Pair Rank Set Sampling

Ranked set sampling (RSS) as suggested by McIntyre (1952) may be modified to introduced a new sampling method called pair rank set sampling (PRSS), which might be used in some area of application instead of the RSS to increase the efficiency of the estimators relative to the simple random sampling (SRS) method. Estimators of the population mean are considered. An example using real data is presented to illustrate computations.     

Estimation of Ratio Using Rank Set Sampling

Ranked set sampling (RSS) as suggested by McIntyre (1952) and developed by Takahasi and Wakimoto (1968) is used to estimate the ratio. It is proved that by using RSS method the efficiency of the estimator relative to the simple random sampling (SRS) method has increased. Computer simulated results are given. An example using real data is presented to illustrate the computations.     

Ranked set sampling: cost and optimal set size

McIntyre (1952, Australian Journal of Agricultural Research 3, 385-390) introduced ranked set sampling (RSS) as a method for improving estimation of a population mean in settings where sampling and ranking of units from the population are inexpensive when compared with actual measurement of the units. Two of the major factors in the usefulness of RSS are the set size and the relative costs of the various operations of sampling, ranking, and measurement. In this article, we consider ranking error models and cost models that enable us to assess the effect of different cost structures on the optimal set size for RSS. For reasonable cost structures, we find that the optimal RSS set sizes are generally larger than had been anticipated previously. These results will provide a useful tool for determining whether RSS is likely to lead to an improvement over simple random sampling in a given setting and, if so, what RSS set size is best to use in this case.     

Estimation of Parameters for One-Way Layout with Rank Set Sampling

Ranked set sampling (RSS) as suggested by McIntyre (1952) and independently by Takahasi and Wakimoto (1968) may be used to estimate the parameters of the one-way layout. The objective is to use the RSS method to increase the efficiency of the estimators relative to the simple random (SRS) method. Estimators of the populations (treatments) effect are considered. Computer simulated results are given, and an example using real data presented to illustrate the computations.     

Unbalanced ranked set sampling for estimating a population proportion

The application of ranked set sampling (RSS) techniques to data from a dichotomous population is currently an active research topic, and it has been shown that balanced RSS leads to improvement in precision over simple random sampling (SRS) for estimation of a population proportion. Balanced RSS, however, is not in general optimal in terms of variance reduction for this setting. The objective of this article is to investigate the application of unbalanced RSS in estimation of a population proportion under perfect ranking, where the probabilities of success for the order statistics are functions of the underlying population proportion. In particular, the Neyman allocation, which assigns sample units for each order statistic proportionally to its standard deviation, is shown to be optimal in the sense that it leads to minimum variance within the class of RSS estimators that are simple averages of the means of the order statistics. We also use a substantial data set, the National Health and Nutrition Examination Survey III (NHANES III) data, to demonstrate the feasibility and benefits of Neyman allocation in RSS for binary variables.     

Improved procedures for estimation of disease prevalence using ranked set sampling

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). When the variable of interest is binary, ranking of the sample observations can be implemented using the estimated probabilities of success obtained from a logistic regression model developed for the binary variable. The main objective of this study is to use substantial data sets to investigate the application of RSS to estimation of a proportion for a population that is different from the one that provides the logistic regression. Our results indicate that precision in estimation of a population proportion is improved through the use of logistic regression to carry out the RSS ranking and, hence, the sample size required to achieve a desired precision is reduced. Further, the choice and the distribution of covariates in the logistic regression model are not overly crucial for the performance of a balanced RSS procedure.     

Efficient regression analysis with ranked-set sampling

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.     

Bayesian Estimation Using Ranked Set Sampling

Bayesian Estimation of the parameter of a distribution is considered using Ranked set sampling (RSS). It is shown that for at least one RSS plan, the Bayes estimator has smaller Bayes risk than the Bayes estimator using simple random sampling (SRS). Furthermore, for exponential family with conjugate prior, the Bayes estimator of the mean using balanced RSS dominates, in terms of its Bayes risk, the Bayes estimator of the mean using SRS. This procedure is used to estimate the average Milk yield of four hundreds and two sheep. The empirical efficiency supports the theoretical findings.     

Non‐Parametric Selected Ranked Set Sampling

A nonparametric selected ranked set sampling is suggested. The estimator of population mean based on the new approach is compared with that using the simple random sampling (SRS), the ranked set sampling (RSS) and the median ranked set sampling (MRSS) methods. The estimator of population mean using the new approach is found to be more efficient than its counter‐parts for almost all the cases considered.     

