Estimator bias and efficiency for adaptive cluster sampling with order statistics and a stopping rule

Practical problems facing adaptive cluster sampling with order statistics (acsord) are explored using Monte Carlo simulation for three simulated fish populations and two known waterfowl populations. First, properties of an unbiased Hansen-Hurwitz (HH) estimator and a biased alternative Horvitz-Thompson (HT) estimator are evaluated. An increase in the level of population aggregation or the initial sample size increases the efficiencies of the two acsord estimators. For less aggregated fish populations, the efficiencies decrease as the order statistic parameter r (the number of units about which adaptive sampling is carried out) increases; for the highly aggregated fish and waterfowl populations, they increase with r. Acsord is almost always more efficient than simple random sampling for the highly aggregated populations. Positive bias is observed for the HT estimator, with the maximum bias usually occurring at small values of r. Secondly, a stopping rule at the Sth iteration of adaptive sampling beyond the initial sampling unit was applied to the acsord design to limit the otherwise open-ended sampling effort. The stopping rule induces relatively high positive bias to the HH estimator if the level of the population aggregation is high, the stopping level S is small, and r is large. The bias of HT is not very sensitive to the stopping rule and its bias is often reduced by the stopping rule at smaller values of r. For more aggregated populations, the stopping rule often reduces the efficiencies of the estimators compared to the non-stopping-rule scheme, but acsord still remains more efficient than simple random sampling. Despite its bias and lack of theoretical grounding, the HT estimator is usually more efficient than the HH estimator. In the stopping rule case, the HT estimator is preferable, because its bias is less sensitive to the stopping level.     

Performance of adaptive cluster sampling estimators in a multivariate setting

Adaptive cluster sampling has been proven to perform well in a univariate setting, but it may not perform well when there are several parameters of interest. The efficiency of adaptive sampling when there are several variables of interest depends on the relationship of the variables with one another.     

Markov Chain Monte Carlo on optimal adaptive sampling selections

Under a Bayesian population model with a given prior distribution, the optimal sampling strategy with a fixed sample size n is an n-phase adaptive one. That is, the selection of the next sampling units should sequentially depend on the information obtained from the previously selected units, including the observed values of interest. Such an optimal strategy is in general not executable in practice due to its intensive computation. In many survey sampling situations, an important problem is that one would like to select a set of units in addition to a certain number of sampling units which have been observed. If the optimal strategy is an adaptive one, the selection of the additional units should take both the labels and the observed values of the already selected units into account. Hence, a simpler optimal two-phase adaptive sampling strategy under a Bayesian population model is proposed in this article for practical interest. A Markov chain Monte Carlo method is used to approximate the posterior joint distribution of the unobserved population units after the first phase sampling, for the optimal selection of the second phase sample. This approximation method is found to be successful to select the optimal second-phase sample. Finally, this optimal strategy is applied to a set of data from a study of geothermal CO₂ emissions in Yellowstone National Park as a practical illustrative example.     

Statistical evaluation of the attainment of interim cleanup standards at hazardous waste sites

Cleanup standards at hazardous waste sites include (i) numeric standards (often risk-based), (ii) background standards in which the remediated site is compared with data from a supposedly clean region, and (iii) interim standards in which the remediated site is compared with preremediation data from the same site. The latter are especially appropriate for verifying progress when an innovative, but unproven, technology is used for remediation. Standards of type (i) require one-sample statistical tests, while those of type (ii) and type (iii) call for two-sample tests. This paper considers two-sample tests with an emphasis upon the type (iii) scenario. Both parametric (likelihood ratio) and nonparametric (linear rank) protocols are examined. The methods are illustrated with preremediation data from a site on the National Priorities List. The results indicate that nonparametric procedures can be quite competitive (in terms of power) with distributional modelling provided a near optimal rank test is selected. Suggestions are given for identifying such rank tests. The results also confirm the importance of sound baseline sampling; no amount of post-remediation sampling can overcome baseline deficiencies.This paper has been prepared with partial support from the United States Environmental Protection Agency under a Cooperative Agreement Number CR-815273. The contents have not been subject to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.     

The reflection method of line intercept sampling to eliminate boundary bias

When a line transect overlaps the boundary of the sampled region, it can be reflected back on top of itself into the region, thereby making it possible to include elements near the edge twice from the same transect. A practical advantage of doing so is the reduction of field time and effort compared to the customary procedure of folding the transect back into another part of the region. An estimator is presented which accounts for this procedure in a way that preserves design-unbiased estimation.     

