This paper presents exponential ratio and product estimators for estimating finite population mean using auxiliary information in double sampling and analyzes their properties. These estimators are compared for their precision with simple mean per unit, usual double sampling ratio and product estimators. An empirical study is also carried out to judge the merits of the suggested estimators.

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This article suggests a family of estimators of population mean using auxiliary information in stratified sampling. The bias and mean-squared error of the suggested family of estimators are derived under large sample approximation. Asymptotic optimum estimator (AOE) in the class of estimators is investigated with its meansquared error formula. It is identified that the usual unbiased estimatorȳst , traditional combined ratio estimatorȳ RC , traditional combined regression estimator y lrc , Kadilar and Cingi (2005) estimatorȳ KC , and Shabbir and Gupta (2006) estimatorȳ SG are particular members of a suggested family of estimators. The new expressions of bias and a mean-square error of Kadilar and Cingi (2005) estimatorȳ KC and a new expression of a mean-square error of Shabbir and Gupta (2006) estimatorȳ SG have been derived. Both theoretical and empirical findings are encouraging and support the soundness of the present study.

Background: As the whole world is experiencing the cascading effect of a new pandemic, almost every aspect of modern life has been disrupted. Because of health emergencies during this period, widespread fear has resulted in compromised patient safety, especially for patients with cancer. It is very challenging to treat such cancer patients because of the complexity of providing care and treatment, along with COVID-19. Hence, an effective treatment comparison strategy is needed. We need to have a handy tool to understand cancer progression in this unprecedented scenario. Linking different events of cancer progression is the need of the hour. It is a huge challenge for the development of new methodology. Methods: This article explores the time lag effect and makes a statistical inference about the best experimental arm using Accelerated Failure Time (AFT) model and regression methods. The work is presented as the occurrence of other events as a hazard rate after the first event (relapse). The time lag effect between the events is linked and analysed. Results: The results were presented as a comprehensive analytical strategy by joining all disease progression. An AFT model applied with the transition states, and the dependency structure between the gap times was used by the autoregression model. The effects of arms were compared using the coefficient of auto-regression and accelerated failure time (AFT) models. Conclusions: We provide the solutions to overcome the issue with intervals between two consecutive events in motivating head and neck cancer (HNC) data. COVID-19 is not going to leave us soon. We have to conduct several cancer clinical trials in the presence of COVID-19. A comprehensive analytical strategy to analyse cancer clinical trial data during COVID-19 pandemic is presented.

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A 10-year-old child presented with small-cell osteosarcoma of the proximal end of the tibia. Pulmonary metastases appeared after a gap of 9 months of ablative surgery, as did late multiple extra-pulmonary skeletal metastases, including the hand and foot bones after 6 months of pulmonary metastases. These late extrapulmonary metastases appear to be secondary to pulmonary metastases.