caa a22 4500 60547608X CHVBK 20210128100354.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s10985-014-9307-7 doi (NATIONALLICENCE)springer-10.1007/s10985-014-9307-7 Parameter inference from hitting times for perturbed Brownian motion [Elektronische Daten] [Massimiliano Tamborrino, Susanne Ditlevsen, Peter Lansky] A latent internal process describes the state of some system, e.g. the social tension in a political conflict, the strength of an industrial component or the health status of a person. When this process reaches a predefined threshold, the process terminates and an observable event occurs, e.g. the political conflict finishes, the industrial component breaks down or the person dies. Imagine an intervention, e.g., a political decision, maintenance of a component or a medical treatment, is initiated to the process before the event occurs. How can we evaluate whether the intervention had an effect? To answer this question we describe the effect of the intervention through parameter changes of the law governing the internal process. Then, the time interval between the start of the process and the final event is divided into two subintervals: the time from the start to the instant of intervention, denoted by $$S$$ S , and the time between the intervention and the threshold crossing, denoted by $$R$$ R . The first question studied here is: What is the joint distribution of $$(S,R)$$ ( S , R ) ? The theoretical expressions are provided and serve as a basis to answer the main question: Can we estimate the parameters of the model from observations of $$S$$ S and $$R$$ R and compare them statistically? Maximum likelihood estimators are calculated and applied on simulated data under the assumption that the process before and after the intervention is described by the same type of model, i.e. a Brownian motion, but with different parameters. Also covariates and handling of censored observations are incorporated into the statistical model, and the method is illustrated on lung cancer data. The Author(s), 2014 First passage times nationallicence Maximum likelihood estimation nationallicence Wiener process nationallicence Degradation process nationallicence Effect of intervention nationallicence Survival analysis nationallicence Tamborrino Massimiliano Department of Mathematical Sciences, Copenhagen University, Universitetsparken 5, 2100, Copenhagen, Denmark aut Ditlevsen Susanne Department of Mathematical Sciences, Copenhagen University, Universitetsparken 5, 2100, Copenhagen, Denmark aut Lansky Peter Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20, Prague 4, Czech Republic aut Lifetime Data Analysis Springer US; http://www.springer-ny.com 21/3(2015-07-01), 331-352 1380-7870 21:3<331 2015 21 10985 https://doi.org/10.1007/s10985-014-9307-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10985-014-9307-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Tamborrino Massimiliano Department of Mathematical Sciences, Copenhagen University, Universitetsparken 5, 2100, Copenhagen, Denmark aut NATIONALLICENCE 700 1- Ditlevsen Susanne Department of Mathematical Sciences, Copenhagen University, Universitetsparken 5, 2100, Copenhagen, Denmark aut NATIONALLICENCE 700 1- Lansky Peter Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20, Prague 4, Czech Republic aut NATIONALLICENCE 773 0- Lifetime Data Analysis Springer US; http://www.springer-ny.com 21/3(2015-07-01), 331-352 1380-7870 21:3<331 2015 21 10985