Quantile regression has shown great promise in censored data analysis. The investigator proposes to broaden the scope of censored quantile regression by developing methods that can accommodate practical situations where censoring mechanism is more complicated than univariate random censoring. Part of research goals for the 3-year plan are: (1) to develop quantile regression methods in the presence of dependent censoring which can provide semiparametric sensitivity analysis of regression quantiles or joint inference on conditional quantiles of the response and response?censoring dependency; (2) to derive a new formulation of doubly censored regression quantiles based on a stochastic integral equation and provide practical remedies for addressing the associated identifiability issues; (3) to develop publicly available software which implements the proposed cutting-edge statistical methodology. The investigator plans to provide rigorous asymptotic studies for the proposed methods utilizing theory in empirical processes, stochastic integral equation, and functional analysis, and other statistical and probabilistic techniques.

The proposed research will have significant impact and many applications in diverse fields including biomedical research, economics, and public health studies. For example, the methods to be developed can appropriately address the problem of nonrandom patient dropout in clinical studies, or account for the occurrence of event before study entry as well as no observation of event by the end of follow-up in many registry studies of chronic disease, thereby contributing to improving disease treatment or prevention. The investigator plans to integrate the results from the proposed research with education through student mentoring and course teaching, which may involve undergraduate students, and to widely disseminate the proposed research via publications, conference presentations, seminars, Internet postings, and free software.

Project Report

Quantile regression has arisen into an important complement to classic linear regression by providing a more comprehensive picture for the relationship between a response and a set of covariates. When the response is subject to censoring, as often occurred with time-to-event outcomes, the standard techniques become inapplicable. Recent research on censored quantile regression reveals that recovering the information loss in censored responses without imposing stringent censoring assumptions can be challenging even in the simplest random right censoring case. The primary objective of this project is to broaden the scope of censored quantile regression by developing methods that allow for more realistic censoring mechanisms. With the support of this grant, we are able to show that quantile regression is a viable statistical tool for analyzing complex survival data frequently arising from clinical trials or observational studies. We have developed new quantile regression methods that can be applied to appropriately analyze semi-competing risks data, competing risks data, recurrent events data, and longitudinal data with censored outcomes. The results from applying the developed methods can provide more complete views of the association between covariates and responses (than traditional methods) while being easy to interpret. More importantly, the new methods all possesses nice computational features so that they can be efficiently and stably implemented. We have made the computation programs available on Internet. This is expected to facilitate future methodological research in relevant fields as well as real applications of the new methods. Research sponsored by this grant has led to 9 journal manuscripts or book chapter published, submitted, or in prepration, and 18 conference presentations. We have broadly disseminate the results to communities of interest via the journal/book publication and conference presentation mentioned above, and 4 departmental seminars, and Internet posting of papers and computation code. In terms of intellectual merits, the research sponsored by this award has contributed theoretically solid and practically sensible quantile regression methods to analyze biomedical data subject to dependent censoring, double censoring or other complications. The new approaches greatly broaden the utility of quantile regression in survival analysis by accommodating more realistic censoring mechanisms or other data complications. Moreover, we propose a novel generalization of quantile regression to model counting processes and render a broader regression framework that accommodate recurrent events. Our work has significantly advanced quantile regression methodology in the area of survival analysis. In addition, the asymptotic studies for quantile regression in the presence of dependent censoring or other data complications are generally nontrivial. Establishing the proposed theoretical results constitutes advancement of theory and is expected to provide useful templates to justify similar statistical procedures in other research endeavors. In terms of broader impact, the developed methods have a wide range of applications in fields such as biomedical research, public health, engineering, economics, and social sciences. Provided the easy interpretation and great flexibility of quantile regression, applying our methods has high potential to render insightful scientific implications beyond those provided by standard analyses. For example, our analysis of a dataset from US Cystic Fibrosis (CF) Registry data revealed more rapid progression to PA infection recurrence in patients with pancreatic insufficiency compared to those without, and suggested a heterogeneous association between gender and PA infection recurrence times in young children with CF. These would not have been identified by traditional Cox regression or classic linear regression. With the forthcoming publications and developed software, we believe that the new methods will be widely employed in scientific settings that involve complicated and yet realistic censorship or other data features, and make significant contributions to scientific discovery. The impact of our research has been evidenced by but is not limited to completed and ongoing field applications to a leukemia clinical trial, Cystic Fibrosis registry, and a stroke clinical trial, and an environmental health epidemiological study. Interdisciplinary collaborations of this kind will ensure methods to be developed in tune with substantive issues in practice, and to be timely transformed into tools that directly impact various aspects of the society. In addition, the research supported by this NSF grant has contributed significantly to the eduation and training of PhD students in Biostatistics at Emory. PI has supervised three PhD students to conduct dissertation research directly related to this NSF grant. The proposed research also contributes new materials for a PhD elective course which PI created in 2009 and re-taught in 2014. Moreover, PI taught a tutorial at 2014 ENAR Spring meeting on the topic of quantile regression for survival analysis. This activity indicates a broader coverage of education and training opportunities stemmed from this grant, which benefit not only graduate students at Emory but also outside researchers in both academia or industry. These efforts are expected to enhance the general knowledge base of quantile regression, to encourage further methodological research, and to foster sensible field applications that promote scientific discovery.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Gabor J. Szekely
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Emory University
United States
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