Mohammad M. Salehi

TWO-STAGE ADAPTIVE CLUSTER SAMPLING

Adaptive cluster sampling is a powerful method for parameter estimation when a population is highly clumped with clumps widely separated. Unfortunately, its use has been somewhat limited until now because of the lack of a suitable theory for using a pilot survey to design an experiment with a given efficiency or expected cost. A two-stage sampling procedure using an initial sample of primary units that fills this role is described. As adaptive cluster sampling amounts to sampling clusters of secondary units, two schemes are possible depending on whether the clusters are allowed to overlap primary unit boundaries or not. For each of these schemes, there are two types of unbiased estimators available based, respectively, on modifications of the well-known Horvitz-Thompson and Hansen-Hurwitz estimators. Questions of cost and efficiency are discussed. A demonstration example is given.

Comparison between Hansen-Hurwitz and Horvitz-Thompson estimators for adaptive cluster sampling

Thompson (1990) introduced the adaptive cluster sampling design. This sampling design has been shown to be a useful sampling method for parameter estimation of a clustered and scattered population (Roesch, 1993; Smith et al., 1995; Thompson and Seber, 1996). Two estimators, the modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators, are available to estimate the mean or total of a population. Empirical results from previous researches indicate that the modified HT estimator has smaller variance than the modified HH estimator. We analytically compare the properties of these two estimators. Some results are obtained in favor of the modified HT estimator so that practitioners are strongly recommended to use the HT estimator despite easiness of computations for the HH estimator.

Two-stage sequential sampling: A neighborhood-free adaptive sampling procedure

Designing an efficient sampling scheme for a rare and clustered population is a challenging area of research. Adaptive cluster sampling, which has been shown to be viable for such a population, is based on sampling a neighborhood of units around a unit that meets a specified condition. However, the edge units produced by sampling neighborhoods have proven to limit the efficiency and applicability of adaptive cluster sampling. We propose a sampling design that is adaptive in the sense that the final sample depends on observed values, but it avoids the use of neighborhoods and the sampling of edge units. Unbiased estimators of population total and its variance are derived using Murthy’s estimator. The modified two-stage sampling design is easy to implement and can be applied to a wider range of populations than adaptive cluster sampling. We evaluate the proposed sampling design by simulating sampling of two real biological populations and an artificial population for which the variable of interest took the value either 0 or 1 (e.g., indicating presence and absence of a rare event). We show that the proposed sampling design is more efficient than conventional sampling in nearly all cases. The approach used to derive estimators (Murthy’s estimator) opens the door for unbiased estimators to be found for similar sequential sampling designs.

Theory & Methods: A New Proof of Murthy's Estimator which Applies to Sequential Sampling

Murthys estimator has been used for constructing an unbiased estimator of a population total or mean from a sample of fixed size when there is unequal probability sampling without replacement. Traditionally, the estimator is derived by constructing an unordered version of Rajs ordered unbiased estimator. This paper presents an elementary proof of Murthys estimator which applies the Rao–Blackwell theorem to a very simple estimator. This proof includes any sequential sampling scheme, thus extending the usefulness of Murthys estimator. We demonstrate this extension by deriving unbiased estimators for inverse sampling.

An adaptive two-stage sequential design for sampling rare and clustered populations

How to design an efficient large-area survey continues to be an interesting question for ecologists. In sampling large areas, as is common in environmental studies, adaptive sampling can be efficient because it ensures survey effort is targeted to subareas of high interest. In two-stage sampling, higher density primary sample units are usually of more interest than lower density primary units when populations are rare and clustered. Two-stage sequential sampling has been suggested as a method for allocating second stage sample effort among primary units. Here, we suggest a modification: adaptive two-stage sequential sampling. In this method, the adaptive part of the allocation process means the design is more flexible in how much extra effort can be directed to higher-abundance primary units. We discuss how best to design an adaptive two-stage sequential sample.

Adaptive survey designs for sampling rare and clustered populations

Designing an efficient large-area survey is a challenge, especially in environmental science when many populations are rare and clustered. Adaptive and unequal probability sampling designs are appealing when populations are rare and clustered because survey effort can be targeted to subareas of high interest. For example, higher density subareas are usually of more interest than lower density areas. Adaptive and unequal probability sampling offer flexibility for designing a long-term survey because they can accommodate changes in survey objectives, changes in underlying environmental habitat, and changes in species-habitat models. There are many different adaptive sampling designs including adaptive cluster sampling, two-phase stratified sampling, two-stage sequential sampling, and complete allocation stratified sampling. Sample efficiency of these designs can be very high compared with simple random sampling. Large gains in efficiency can be made when survey effort is targeted to the subareas of the study site where there are clusters of individuals from the underlying population. These survey methods work by partitioning the study area in some way, into strata, or primary sample units, or in the case of adaptive cluster sampling, into networks. Survey effort is then adaptively allocated to the strata or primary unit where there is some indication of higher species counts. Having smaller, and more numerous, strata improves efficiency because it allows more effective targeting of the adaptive, second-phase survey effort.

