Periodic Reporting for period 5 - COSMOS (Semiparametric Inference for Complex and Structural Models in Survival Analysis)
Periodo di rendicontazione: 2021-06-01 al 2022-08-31
In survival analysis investigators are interested in modeling and analysing the time until an event happens. It often happens that the available data are right censored, which means that only a lower bound of the time of interest is observed. This feature complicates substantially the statistical analysis of this kind of data. The aim of this project was to solve a number of open problems related to time-to-event data, that represent a major step forward in the area of survival analysis.
The project had three objectives:
[WP1] Cure models take into account that a certain fraction of the subjects under study will never experience the event of interest. Because of the complex nature of these models, many problems are still open and rigorous theory is rather scarce in this area. Our goal was to fill this gap, which is a challenging but important task.
[WP2] Copulas are nowadays widespread in many areas in statistics. However, they can contribute more substantially to resolving a number of the outstanding issues in survival analysis, such as in quantile regression and dependent censoring. Finding answers to these open questions, opens up new horizons for a wide variety of problems.
[WP3] We wished to develop new methods for doing correct inference in some of the common models in survival analysis in the presence of endogeneity or measurement errors. The present methodology has serious shortcomings, and we liked to propose, develop and validate new methods and major breakthroughs.
The above objectives were achieved by using mostly semiparametric models. The development of mathematical properties under these models is often a challenging task, as complex tools from the theory on empirical processes and semiparametric efficiency are required. The project therefore required an innovative combination of highly complex mathematical skills and cutting edge results from modern theory for semiparametric models. The theoretical results were illustrated on simulated and real data sets from medical and economic studies.
The project had three objectives:
[WP1] Cure models take into account that a certain fraction of the subjects under study will never experience the event of interest. Because of the complex nature of these models, many problems are still open and rigorous theory is rather scarce in this area. Our goal was to fill this gap, which is a challenging but important task.
[WP2] Copulas are nowadays widespread in many areas in statistics. However, they can contribute more substantially to resolving a number of the outstanding issues in survival analysis, such as in quantile regression and dependent censoring. Finding answers to these open questions, opens up new horizons for a wide variety of problems.
[WP3] We wished to develop new methods for doing correct inference in some of the common models in survival analysis in the presence of endogeneity or measurement errors. The present methodology has serious shortcomings, and we liked to propose, develop and validate new methods and major breakthroughs.
The above objectives were achieved by using mostly semiparametric models. The development of mathematical properties under these models is often a challenging task, as complex tools from the theory on empirical processes and semiparametric efficiency are required. The project therefore required an innovative combination of highly complex mathematical skills and cutting edge results from modern theory for semiparametric models. The theoretical results were illustrated on simulated and real data sets from medical and economic studies.
Important results and achievements have been made for each work package. For instance, in WP1 we were able to give solid statistical and mathematical foundations in the area of cure models, which had been studied so far mostly from an applied point of view, often without paying lots of attention to the methodology and asymptotic theory underlying these models. For WP2 we were able to propose a very promising model in which dependent censoring can be identified, and which has excellent potential for future research. Finally, in WP3 we managed to obtain important identifiability and estimation results in the context of measurement errors and endogeneity in the presence of censored data.
In each WP important novel methodologies have been developed that lead to new insights in the area. For example, in the context of measurement errors (WP3) a new method was developed that allows to identify and estimate the variance of the measurement error without having additional data at ones disposal. Competing methods assume that additional data like replicated data, validation data or instrumental variables, are available.