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.

Efficient designs for sampling and subsampling in fisheries research based on ranked sets

Sampling strategies are developed based on the idea of ranked set sampling (RSS) to increase efficiency and therefore to reduce the cost of sampling in fishery research. The RSS incorporates information on concomitant variables that are correlated with the variable of interest in the selection of samples. For example, estimating a monitoring survey abundance index would be more efficient if the sampling sites were selected based on the information from previous surveys or catch rates of the fishery. We use two practical fishery examples to demonstrate the approach: site selection for a fishery-independent monitoring survey in the Australian northern prawn fishery (NPF) and fish age prediction by simple linear regression modelling a short-lived tropical clupeoid. The relative efficiencies of the new designs were derived analytically and compared with the traditional simple random sampling (SRS). Optimal sampling schemes were measured by different optimality criteria. For the NPF monitoring survey, the efficiency in terms of variance or mean squared errors of the estimated mean abundance index ranged from 114 to 199% compared with the SRS. In the case of a fish ageing study for Tenualosa ilisha in Bangladesh, the efficiency of age prediction from fish body weight reached 140%.

Weighted rank regression for clustered data analysis

We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration.

Optimal sign tests for data from ranked set samples

This paper considers the one-sample sign test for data obtained from general ranked set sampling when the number of observations for each rank are not necessarily the same, and proposes a weighted sign test because observations with different ranks are not identically distributed. The optimal weight for each observation is distribution free and only depends on its associated rank. It is shown analytically that (1) the weighted version always improves the Pitman efficiency for all distributions; and (2) the optimal design is to select the median from each ranked set.

General ranked set sampling with cost considerations

Nahhas, Wolfe, and Chen (2002, Biometrics 58, 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, Biometrics 58, 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.

Elicitator : an expert elicitation tool for regression in ecology

Expert elicitation is the process of retrieving and quantifying expert knowledge in a particular domain. Such information is of particular value when the empirical data is expensive, limited, or unreliable. This paper describes a new software tool, called Elicitator, which assists in quantifying expert knowledge in a form suitable for use as a prior model in Bayesian regression. Potential environmental domains for applying this elicitation tool include habitat modeling, assessing detectability or eradication, ecological condition assessments, risk analysis, and quantifying inputs to complex models of ecological processes. The tool has been developed to be user-friendly, extensible, and facilitate consistent and repeatable elicitation of expert knowledge across these various domains. We demonstrate its application to elicitation for logistic regression in a geographically based ecological context. The underlying statistical methodology is also novel, utilizing an indirect elicitation approach to target expert knowledge on a case-by-case basis. For several elicitation sites (or cases), experts are asked simply to quantify their estimated ecological response (e.g. probability of presence), and its range of plausible values, after inspecting (habitat) covariates via GIS.

Comparison of three expert elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby petrogale penicillata

Numerous expert elicitation methods have been suggested for generalised linear models (GLMs). This paper compares three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression. These methods were trialled on two experts in order to model the habitat suitability of the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The first elicitation approach is a geographically assisted indirect predictive method with a geographic information system (GIS) interface. The second approach is a predictive indirect method which uses an interactive graphical tool. The third method uses a questionnaire to elicit expert knowledge directly about the impact of a habitat variable on the response. Two variables (slope and aspect) are used to examine prior and posterior distributions of the three methods. The results indicate that there are some similarities and dissimilarities between the expert informed priors of the two experts formulated from the different approaches. The choice of elicitation method depends on the statistical knowledge of the expert, their mapping skills, time constraints, accessibility to experts and funding available. This trial reveals that expert knowledge can be important when modelling rare event data, such as threatened species, because experts can provide additional information that may not be represented in the dataset. However care must be taken with the way in which this information is elicited and formulated.

In vivo knockdown of the androgen receptor results in growth inhibition and regression of well-established, castration-resistant prostate tumours

Purpose: Progression to the castration-resistant state is the incurable and lethal end stage of prostate cancer, and there is strong evidence that androgen receptor (AR) still plays a central role in this process. We hypothesize that knocking down AR will have a major effect on inhibiting growth of castration-resistant tumors. Experimental Design: Castration-resistant C4-2 human prostate cancer cells stably expressing a tetracycline-inducible AR-targeted short hairpin RNA (shRNA) were generated to directly test the effects of AR knockdown in C4-2 human prostate cancer cells and tumors. Results:In vitro expression of AR shRNA resulted in decreased levels of AR mRNA and protein, decreased expression of prostate-specific antigen (PSA), reduced activation of the PSA-luciferase reporter, and growth inhibition of C4-2 cells. Gene microarray analyses revealed that AR knockdown under hormone-deprived conditions resulted in activation of genes involved in apoptosis, cell cycle regulation, protein synthesis, and tumorigenesis. To ensure that tumors were truly castration-resistant in vivo, inducible AR shRNA expressing C4-2 tumors were grown in castrated mice to an average volume of 450 mm3. In all of the animals, serum PSA decreased, and in 50% of them, there was complete tumor regression and disappearance of serum PSA. Conclusions: Whereas castration is ineffective in castration-resistant prostate tumors, knockdown of AR can decrease serum PSA, inhibit tumor growth, and frequently cause tumor regression. This study is the first direct evidence that knockdown of AR is a viable therapeutic strategy for treatment of prostate tumors that have already progressed to the castration-resistant state.