On Estimating a Population Proportion via Ranked Set Sampling

This paper explores the use of the rank set sampling (RSS) protocol as it pertains to the estimation of a population proportion. The maximum likelihood estimator (MLE) and the sample proportion, both based on the RSS data, are discussed and their corresponding asymptotic distributions are derived. Based on these results the MLE is found to be uniformly more efficient than the sample proportion. Nevertheless, both estimators are more efficient than the simple random sample proportion. The greatest gains in efficiency are obtained at the center of the parameter space. Finally, these results remain valid in the presence of judgment error. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Population approaches to estimate minimal model indexes of insulin sensitivity and glucose effectiveness using full and reduced sampling schedules

The intravenous glucose tolerance test (IVGTT) interpreted with the minimal model provides individual indexes of insulin sensitivity (S(I)) and glucose effectiveness (S(G)). In population studies, the traditional approach, the standard two-stage (STS) method, fails to account for uncertainty in individual estimates, resulting in an overestimation of between-subject variability. Furthermore, in the presence of reduced sampling and/or insulin resistance, individual estimates may be unobtainable, biasing population information. Therefore, we investigated the use of two population approaches, the iterative two-stage (ITS) method and nonlinear mixed-effects modeling (NM), in a population (n = 235) of insulin-sensitive and insulin-resistant subjects under full (FSS, 33 samples) and reduced [RSS(240-min), 13 samples and RSS(180-min), 12 samples] IVGTT sampling schedules. All three population methods gave similar results with the FSS. Using RSS(240), the three methods gave similar results for S(I), but S(G) population means were overestimated. With RSS(180), S(I) and S(G) population means were higher for all three methods compared with their FSS counterparts. NM estimated similar between-subject variability (19% S(G), 53% S(I)) with RSS(180), whereas ITS showed regression to the mean for S(G) (0.01% S(G), 56% S(I)) and STS provided larger population variability in S(I) (29% S(G), 91% S(I)). NM provided individual estimates for all subjects, whereas the two-stage methods failed in 16-18% of the subjects using RSS(180) and 6-14% using RSS(240). We conclude that population approaches, specifically NM, are useful in studies with a sparsely sampled IVGTT ( approximately 12 samples) of short duration ( approximately 3 h) and when individual parameter estimates in all subjects are desired.     

Ranked set sampling with unequal samples

A ranked set sampling procedure with unequal samples (RSSU) is proposed and used to estimate the population mean. This estimator is then compared with the estimators based on the ranked set sampling (RSS) and median ranked set sampling (MRSS) procedures. It is shown that the relative precisions of the estimator based on RSSU are higher than those of the estimators based on RSS and MRSS. An example of estimating the mean diameter at breast height of longleaf-pine trees on the Wade Tract in Thomas County, Georgia, is presented.     

Reduced sampling schedule for the glucose minimal model: importance of Bayesian estimation

The minimal model (MM) of glucose kinetics during an intravenous glucose tolerance test (IVGTT) is widely used in clinical studies to measure metabolic indexes such as glucose effectiveness (S(G)) and insulin sensitivity (S(I)). The standard (frequent) IVGTT sampling schedule (FSS) for MM identification consists of 30 points over 4 h. To facilitate clinical application of the MM, reduced sampling schedules (RSS) of 13-14 samples have also been derived for normal subjects. These RSS are especially appealing in large-scale studies. However, with RSS, the precision of S(G) and S(I) estimates deteriorates and, in certain cases, becomes unacceptably poor. To overcome this difficulty, population approaches such as the iterative two-stage (ITS) approach have been recently proposed, but, besides leaving some theoretical issues open, they appear to be oversized for the problem at hand. Here, we show that a Bayesian methodology operating at the single individual level allows an accurate determination of MM parameter estimates together with a credible measure of their precision. Results of 16 subjects show that, in passing from FSS to RSS, there are no significant changes of point estimates in nearly all of the subjects and that only a limited deterioration of parameter precision occurs. In addition, in contrast with the previously proposed ITS method, credible confidence intervals (e.g., excluding negative values) are obtained. They can be crucial for a subsequent use of the estimated MM parameters, such as in classification, clustering, regression, or risk analysis.     

