Sampling Plan Optimization: A Data Review and Sampling Frequency Evaluation Process

Lawrence Livermore National Laboratory (LLNL) uses a cost-effective sampling (CES) methodology to evaluate and review ground water contaminant data and optimize the site's ground water monitoring plan. The CES methodology is part of LLNL's regulatory approved compliance monitoring plan (Lamarre et al., 1996 Lamarre, A. L., Nichols, E. M., Berg, L. L., Dresen, M. D., Gelinas, R. J., Bainer, R. W. and Folsom, E. N. 1996. Compliance monitoring plan for the Lawrence Livermore National Laboratory Livermore Site UCRL-AR-120936 [Google Scholar]). It allows LLNL to adjust the ground water sampling plan every quarter in response to changing conditions at the site. Since the use of the CES methodology has been approved by the appropriate regulatory agencies, such adjustments do not need additional regulatory approval. This permits LLNL to respond more quickly to changing conditions. The CES methodology bases the sampling frequency for each location on trend, variability, and magnitude statistics describing the contaminants at that location, and on the input of the technical staff (hydrologists, chemists, statisticians, and project leaders). After initial setup is complete, each application of CES takes only a few days for as many as 400 wells. Effective use of the CES methodology requires sufficient data, an understanding of contaminant transport at the site, and an adequate number of monitoring wells downgradient of the contamination. The initial implementation of CES at LLNL in 1992 produced a 40% reduction in the required number of annual routine ground water samples at LLNL. This has saved LLNL $390,000 annually in sampling, analysis, and data management costs.     

Design considerations for efficient and effective microarray studies

This article describes the theoretical and practical issues in experimental design for gene expression microarrays. Specifically, this article 1) discusses the basic principles of design (randomization, replication, and blocking) as they pertain to microarrays, and 2) provides some general guidelines for statisticians designing microarray studies.     

Bayesian modeling of time-varying and waning exposure effects

In epidemiologic studies, there is often interest in assessing the association between exposure history and disease incidence. For many diseases, incidence may depend not only on cumulative exposure, but also on the ages at which exposure occurred. This article proposes a flexible Bayesian approach for modeling age-varying and waning exposure effects. The Cox model is generalized to allow the hazard of disease to depend on an integral, across the exposed ages, of a piecewise polynomial function of age, multiplied by an exponential decay term. Linearity properties of the model facilitate posterior computation via a Gibbs sampler, which generalizes previous algorithms for Cox regression with time-dependent covariates. The approach is illustrated by an application to the study of protective effects of breastfeeding on incidence of childhood asthma.     

Blend uniformity analysis using stream sampling and near infrared spectroscopy

A near infrared spectroscopic method was developed to determine drug content in a 20% (wt/wt) ibuprofen and spray-dried hydous lactose blend. A blending profile was obtained after blending for 0.5, 1, 3, 5, 10, and 20 minutes. Stream sampling was used to collect about 20 blend samples at each of the blending times from a laboratory scale V-blender. The samples collected were used to develop a near infrared calibration model. The calibration model was then used to determine the drug content of unknown samples from 2 validation blends. The validation blends were not included in the calibration model; they were used to evaluate the effectiveness of the calibration model. A total of 45 samples from the 2 validation blends were predicted by the near infrared calibration model and then analyzed by a validated UV spectrophotometric method. The root mean square error of prediction for the first validation blend was 5.69 mg/g and 3.30 mg/g for the samples from the second blend. A paired t test at the 95% confidence level did not indicate any differences between the drug content predicted by the near infrared spectroscopy (NIRS) method and the validated UV method for the 2 blends. The results show that the NIRS method could be developed while the blending profile is generated and used to thoroughly characterize a new formulation during development by analyzing a large number of samples. The new formulation could be transferred to a manufacturing plant with an NIRS method to facilitate blend uniformity analysis.     

Male bimaturism and reproductive success in Sumatran orang-utans

Although orang-utans live solitary lives most of the time, theyhave a complex social structure and are characterized by extremesexual dimorphism. However, whereas some adult male orang-utansdevelop full secondary sexual characteristics, such as cheekflanges, others may stay in an "arrested" unflanged conditionfor up to 20 years after reaching sexual maturity. The resultis a marked bimaturism among adult males. Flanged males allowfemales to overlap with their home range and often toleratethe presence of unflanged males. However, wherever possibleflanged males actively prevent unflanged males from copulatingwith females. Two competing hypotheses, previously untested,have been advanced to explain male reproductive behavior andbimaturism in orang-utans: (1) the "range-guardian" hypothesis,which asserts that the flanged males are postreproductive anddefend a range in which they tolerate sexually active, unflangedmale relatives; and (2) the "female choice" hypothesis, whichasserts that flanged males tolerate unflanged males in their range because they rely on female preference to favor flangedmales. We investigated these hypotheses and a third hypothesisthat the two male morphs represent co-existing alternativemale reproductive strategies ("sitting, calling, and waiting"for flanged males versus "going, searching, and finding" forunflanged males). Fecal samples were collected from a well-studiedpopulation in Indonesia, and eight human microsatellites wereanalyzed for 30 individuals that have been behaviorally monitoredfor up to 27 years. By carrying out paternity analysis on 11offspring born over 15 years, we found that unflanged malesfathered about half (6) of the offspring. Relatedness betweensuccessful unflanged males and resident dominant males wassignificantly lower than 0.5, and for some unflanged/flangedmale pairs, relatedness values were negative, indicating thatunflanged males are not offspring of the flanged males.     

