Stratified Ranked Set Sampling (SRSS) for Estimating the Population Mean With Ratio-Type Imputation of the Missing Values

2022 ◽  
pp. 141-170
Author(s):  
Carmen Elena Viada- Gonzalez ◽  
Sira María Allende-Alonso

In this chapter, the authors develop stratified ranked set sampling (RSS) under missing observations. Imputation based of ratio rules is used for completing the information for estimating the mean. They introduce the needed elements on imputation and on the sample selection procedures. They extend RSS models to imputation in stratified populations. A theory on ratio-based imputation rules for estimating the mean is presented. Some numerical studies, based on real-world problems, are developed for illustrating the behaviour of the accuracy of the estimators due to their proposals.

2022 ◽  
pp. 209-232
Author(s):  
Carlos N. Bouza-Herrera

The authors develop the estimation of the difference of means of a pair of variables X and Y when we deal with missing observations. A seminal paper in this line is due to Bouza and Prabhu-Ajgaonkar when the sample and the subsamples are selected using simple random sampling. In this this chapter, the authors consider the use of ranked set-sampling for estimating the difference when we deal with a stratified population. The sample error is deduced. Numerical comparisons with the classic stratified model are developed using simulated and real data.


Author(s):  
Hani M. Samawi ◽  
Eman M. Tawalbeh

The performance of a regression estimator based on the double ranked set sample (DRSS) scheme, introduced by Al-Saleh and Al-Kadiri (2000), is investigated when the mean of the auxiliary variable X is unknown. Our primary analysis and simulation indicates that using the DRSS regression estimator for estimating the population mean substantially increases relative efficiency compared to using regression estimator based on simple random sampling (SRS) or ranked set sampling (RSS) (Yu and Lam, 1997) regression estimator.  Moreover, the regression estimator using DRSS is also more efficient than the naïve estimators of the population mean using SRS, RSS (when the correlation coefficient is at least 0.4) and DRSS for high correlation coefficient (at least 0.91.) The theory is illustrated using a real data set of trees.  


2016 ◽  
Vol 42 (3) ◽  
pp. 137-148 ◽  
Author(s):  
V.L. Mandowara ◽  
Nitu Mehta

In this paper we suggest two modified estimators of the population mean using the power transformation based on ranked set sampling (RSS). The first order approximation of the bias and of the mean squared error of the proposed estimators are obtained. A generalized version of the suggested estimators by applying the power transformation is also presented. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in simple random sampling (SRS). A numerical illustration is also carried out to demonstrate the merits of the proposed estimators using RSS over the usual estimators in SRS.


Blood ◽  
2021 ◽  
Vol 138 (Supplement 1) ◽  
pp. 3028-3028
Author(s):  
Katharine Batt ◽  
Bob G Schultz ◽  
Jorge Caicedo ◽  
Christopher S Hollenbeak ◽  
Neha Agrawal ◽  
...  