General ranked set sampling with cost considerations

Nahhas, Wolfe, and Chen (2002, Biometrics58, 964-971) considered optimal set size for ranked set sampling (RSS) with fixed operational costs. This framework can be very useful in practice to determine whether RSS is beneficial and to obtain the optimal set size that minimizes the variance of the population estimator for a fixed total cost. In this article, we propose a scheme of general RSS in which more than one observation can be taken from each ranked set. This is shown to be more cost-effective in some cases when the cost of ranking is not so small. We demonstrate using the example in Nahhas, Wolfe, and Chen (2002, Biometrics58, 964-971), by taking two or more observations from one set even with the optimal set size from the RSS design can be more beneficial.     

Enhanced Cumulative Sum Charts for Monitoring Process Dispersion

The cumulative sum (CUSUM) control chart is widely used in industry for the detection of small and moderate shifts in process location and dispersion. For efficient monitoring of process variability, we present several CUSUM control charts for monitoring changes in standard deviation of a normal process. The newly developed control charts based on well-structured sampling techniques - extreme ranked set sampling, extreme double ranked set sampling and double extreme ranked set sampling, have significantly enhanced CUSUM chart ability to detect a wide range of shifts in process variability. The relative performances of the proposed CUSUM scale charts are evaluated in terms of the average run length (ARL) and standard deviation of run length, for point shift in variability. Moreover, for overall performance, we implore the use of the average ratio ARL and average extra quadratic loss. A comparison of the proposed CUSUM control charts with the classical CUSUM R chart, the classical CUSUM S chart, the fast initial response (FIR) CUSUM R chart, the FIR CUSUM S chart, the ranked set sampling (RSS) based CUSUM R chart and the RSS based CUSUM S chart, among others, are presented. An illustrative example using real dataset is given to demonstrate the practicability of the application of the proposed schemes.     

The respective roles of polar/nonpolar binary patterns and amino acid composition in protein regular secondary structures explored exhaustively using hydrophobic cluster analysis

Several studies have highlighted the leading role of the sequence periodicity of polar and nonpolar amino acids (binary patterns) in the formation of regular secondary structures (RSS). However, these were based on the analysis of only a few simple cases, with no direct mean to correlate binary patterns with the limits of RSS. Here, HCA‐derived hydrophobic clusters (HC) which are conditioned binary patterns whose positions fit well those of RSS, were considered. All the HC types, defined by unique binary patterns, which were commonly observed in three‐dimensional (3D) structures of globular domains, were analyzed. The 180 HC types with preferences for either α‐helices or β‐strands distinctly contain basic binary units typical of these RSS. Therefore a general trend supporting the “binary pattern preference” assumption was observed. HC for which observed RSS are in disagreement with their expected behavior (discordant HC) were also examined. They were separated in HC types with moderate preferences for RSS, having “weak” binary patterns and versatile RSS and HC types with high preferences for RSS, having “strong” binary patterns and then displaying nonpolar amino acids at the protein surface. It was shown that in both cases, discordant HC could be distinguished from concordant ones by well‐differentiated amino acid compositions. The obtained results could, thus, help to complement the currently available methods for the accurate prediction of secondary structures in proteins from the only information of a single amino acid sequence. This can be especially useful for characterizing orphan sequences and for assisting protein engineering and design. Proteins 2016; 84:624–638. © 2016 Wiley Periodicals, Inc.     

Application of Numerical Classification to Study the Grazing Retrogressive Succession Stages of the Kobresia Vegetation on the Subalpine Meadow

Using the nearest-neighbour method in the course of numerical classification the four stages of the grazing retrogressive succession .of the Kobresia vegetation in Maqu Xian are divided: Ligularia virgaurea +Stipa aliena -Saussurea sp community and Leontopodium sp-Saussurea superba f. Pygmaea community belongs to the RSS (Retrogressive Succession Stages) of the grazing extremely; Anemone rivularis var fioreminore-Ligularia virgaurea-Kobresia spp community belongs to the RSS of the grazing seriously; Brachy-podium sylvaticum var gracile-Kobresia spp, Kobresia spp-Polygonum viviparum-Festuca rubra and Kobresia spp-Blysmus sinocompressus -Potentilla anserina communities belong to the RSS of the grazing moderately; Kobresia spp-Trollius farrei community belongs to the RSS of the grazing properly. Such classification method gives the same result as the traditional classificational methods of the RSS do. But it gives the numerical bases.     