Complete allocation sampling: An efficient and easily implemented adaptive sampling design

Adaptive sampling designs are becoming increasingly popular in environmental science, particularly for surveying rare and aggregated populations. An adaptive sample is one in which the survey design is modified, or adapted, in some way on the basis of information gained during the survey. There are many different adaptive survey designs that can be used to estimate animal and plant abundance. In adaptive cluster sampling, additional sample effort is allocated during the survey to the immediate neighborhood in which the species is found. In adaptive stratified sampling, additional sample effort is allocated during the survey to strata of high abundance. The appealing feature of these adaptive designs is that the field biologist gets to do what innately seems sensible when working with rare and aggregated populations—field effort is targeted around where the species is observed in the first wave of the survey. However, there are logistical challenges of applying this principle of targeted field effort while remaining in the framework of probability-based sampling. We propose a simplified adaptive survey design that incorporates both targeting field effort and being logistically feasible. We show with a case study population of rockfish that complete allocation stratified sampling is a very efficient design.

Assessing the effectiveness of a pharmacist-delivered smoking cessation program in the State of Qatar: study protocol for a randomized controlled trial

BackgroundIt had been reported that up to 37% of the adult male population smokes cigarettes in Qatar. The Global Youth Tobacco Survey also stated that 13.4% of male school students aged 13 to 15 years in Qatar smoke cigarettes. Smoking cessation is key to reducing smoking-related diseases and deaths. Healthcare providers are in an ideal position to encourage smoking cessation. Pharmacists are the most accessible healthcare providers and are uniquely situated to initiate behavior change among patients. Many studies have shown that pharmacists can be successful in helping patients quit smoking. Studies demonstrating the effectiveness of pharmacist-delivered smoking cessation programs are lacking in Qatar. This proposal aims to test the effect of a structured smoking cessation program delivered by trained ambulatory pharmacists in Qatar.Methods/DesignA prospective, randomized, controlled trial is conducted at eight ambulatory pharmacies in Qatar. Participants are randomly assigned to receive an at least four-session face-to-face structured patient-specific smoking cessation program conducted by the pharmacist or 5 to 10 min of unstructured brief smoking cessation advice (emulating current practice) given by the pharmacist. Both groups are offered nicotine replacement therapy if feasible. The primary outcome of smoking cessation will be confirmed by an exhaled carbon monoxide test at 12 months. Secondary outcomes constitute quality-of-life adjustment as well as cost analysis of program resources consumed, including per case and patient outcome.DiscussionIf proven to be effective, this smoking cessation program will be considered as a model that Qatar and the region can apply to decrease the smoking burden.Trial registrationClinical Trials NCT02123329.

Two-Stage Cluster Sampling with Ranked Set Sampling in the Secondary Sampling Frame

Motivated by a real-life problem, we develop a Two-Stage Cluster Sampling with Ranked Set Sampling (TSCRSS) design in the second stage for which we derive an unbiased estimator of population mean and its variance. An unbiased estimator of the variance of mean estimator is also derived. It is proved that the TSCRSS is more efficient—in the sense of having smaller variance—than the conventional two-stage cluster simple random sampling in which the second-stage sampling is with replacement. Using a simulation study on a real-life population, we show that the TSCRSS is more efficient than the conventional two-stage cluster sampling when simple random sampling without replacement is used in both stages.

Two-stage complete allocation sampling: Two-stage complete allocation sampling

An adaptive sample involves modifying the sampling design on the basis of information obtained during the survey while remaining in the probability sampling framework. Complete allocation sampling is an efficient and easily implemented 2‐phase adaptive sampling design that targets field effort to rare species and is logistically feasible. The population is partitioned into strata that contain (secondary) units, and a simple random sample of secondary units is selected from each of the strata. If an individual is observed in any selected unit, all the units in its stratum will then be sampled in the second phase. However, the condition of observing at least 1 individual in a unit to survey all units in its stratum might be too restrictive for some populations and too expensive. We extend the design 2 ways. First, we introduce a 2‐stage sampling scheme with primary units taking over the role of strata and taking a random sample of primary units. A simple random sample of the secondary units in each selected primary unit is then carried out and if any more than a certain number of rare units (and not just any) are found, the whole primary unit is sampled. This more general criterion for selection is the second extension. If we choose all the primary units, then we are back to complete allocation sampling with strata. We derive an unbiased estimator for the total and its variance estimator for this new 2‐stage design. Using a real‐life population of buttercups, we show that this 2‐stage design observes more buttercups and its estimator can be considerably more precise compared to its conventional sampling design counterpart.