Abstract Background Hemophilia A (HA) is a rare genetic disease characterized by a deficiency in clotting factor VIII (FVIII). Persons with HA suffer from spontaneous and traumatic bleeds which significantly impact short- and long-term quality of life. Prophylaxis treatment with FVIII replacement or non-factor replacement (e.g. emicizumab) intends to prevent bleeding episodes. To date, clinical comparisons between FVIII and emicizumab are limited to non-interventional studies and indirect comparisons. Comparisons of costs are limited to cost-effectiveness models or observational studies that include patients with and without inhibitors. An increase in availability of real-world data since emicizumab's approval in 2018 has created opportunity for comparative outcomes research in the non-inhibitor HA population. Objective To compare billed annualized bleed rates (ABR b) and all-cause costs (ACC) among non-inhibitor HA patients switching from prophylaxis with FVIII replacement to emicizumab. Methods This retrospective, observational, pre-post study used the IQVIA PharMetrics® Plus database (2015-2020)-a large longitudinal US commercial health plan database with over 190 million lives. International Classification of Diseases codes (ICD-10), National Drug Codes, and Healthcare Common Procedure Coding System were used to identify diagnoses, therapies, and procedures. Males with ≥1 claim for emicizumab who were on prophylaxis treatment with FVIII prior to initiating emicizumab were included in the analysis. Patients who received bypassing agents, immune tolerance induction, or rituximab were assumed to have inhibitors and were excluded. Patients with ≥2 occurrences of any of the following diagnoses were excluded: von Willebrand disease, hemophilia B, acquired HA, or other coagulation disorders. Annualized bleed rate was defined as billed ABR and represents bleeding episodes that required evaluation, treatment, or procedure resulting in an ICD-10 claim. Therefore, bleeds treated at home and untreated bleeds were not captured. A clinical review of ICD-10 codes resulted in a list of 535 codes used to identify HA-related bleeding episodes (e.g. hemarthrosis). The ACC were calculated as the mean cost per patient per year in 2020 US dollars actually paid by the insurer. Descriptive statistics were used to summarize, and Bayesian models were developed to compare, ABR b and ACC in the pre- and post-switch periods. Bayesian inferences estimated the population mean difference in ABR b and ACC after switching from FVIII prophylaxis to emicizumab. Inferences were conducted by computing posterior probabilities for hypotheses and summarized with 95% credible intervals (CrI). Results A total of 121 patients were included with mean age [range] of 25.9 [2-63] years. The majority of patients were over the age of 18 (60.3%), 33.1% were ≥7-18, and 6.6% were <7. The mean (SD) years on FVIII replacement (pre-switch) and emicizumab (post-switch) were 2.5 (1.5) and 1.1 (0.4), respectively (Table 1). Descriptive In the majority of patients, ABR b remained unchanged from pre-switch to post-switch (42%) while 38% had some magnitude of improvement, and 20% experienced a worsening of ABR b. The mean observed ABR b and ACC were 0.68 and $518,151, respectively, in the pre-switch period, and 0.55 and $652,679, respectively, in the post-switch period. Bayesian Model The Bayesian model demonstrated a mean change in ABR b of -0.128 [95% CrI: -0.441 to 0.184] after switch (Table 2). The mean change in ACC was +$159,680 [95% CrI: $74,842 to $247,841] after switch. The model determined there is a 21.0% probability ABR b will worsen after switch and a 99.9% probability ACC will increase after switch. Conclusions Prophylaxis with FVIII replacement and emicizumab result in similar prevention of billed bleeds in a real-world switch population. Although the population mean ABR b is more likely to fall after switching from FVIII replacement to emicizumab, there is only a 1.02% posterior probability the population mean ABR b will fall by ≥0.5 after switching to emicizumab and a 21.0% probability the ABR b will worsen after switch. Additionaly, ACC are almost certain to substantially increase after switching to emicizumab (99.9%). As additional real-world data becomes available in the non-inhibitor HA population, further research should help to strengthen clinical and economic outcomes for different prophylaxis treatment options. Figure 1 Figure 1. Disclosures Batt: Sanofi: Current equity holder in publicly-traded company; Bayer Therapeutics: Consultancy; Sprouts Consulting: Other: CEO, Principal Consultant; Merck: Current equity holder in publicly-traded company; Forma: Consultancy, Current equity holder in publicly-traded company; Precision Health: Consultancy; Takeda Pharmaceuticals U.S.A.: Consultancy. Schultz: Takeda Pharmaceuticals U.S.A., Inc.: Current Employment, Current holder of individual stocks in a privately-held company. Caicedo: Takeda Pharmaceuticals U.S.A., Inc.: Current Employment, Current holder of individual stocks in a privately-held company, Current holder of stock options in a privately-held company. Hollenbeak: Takeda Pharmaceuticals U.S.A., Inc.: Consultancy. Agrawal: Takeda Pharmaceuticals U.S.A., Inc.: Consultancy. Chatterjee: Takeda Pharmaceuticals U.S.A., Inc.: Consultancy. Dayma: Takeda Pharmaceuticals U.S.A., Inc.: Consultancy. Bullano: Takeda Pharmaceuticals U.S.A., Inc.: Current Employment, Current holder of individual stocks in a privately-held company.


Author(s):  
Zahid Khan ◽  
Muhammad Ismail

In this paper, we propose modified ratio estimators using some known values of coefficient of variation, coefficient of skewness and coefficient of kurtosis of auxiliary variable under ranked set sampling (RSS).  The mean square error (MSE) of the proposed ratio estimators under ranked set sampling is derived and compared with some existing ratio estimators under RSS. Through this comparison, we prove theoretically that MSC of proposed estimators is less than some existing ratio estimators in RSS under some conditions. The MSE of proposed estimators along with some existing estimator are also calculated numerically. We observe from numerical results that the suggested ratio estimators are more efficient than some existing ratio estimators under RSS.


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