The iterative two-stage population approach to IVGTT minimal modeling: improved precision with reduced sampling. Intravenous glucose tolerance test

The minimal model method is widely used to estimate glucose effectiveness (S(G)) and insulin sensitivity (S(I)) from intravenous glucose tolerance test (IVGTT) data. In the standard protocol (sIVGTT, 0.33 g/kg glucose bolus given at time 0), which allows the simultaneous assessment of beta-cell function, the precision of the individualized estimates often degrades and particularly so in the presence of reduced sampling schedules. Here, we investigated the use of a population approach, the iterative two-stage (ITS) approach, to analyze 16 sIVGTTs in healthy subjects and to obtain refined estimates of S(G) and S(I) in the population and in the individual subjects. The ITS is based on calculation of the population mean and standard deviation of the parameters at each iteration and then use of them as prior information for the individual analyses. Theoretically, the use of a prior in the ITS should improve the precision of the individual estimates. The customary approach (standard two stage, STS), where modeling is performed separately for each individual subject, does not take the population knowledge into account. We used both frequent (FSS, 30 samples) and (quasi-optimally) reduced (RSS, 14 samples) sampling schedules. For the FSS, STS gave estimates (mean +/- SD) for S(G) = 2.66 +/- 1.09 x 10(-2). min(-1) and S(I) = 6.46 +/- 6.99 10(-4). min(-1). microU(-1). ml, with an average precision of 51 (range 5-176) and 33% (3-91), respectively. RSS radically worsened the precision of both S(G) and S(I). However, RSS and ITS gave S(G) = 2.59 +/- 0.73 and S(I) = 6.06 +/- 7.28, with an average precision of 23 (12-42) and 27% (), respectively. In conclusion, population minimal modeling of sIVGTT data improves the precision of individual estimates of glucose effectiveness and insulin sensitivity, as the theory predicts, and, even with reduced sampling, the improvement is substantial.     

Initiation of V(D)J recombination in vivo: role of recombination signal sequences in formation of single and paired double-strand breaks.

In V(D)J recombination, double-strand breaks (DSBs) are introduced at recombination signal sequences (RSSs) which consist of three distinct elements: a heptamer, a 12 or 23 nucleotide spacer and a nonamer. Efficient DSB formation requires a 12/23 RSS pair and occurs at both RSS in a temporally coupled fashion (coupled cleavage). It remains unknown which RSS elements are important for coupled cleavage. Furthermore, it has not been established whether some RSS components are critical only for cleavage in cis, with others mainly promoting cleavage in trans at the partner RSS. We investigated these questions by analyzing the effects of RSS mutations on the formation of DSBs in vivo. The abundance of DSBs in cis (at the mutant RSS) and in trans (at the consensus RSS) was determined using an established ligation-mediated PCR assay. We also developed a Southern blotting approach that allows the first direct measurement of dual and single RSS cleavage in vivo. Our results demonstrate that the heptamer, spacer and nonamer elements are all required for coupled cleavage in vivo. These studies also provide evidence for cleavage events involving a single RSS both in mutant substrates and in substrates containing a consensus 12/23 RSS pair.     

Assembly Pathway and Characterization of the RAG1/2-DNA Paired and Signal-end Complexes

Mammalian immune receptor diversity is established via a unique restricted set of site-specific DNA rearrangements in lymphoid cells, known as V(D)J recombination. The lymphoid-specific RAG1-RAG2 protein complex (RAG1/2) initiates this process by binding to two types of recombination signal sequences (RSS), 12RSS and 23RSS, and cleaving at the boundaries of RSS and V, D, or J gene segments, which are to be assembled into immunoglobulins and T-cell receptors. Here we dissect the ordered assembly of the RAG1/2 heterotetramer with 12RSS and 23RSS DNAs. We find that RAG1/2 binds only a single 12RSS or 23RSS and reserves the second DNA-binding site specifically for the complementary RSS, to form a paired complex that reflects the known 12/23 rule of V(D)J recombination. The assembled RAG1/2 paired complex is active in the presence of Mg²⁺, the physiologically relevant metal ion, in nicking and double-strand cleavage of both RSS DNAs to produce a signal-end complex. We report here the purification and initial crystallization of the RAG1/2 signal-end complex for atomic-resolution structure elucidation. Strict pairing of the 12RSS and 23RSS at the binding step, together with information from the crystal structure of RAG1/2, leads to a molecular explanation of the 12/23 rule.