Cancer incidence and/or mortality among individuals varies with diet, socio-culture, ethnicity, race, gender, and age. Similarly, environmental temperature modulates many biological functions. To study the effect of environment temperature on cancer incidence, the US population was selected. Because, county-wise cancer incidence rate data of various anatomical site-specific cancers and different races/ethnicities for both males and females are available. Moreover, the differences amongst the aforementioned factors among individuals are much less, as compared to the world population. Statistical analysis showed a negative correlation between the average annual temperature and cancer incidence rate at all anatomical sites and individually for 13 types (out of 16 types) of anatomical site-specific cancer incidence rates (e.g. uterine, bladder, thyroid, breast, esophagus, ovary, melanoma, non-Hodgkin lymphoma, leukemia, brain, pancreas, etc.) for females. Further analysis found a similar inverse trend in all races/ethnicities of the female population but not in all male races/ethnicities or anatomical site-specific cancers. Moreover, the majority of the counties having the top-most cancer incidence rate in females are located above the latitude 36.5°N. These findings indicate that living in a cold county in the United States might have a higher risk of cancer irrespective of cancer type (except cervical and liver) and races/ethnicities for females but not in all such cases for the male population.
This paper tries to derive maximum likelihood estimators (MLEs) for the parameters of the inverse Rayleigh distribution (IRD) when the observed data is masked. MLEs, asymptotic confidence intervals (ACIs) and boot-p confidence intervals (boot-p CIs) for the lifetime parameters have been discussed. The simulation illustrations provided that as the sample size increases the estimated value approaches to the true value, and the mean square error decreases with the increase in sample size, and mean square error increases with increase in level of masking, the ACIs are always symmetric and the boot-p CIs approaches to symmetry as the sample size increases whereas the mean life time due to the local spread of the disease is less than that due to the metastasis spread in case of real data set..
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