Chorionic mosaicism: Association with fetal loss but not with adverse perinatal outcome

Cytogenetic data from the United States NICHD collaborative study of chorionic villus sampling (CVS) were used to evaluate the clinical significance of chorionic mosaicism. The 10 754 patients with normal cytogenetic results were compared wtih 108 patients (1.0 per cent) with placental mosaicism and 181 patients (1.6 per cent) with pseudomosaicism. Of the pregnancies intended to continue, the pregnancy loss rate was significantly greater in patients with placental mosaicism than in the cytogenetically normal cohort (8.6 vs. 3.4 per cent, p <0.05). However, there was no difference in the frequencies of abruptio placenta, preterm labour or delivery, small-for-gestational-age newborns, pregnancy-induced hypertension, or neonates with Apgar scores less than 7.     

Transabdominal chorionic villus sampling for fetal genetic diagnosis. Technical and obstetrical evaluation of 100 cases

First trimester fetal diagnosis was established in 100 pregnancies at risk by transabdominal chorionic villus sampling (TA-CVS). Forty-eight per cent of the women were 35 years or more at the time of sampling. Using the double needle technique, both the aspiration and the diagnostic success rate were 100 per cent. The mean amount of villi aspirated was 28·2 mg (10–50 mg). The mean needle time was 3 min. Vaginal spotting appeared in 2 per cent of the women. Four women had therapeutic abortion due to abnormal findings and one for social reasons. Three fetuses with normal karyotypes were lost. Excluding the therapeutic abortions, the fetal loss rate was 3±2 per cent. The fetal loss rate in the amniocentesis control group (n = 200) was 3±6 per cent. The cytogenetic diagnosis was carried out by the direct preparation technique as well as by chorion villus cultivation. All karyotypes were confirmed by lymphocyte cultures from umbilical cord blood or heel blood from the newborn or from aborted fetal tissue. Transabdominal CVS is deemed a safe and easy tool for achieving chorionic villi in the first trimester.     

Maternal cell contamination in chorionic villus samples assessed by direct preparations and three different culture methods

Presumptive maternal cell contamination (MCC) was monitored in identified male cases during cytogenetic comparison of direct techniques and three different culture regimes from 140 thoroughly dissected chorionic villus samples. Of the 66 identified male cases, 11(16·7 per cent) showed MCC, the mean number of cells examined per case being 8·2 (direct) and 14·5 (cultures); in the direct preparations only one of a total of 457 cells examined was female, while preparations from cultures revealed MCC in 11 cases. Four of these had MCC in more than one culture regime and four had only a single female cell. The results showed that (1) dependence on the culture system alone would have given a diagnosis based on maternal cells in one (1·5 per cent) male case, thus underlining the danger of this approach (a similar undetected rate of misdiagnosis being expected in the female cases) and (2) MCC was significantly lower in cultures grown in Chang medium as compared with the other two regimes, McCoy's 5A + 15 per cent fetal calf serum and 1 per cent Ultroser G, and McCoy's 5A + 25 per cent fetal calf serum, the latter expressing the highest level of MCC.     

Confined placental mosaicism,IUGR, and adverse pregnancy outcome: A controlled retrospective U.K. collaborative survey

In a retrospective collaborative study involving 21 U.K. laboratories and 11775 CVS prenatal diagnostic procedures, a total of 73 cases of confined placental mosaicism (CPM) were identified among the 8004 first-trimester referrals because of advanced maternal age, a previous child with a numerical chromosome abnormality, or a family history of the same. Data were collected on subsequent cytogenetic follow-up and pregnancy outcome for each case and a referral matched control. Comparison with the control population failed to demonstrate a marked increase in adverse pregnancy outcome in the CPM group, but a significant increase in both low and high birth weight infants was recorded. In a parallel study, 7 out of 108 cases, referred for prenatal diagnosis because of ultrasound detection of isolated intrauterine growth retardation (IUGR) in the second or third trimester, were shown to have a chromosome abnormality restricted to the extraembryonic tissues. These included cases of CPM involving trisomy 9 and del(13)(q13), neither of which has previously been reported in association with IUGR.