power for their corresponding association tests, the best solution is to obtain them under a cost-efficient sampling design and to use efficient statistical methods that lead to efficient estimates and powerful association tests. It is known that selecting an informative subset of individuals from an existing cohort based on response-dependent sampling can improve cost-efficiency of studies. We will consider outcome-dependent two-phase sampling designs: in phase one, we have easily measured variables for all individuals in the cohort or in a large random sample from the population, and in phase two, we obtain expensive variables for a subset of individuals selected according to their response variable obtained in phase one. In response-dependent sampling designs, inference based on standard statistical methods, ignoring the selection, may be misleading. **There have been many studies on developing methods to efficiently analyze response-dependent multi-phase sampling designs in the literature. However, there has not been sufficient work on identifying efficient outcome-dependent multi-phase sampling designs. The objective of this proposal is to develop analytic and simulation-based approaches to compare various sampling designs under each proposed method according to the allocation of the phase two samples, the distribution of the expensive covariate and associated effect size, as well as to check the robustness of methods under misspecification of model assumptions. We will consider response-dependent sampling designs under different data type settings. For example, the response variable can be a time-to-event variable, which may not be completely observed but censored for some individuals; or there can be multiple continuous uncensored or time-to-event response variables and the sampling in the second phase may depend on multiple response variables. **This study will be helpful in addressing how to optimally sample subjects to obtain the best power to identify the associations between response variable(s) and expensive covariate(s) for a given sample size, and which method of analysis leads to more powerful association tests under specified modeling assumptions. It will also be helpful to identify sampling designs and statistical methods which are less than optimal but may be more robust to model misspecification. Hence, it is anticipated that we will have a better understanding about cost-efficient sampling designs that will be beneficial in reducing costs of many research studies in Natural Sciences, Social Sciences and Health Sciences, and therefore, be beneficial to the economy of Canada. In addition, statistical methods will be developed under complex modeling assumptions for response-selective problems, which have not been considered deeply in the literature.