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This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter () of Generalized Rayleigh distribution in a region (R) around available prior knowledge ( 0 ) about the actual value () as initial estimate in case when the scale parameter () is known . In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator. The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor () and suitable region R. Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/, R)], Expected sample size proportion [E(n/,R)/n], probability for avoiding the second sample and percentage of overall sample saved for the proposed estimator are derived. Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significance.Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.

The present  paper agrees  with estimation of scale parameter θ of the Inverted Gamma (IG) Distribution when the shape parameter α is known (α=1), bypreliminarytestsinglestage shrinkage estimators using  suitable  shrinkage weight factor and region.  The expressions for the Bias, Mean Squared Error [MSE] for the proposed estimators are derived. Comparisons between the considered estimator with the usual estimator (MLE) and with the existing estimator  are performed .The results are presented in attached tables.

Background: Metachronous brain-only oligorecurrence in patients with non-small cell lung cancer (NSCLC) is a rare event with favorable prognosis, but the clinical outcome has not been fully determined. We retrospectively analyzed clinical outcomes and prognostic factors in metachronous brain-only oligorecurrence in patients with NSCLC who underwent definitive treatment. Methods: We reviewed 4,437 NSCLC patients without oncogenic driver mutations who underwent definitive treatment between 2008 and 2018. Among them, we identified 327 patients who developed 1 to 5 brain metastases with or without systemic metastasis. Of the 327 patients, 71 had metachronous oligo-brain metastasis without extracranial progression and were treated with local therapy to the brain, while 17 had synchronous oligometastases. Clinical outcomes of overall survival (OS), progression-free survival (PFS), and prognostic factors affecting OS were analyzed. Results: Over 41.2 months of follow-up, the median OS was 38.9 months (95% CI, 21.8 to 56.1 months) in 71 patients. The 2-year OS rate was 67.8% and the 5-year OS rate was 33.1%. The median PFS was 25.5 months (95% CI, 12.2 to 14.4 months). The longest surviving patient had a survival period of 115 months. Through multivariate analysis, ECOG ≥1 (hazard ratio: 5.85, 95% CI: 1.92 to 17.79, P = 0.002) and nonadenocarcinoma (hazard ratio: 2.51, 95% CI: 1.07 to 5.89, P = 0.03) were associated with poor survival. There was no significant difference in OS between patients with local therapy and those with local plus systemic therapy (18.5 vs. 34.7 months, P = 0.82). Clinical outcomes of OS between synchronous and metachronous brain-only oligorecurrence NSCLC patients were comparable. Conclusions: Metachronous brain-only oligorecurrence NSCLC patients who underwent definitive treatment experienced long-term survival with local therapy, highlighting the unique patient population. The role of systemic chemotherapy in this patient population requires further investigation.Legal entity responsible for the study: The authors. Funding: Has not received any funding. Disclosure: All authors have declared no conflicts of interest.

The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.  Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.  Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.