Statistical inference for familial disease clusters

In many epidemiologic studies, the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units. The concept of clustering is contrasted with incidence. We assume that all individuals are exchangeable except for their disease status. This assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease, conditional on the number of diseased cases and the distribution of the sizes of the various family units. New parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering. We consider models and an example that takes covariates into account. Ascertainment bias is described and the appropriate sampling distribution is demonstrated. Four numerical examples with real data illustrate these methods.     

Ranked set sampling for replicated sampling designs

In practical ecological sampling studies, a certain design (such as plot sampling or line-intercept sampling) is usually replicated more than once. For each replication, the Horvitz-Thompson estimation of the objective parameter is considered. Finally, an overall estimator is achieved by averaging the single Horvitz-Thompson estimators. Because the design replications are drawn independently and under the same conditions, the overall estimator is simply the sample mean of the Horvitz-Thompson estimators under simple random sampling. This procedure may be wisely improved by using ranked set sampling. Hence, we propose the replicated protocol under ranked set sampling, which gives rise to a more accurate estimation than the replicated protocol under simple random sampling.     

Basal euteleostean relationships: a mitogenomic perspective on the phylogenetic reality of the "Protacanthopterygii"

Higher-level relationships of the basal Euteleostei (=Protacanthopterygii) are so complex and controversial that at least nine different morphology-based phylogenetic hypotheses have been proposed during the last 30 years. Relationships of the Protacanthopterygii were investigated using mitochondrial genomic (mitogenomic) data from 34 purposefully chosen species (data for 12 species being newly determined during the study) that fully represented major basal euteleostean lineages and some basal teleosts plus neoteleosts as outgroups. Unweighted and weighted maximum parsimony (MP) and maximum likelihood (ML) analyses were conducted with the data set that comprised concatenated nucleotide sequences from 12 protein-coding genes (excluding the ND6 gene and 3rd codon positions) and 22 transfer RNA (tRNA) genes (stem regions only) from the 34 species. The resultant trees were well resolved and largely congruent, with most internal branches being supported by high statistical values. Monophyly of the protacanthopterygians was confidently rejected by the mitogenomic data. Of the five major monophyletic groups that received high statistical support within the protacanthopterygians, a clade comprising members of the alepocephaloids was unexpectedly nested within the Otocephala, sister-group of the euteleosts. The remaining four major monophyletic groups, on the other hand, occupied phylogenetic positions intermediate between the otocephalans and neoteleosts, with a clade comprising esociforms + salmoniforms being more basal to the argentinoids and osmeroids. Although interrelationships of the latter two clades (argentinoids and osmeroids) with the neoteleosts remained ambiguous, the present results indicated explicitly that the protacanthopterygians as currently defined merely represent a collective, polyphyletic group of the basal euteleosts, located between the basal teleosts (elopomorphs and below) and neoteleosts (stomiiforms and above).     

Components of spatial patterning in a serpentine grassland

We analyzed the components of spatial patterning in species abundance in a diverse grassland dominated by early season, annual forbs. Species abundance, soil depth and gopher disturbances were measured by means of a nested spatial design on two 8m×20m plots that differed in the amount of larger scale variability in soil depth. Species distributions at the scale of the 10cm×10cm quadrat were highly clumped, with a decline in clumping with mean abundance. Even with the effect of abundance on clumping removed, species showed differences in the degree of clumping and these differences were consistent between the two plots. The abundance of the species and the frequency of disturbance correlated weakly to moderately with soil depth. Semivariance analyses indicated that the most common species all showed complex spatial patterning at a range of scales. Some of this variation corresponded to patterns of soil depth variation and patterns of gopher disturbance; however, a large amount of the spatial patterning in species abundance remains unexplained.     

Optimizing resolution in multidimensional NMR by three-way decomposition

Resolution depends on the number of points sampled in a FID; in indirectly detected dimensions it is an important determinant of the total experiment time. Based on the high redundancy present in NMR data, we propose the following timesaving scheme for three-dimensional spectra. An extensive grid of discrete t1- and t2-values is used, which increases resolution while preserving the spectral width. Total experiment time is reduced by avoiding the recording of t3-FIDs for selected pairs of t1 and t2; typically the recording is omitted for about 75% of the (t1,t2) combinations. These data sets are referred to as sparse, and post-experimental processing making optimal use of spectral redundancy provides the missing, non-recorded data. We have previously shown that three-way decomposition (TWD) within the MUNIN approach provides a practical way to process dense NMR data sets. Here, a novel TWD algorithm [Ibraghimov, (2002) Numer. Linear Algebra Appl. 9, 551–565] is used to complement a sparselyrecorded time-domain data set by providing the missing FIDs for all (t1,t2) combinations omitted in the experiment. A necessary condition is that for each t1-value at least a few FIDs are recorded, and similar for each t2-value. The method is demonstrated on non-uniformly sampled ¹⁵N-NOESY-HSQC data sets recorded for the 14 kD protein azurin. The spectra obtained by TWD, reconstruction and ordinary transform to frequency-domain are, in spite of the large number of signals and the high dynamic range typical for NOESYs, highly similar to a corresponding reference spectrum, for which all (t1,t2) combinations were recorded.