Double Bias: Group comparison and variable selection under length-biased sampling and covariate imbalance.

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In the current literature, methodologies for drawing causal inference about a target population when the sampling population constitutes a systematically biased subpopulation are not available. In such situations, investigators must simultaneously tackle two distinct types of bias that plague the data: first, observations do not form a representative sample from the target population, and second, owing to observational nature of these data, the distribution of covariates differs for each stratum of the sampling population, leading to covariate imbalance precluding direct causal comparisons without appropriate adjustment. While each of these biases has received substantial attention in the literature in recent years, there is no methodology in the current literature that can account for both types of bias simultaneously. The aim of this research program within the next five years is to develop statistical methodologies specifically tailored for analysing data subject to these two types of biases. In particular, we will develop semiparametric methods to address this problem. Amongst other approaches, we will adapt Propensity Score Regression (PSR) and Inverse Probability of Treatment Weighting (IPTW) methods to account for length-bias sampling. Subsequently, we will develop techniques for variable selection under double bias. Feature selection under covariate imbalance is, in and of itself, a novel notion with important applications. The roots of biased sampling stem from the broad field of stereology, and practical applications of methodologies for biased sampling abound. Areas of application include, amongst others, the social sciences, biology and medical sciences, labor force studies in economics, quality control in the manufacturing industry, and physics. Two commonly cited examples of such are the Canadian Study of Health and Aging (CSHA), a nationwide cross-sectional study of dementia with follow-up conducted in Canada, and the Labor Force Survey of the Spanish Institute for Statistics. Novel applications to nanotechnology have also been discussed recently. We expect the methodology we will devise will spur the development of further methodologies for analyzing data from current and future studies.