A Heuristic Solution of the Identifiability Problem of the Age-Period-Cohort Analysis of Cancer Occurrence: Lung Cancer Example

Background: The Age–Period–Cohort (APC) analysis is aimed at estimating the following effects on disease incidence: (i) the age of the subject at the time of disease diagnosis; (ii) the time period, when the disease occurred; and (iii) the date of birth of the subject. These effects can help in evaluating the biological events leading to the disease, in estimating the influence of distinct risk factors on disease occurrence, and in the development of new strategies for disease prevention and treatment. Methodology/Principal Findings: We developed a novel approach for estimating the APC effects on disease incidence rates in the frame of the Log-Linear Age-Period-Cohort (LLAPC) model. Since the APC effects are linearly interdependent and cannot be uniquely estimated, solving this identifiability problem requires setting four redundant parameters within a set of unknown parameters. By setting three parameters (one of the time-period and the birth-cohort effects and the corresponding age effect) to zero, we reduced this problem to the problem of determining one redundant parameter and, used as such, the effect of the time-period adjacent to the anchored time period. By varying this identification parameter, a family of estimates of the APC effects can be obtained. Using a heuristic assumption that the differences between the adjacent birth-cohort effects are small, we developed a numerical method for determining the optimal value of the identification parameter, by which a unique set of all APC effects is determined and the identifiability problem is solved

Search for OB stars running away from young star clusters. II. The NGC 6357 star-forming region

Dynamical few-body encounters in the dense cores of young massive star clusters are responsible for the loss of a significant fraction of their massive stellar content. Some of the escaping (runaway) stars move through the ambient medium supersonically and can be revealed via detection of their bow shocks (visible in the infrared, optical or radio). In this paper, which is the second of a series of papers devoted to the search for OB stars running away from young (several Myr) Galactic clusters and OB associations, we present the results of the search for bow shocks around the star-forming region NGC 6357. Using the archival data of the Midcourse Space Experiment (MSX) satellite and the Spitzer Space Telescope, and the preliminary data release of the Wide-Field Infrared Survey Explorer (WISE), we discovered seven bow shocks, whose geometry is consistent with the possibility that they are generated by stars expelled from the young star clusters, Pismis 24 and AH03 J1725-34.4, associated with NGC 6357. Two of the seven bow shocks are driven by the already known O stars. Follow-up spectroscopy of three other bow shock-producing stars showed that they are O-type stars as well, while the 2MASS photometry of the remaining two stars suggests that they could be B0 V stars, provided that both are located at the same distance as NGC 6357. Detection of numerous massive stars ejected from the very young clusters is consistent with the theoretical expectation that star clusters can effectively lose massive stars at the very beginning of their dynamical evolution and lends strong support to the idea that probably all field OB stars have been dynamically ejected from their birth clusters. A by-product of our search for bow shocks around NGC 6357 is the detection of three circular shells typical of luminous blue variable and late WN-type Wolf-Rayet stars.Comment: 13 pages, 16 figures, accepted for publication in A&