Comparison of sequential and fixed-structure sampling of pedigrees in complex segregation analysis of a quantitative trait.

In designing a study to demonstrate the existence of a major locus for a quantitative trait, an investigator chooses a sampling rule to ascertain pedigrees. The choice of sampling rule can significantly affect the study's power. Here, we compare two types of sampling rules for family studies: fixed-structure rules, in which the same set of relatives are sampled for each proband, and sequential rules, in which the relative or relatives to be sampled next may depend on the trait values of the individuals already observed. We compare fixed-structure and sequential sampling in the setting of extended pedigrees, a quantitative trait, and the genetic mixed model. Using computer simulation, we show that sequential sampling can increase power to detect segregation at a dominant major locus by over 60% in comparison with fixed-structure sampling. Just as important, this substantially increased power is obtained with an easily implemented sampling rule, one that might reasonably be employed in a family study of a quantitative trait.     

A note on 'stomaching' for the quantitative sampling of epiphyton

SUMMARY. 1. Methods for the quantitative removal of epiphyton from Cladophora glomerata were compared.
2. Stomaching for 3–5 min effected maximum epiphyte release. Agitation for up to 40 min in water or hydroiysing solutions of hydrochloric acid or F.A.A. removed significantly fewer epiphytes.
3. Stomaching is recommended as a new, simple, quick and effective method for quantitative epiphyton sampling.     

A note on algorithms for genotype and allele elimination in complex pedigrees with incomplete genotype data

Elimination of genotypes or alleles for each individual or meiosis, which are inconsistent with observed genotypes, is a component of various genetic analyses of complex pedigrees. Computational efficiency of the elimination algorithm is critical in some applications such as genotype sampling via descent graph Markov chains. We present an allele elimination algorithm and two genotype elimination algorithms for complex pedigrees with incomplete genotype data. We modify all three algorithms to incorporate inheritance restrictions imposed by a complete or incomplete descent graph such that every inconsistent complete descent graph is detected in any pedigree, and every inconsistent incomplete descent graph is detected in any pedigree without loops with the genotype elimination algorithms. Allele elimination requires less CPU time and memory, but does not always eliminate all inconsistent alleles, even in pedigrees without loops. The first genotype algorithm produces genotype lists for each individual, which are identical to those obtained from the Lange-Goradia algorithm, but exploits the half-sib structure of some populations and reduces CPU time. The second genotype elimination algorithm deletes more inconsistent genotypes in pedigrees with loops and detects more illegal, incomplete descent graphs in such pedigrees.     

Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops.

We apply the method of "blocking Gibbs" sampling to a problem of great importance and complexity-linkage analysis. Blocking Gibbs sampling combines exact local computations with Gibbs sampling, in a way that complements the strengths of both. The method is able to handle problems with very high complexity, such as linkage analysis in large pedigrees with many loops, a task that no other known method is able to handle. New developments of the method are outlined, and it is applied to a highly complex linkage problem in a human pedigree.     

A note on a method to aid sampling populations for characteristics

A method is described for determining the minimum sample size for examining characters in animal or microbial populations.     

Improved techniques for sampling complex pedigrees with the Gibbs sampler

Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler.     

A note on the sampling theory for infinite alleles and infinite sites models

This note considers sampling theory for a selectively neutral locus where it is supposed that the data provide nucleotide sequences for the genes sampled. It thus anticipates that technical advances will soon provide data of this form in volume approaching that currently obtained from electrophoresis. The assumption made on the nature of the data will require us to use, in the terminology ofKimura (Theor. Pop. Biol.2, 174–208 (1971)), the “infinite sites” model of Karlin and McGregor (Proc. Fifth Berkeley Symp. Math. Statist. Prob.4, 415–438 (1967)) rather that the “infinite alleles” model of Kimura and Crow (Genetics49, 174–738 (1964)). We emphasize that these two models refer not to two different real-world circumstances, but rather to two different assumptions concerning our capacity to investigate the real world. We compare our results where appropriate with corresponding sampling theory of Ewens (Theor. Pop. Biol.3, 87–112 (1972)) for the “infinite alleles” model. Note finally that some of our results depend on an assumption of independence of behavior at individual sites; a parallel paper byWatterson (submitted for publication (1974)) assumes no recombination between sites. Real-world behavior will lie between these two assumptions, closer to the situation assumed by Watterson than in this note. Our analysis provides upper bounds for increased efficiency in using complete nucleotide sequences.     

Accounting for cluster sampling in constructing enumerative sequential sampling plans

Green's sequential sampling plan is widely used in applied entomology. Green's equation can be used to construct sampling stop charts, and a crop can then be surveyed using a simple random sampling (SRS) approach. In practice, however, crops are rarely surveyed according to SRS. Rather, some type of hierarchical design is usually used, such as cluster sampling, where sampling units form distinct groups. This article explains how to make adjustments to sampling plans that intend to use cluster sampling, a commonly used hierarchical design, rather than SRS. The methodologies are illustrated using diamondback moth, Plutella xylostella (L.), a pest of Brassica crops, as an example.     

A note on case-control sampling to estimate kappa coefficients

The feasibility and cost-effectiveness of estimation of kappa using a case-control method of sampling, proposed by Jannarone, Macera, and Garrison (1987, Biometrics 43, 433-437), is provided support. However, in this article unrealistic assumptions in their presentation are identified and more general results for more realistic settings are provided.     

