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The motivation for this paper is to account for subject specific variations in a Cox proportional hazard model for alternating recurrent events. This is done through two sets of frailty components, whose marginal distributions are bound together by a copula function. The likelihood function involves unobservable variables, which requires the use of the EM algorithm. This leads to intractable integrals, which after some approximations, are solved using computationally intensive techniques. The results are applied to a real-life data. A simulation study is also carried out to check for consistency.

In this article, we model alternately occurring recurrent events and study the effects of covariates on each of the survival times. This is done through the accelerated failure time models, where we use lagged event times to capture the dependence over both the cycles and the two events. However, since the errors of the two regression models are likely to be correlated, we assume a bivariate error distribution. Since most event time distributions do not readily extend to bivariate forms, we take recourse to copula functions to build up the bivariate distributions from the marginals. The model parameters are then estimated using the maximum likelihood method and the properties of the estimators studied. A data on respiratory disease is used to illustrate the technique. A simulation study is also conducted to check for consistency., (© 2020 Walter de Gruyter GmbH, Berlin/Boston.)

Remediation aimed at reducing human exposure to groundwater arsenic in West Bengal, one of the regions most impacted by this environmental hazard, are currently largely focussed on reducing arsenic in drinking water. Rice and cooking of rice, however, have also been identified as important or potentially important exposure routes. Quantifying the relative importance of these exposure routes is critically required to inform the prioritisation and selection of remediation strategies. The aim of our study, therefore, was to determine the relative contributions of drinking water, rice and cooking of rice to human exposure in three contrasting areas of West Bengal with different overall levels of exposure to arsenic, viz. high (Bhawangola-I Block, Murshidibad District), moderate (Chakdha Block, Nadia District) and low (Khejuri-I Block, Midnapur District). Arsenic exposure from water was highly variable, median exposures being 0.02 μg/kg/d (Midnapur), 0.77 μg/kg/d (Nadia) and 2.03 μg/kg/d (Murshidabad). In contrast arsenic exposure from cooked rice was relatively uniform, with median exposures being 0.30 μg/kg/d (Midnapur), 0.50 μg/kg/d (Nadia) and 0.84 μg/kg/d (Murshidabad). Cooking rice typically resulted in arsenic exposures of lower magnitude, indeed in Midnapur, median exposure from cooking was slightly negative. Water was the dominant route of exposure in Murshidabad, both water and rice were major exposure routes in Nadia, whereas rice was the dominant exposure route in Midnapur. Notwithstanding the differences in balance of exposure routes, median excess lifetime cancer risk for all the blocks were found to exceed the USEPA regulatory threshold target cancer risk level of 10(-4)-10(-6). The difference in balance of exposure routes indicate a difference in balance of remediation approaches in the three districts.