A note on P-values under group sequential testing and nonproportional hazards

Summary .   Group sequential designs are often used for periodically assessing treatment efficacy during the course of a clinical trial. Following a group sequential test, P -values computed under the assumption that the data were gathered according to a fixed sample design are no longer uniformly distributed under the null hypothesis of no treatment effect. Various sample space orderings have been proposed for computing proper P -values following a group sequential test. Although many of the proposed orderings have been compared in the setting of time-invariant treatment effects, little attention has been given to their performance when the effect of treatment within an individual varies over time. Our interest here is to compare two of the most commonly used methods for computing proper P -values following a group sequential test, based upon the analysis time (AT) and Z -statistic orderings, with respect to resulting power functions when treatment effects on survival are delayed. Power under the AT ordering is shown to be heavily influenced by the presence of a delayed treatment effect, while power functions corresponding to the Z -statistic ordering remain robust under time-varying treatment effects.     

An algorithm for sampling descent graphs in large complex pedigrees efficiently

No exact method for determining genotypic and identity-by-descent probabilities is available for large complex pedigrees. Approximate methods for such pedigrees cannot be guaranteed to be unbiased. A new method is proposed that uses the Metropolis-Hastings algorithm to sample a Markov chain of descent graphs which fit the pedigree and known genotypes. Unknown genotypes are determined from each descent graph. Genotypic probabilities are estimated as their means. The algorithm is shown to be unbiased for small complex pedigrees and feasible and consistent for moderately large complex pedigrees.     

Why sampling scheme matters: the effect of sampling scheme on landscape genetic results

There has been a recent trend in genetic studies of wild populations where researchers have changed their sampling schemes from sampling pre-defined populations to sampling individuals uniformly across landscapes. This reflects the fact that many species under study are continuously distributed rather than clumped into obvious “populations”. Once individual samples are collected, many landscape genetic studies use clustering algorithms and multilocus genetic data to group samples into subpopulations. After clusters are derived, landscape features that may be acting as barriers are examined and described. In theory, if populations were evenly sampled, this course of action should reliably identify population structure. However, genetic gradients and irregularly collected samples may impact the composition and location of clusters. We built genetic models where individual genotypes were either randomly distributed across a landscape or contained gradients created by neighbor mating for multiple generations. We investigated the influence of six different sampling protocols on population clustering using program STRUCTURE, the most commonly used model-based clustering method for multilocus genotype data. For models where individuals (and their alleles) were randomly distributed across a landscape, STRUCTURE correctly predicted that only one population was being sampled. However, when gradients created by neighbor mating existed, STRUCTURE detected multiple, but different numbers of clusters, depending on sampling protocols. We recommend testing for fine scale autocorrelation patterns prior to sample clustering, as the scale of the autocorrelation appears to influence the results. Further, we recommend that researchers pay attention to the impacts that sampling may have on subsequent population and landscape genetic results. The U.S. Government's right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

A refined method for sequential blood sampling by tail incision in rats

Levels of endogenous or administered substances can be estimated by blood sampling. This allows an evaluation of the relationship between clinical signs, physiological parameters, pharmacological treatments and behaviour of the animal. We show that blood samples can be taken occasionally as well as sequentially by means of a small incision at the end of the rats' tails. Up to 300 microl of blood can be collected within 90 s. The advantages of this method are: (i) anaesthesia and surgery or restraint of the animal are not necessary; (ii) the procedure can be considered stress-free as indicated by the low, basal levels of the stress hormone corticosterone, even with frequent sequential blood sampling over 3 h; and (iii) it can be used for longitudinal studies allowing intra-individual comparisons over months and even years. Blood samples collected via an intravenous catheter and, at the same time, by our tail incision method resulted in comparable amounts of corticosterone. Moreover, we consider the tail incision method for rats to be 'animal-friendly' and a real alternative to other conventionally used blood sampling techniques.     

An optimization-based sampling scheme for phylogenetic trees

Much modern work in phylogenetics depends on statistical sampling approaches to phylogeny construction to estimate probability distributions of possible trees for any given input data set. Our theoretical understanding of sampling approaches to phylogenetics remains far less developed than that for optimization approaches, however, particularly with regard to the number of sampling steps needed to produce accurate samples of tree partition functions. Despite the many advantages in principle of being able to sample trees from sophisticated probabilistic models, we have little theoretical basis for concluding that the prevailing sampling approaches do in fact yield accurate samples from those models within realistic numbers of steps. We propose a novel approach to phylogenetic sampling intended to be both efficient in practice and more amenable to theoretical analysis than the prevailing methods. The method depends on replacing the standard tree rearrangement moves with an alternative Markov model in which one solves a theoretically hard but practically tractable optimization problem on each step of sampling. The resulting method can be applied to a broad range of standard probability models, yielding practical algorithms for efficient sampling and rigorous proofs of accurate sampling for heated versions of some important special cases. We demonstrate the efficiency and versatility of the method by an analysis of uncertainty in tree inference over varying input sizes. In addition to providing a new practical method for phylogenetic sampling, the technique is likely to prove applicable to many similar problems involving sampling over combinatorial objects weighted by a likelihood model.     

A note on semiparametric efficient inference for two-stage outcome-dependent sampling with a continuous outcome

Outcome-dependent sampling designs have been shown to be a cost-effectiveway to enhance study efficiency. We show that the outcome-dependentsampling design with a continuous outcome can be viewed as anextension of the two-stage case-control designs to the continuous-outcomecase. We further show that the two-stage outcome-dependent samplinghas a natural link with the missing-data and biased-samplingframeworks. Through the use of semiparametric inference andmissing-data techniques, we show that a certain semiparametricmaximum-likelihood estimator is computationally convenient andachieves the semiparametric efficient information bound. Wedemonstrate this both theoretically and through simulation.