Robert Graham Clark

An introduction to model-based survey sampling with applications

PART I: BASICS OF MODEL-BASED SURVEY INFERENCE 1. Introduction 2. The Model-Based Approach 3. Homogeneous Populations 4. Stratified Populations 5. Populations with Regression Structure 6. Clustered Populations 7. The General Linear Population Model PART II: ROBUST MODEL-BASED INFERENCE 8. Robust Prediction under Model Misspecification 9. Robust Estimation of the Prediction Variance 10. Outlier Robust Prediction PART III: APPLICATIONS OF MODEL-BASED SURVEY INFERENCE 11. Inference for Nonlinear Population Parameters 12. Survey Inference via Sub-Sampling 13. Estimation for Multipurpose Surveys 14. Inference for Domains 15. Prediction for Small Areas 16. Model-Based Inference for Distributions and Quantiles 17. Using Transformations in Sample Survey Inference Exercises

Sampling of subpopulations in two‐stage surveys

Many health and other surveys aim to produce statistics on small subpopulations, such as specific ethnic groups or the indigenous population of a country. In most countries, there is no reliable sampling frame of the subpopulations of interest, hence it is necessary to sample from the general population, which can be very expensive. A range of issues and strategies for sampling rare subpopulations is reviewed. The most common approaches in practice are the use of a large screening sample, and disproportionate sampling by strata. Optimal sample designs have been derived for the case of one-stage sampling, but most household interview surveys use two or more stages of selection. This paper develops optimal designs for two-stage sampling, where there is auxiliary information on subpopulation numbers for each primary sampling unit. Various alternative designs are evaluated using a simulated population derived from the New Zealand Census.

The ecology of avian influenza viruses in wild dabbling ducks ( Anas spp.) in Canada

Avian influenza virus (AIV) occurrence and transmission remain important wildlife and human health issues in much of the world, including in North America. Through Canada’s Inter-Agency Wild Bird Influenza Survey, close to 20,000 apparently healthy, wild dabbling ducks (of seven species) were tested for AIV between 2005 and 2011. We used these data to identify and evaluate ecological and demographic correlates of infection with low pathogenic AIVs in wild dabbling ducks (Anas spp.) across Canada. Generalized linear mixed effects model analyses revealed that risk of AIV infection was higher in hatch-year birds compared to adults, and was positively associated with a high proportion of hatch-year birds in the population. Males were more likely to be infected than females in British Columbia and in Eastern Provinces of Canada, but more complex relationships among age and sex cohorts were found in the Prairie Provinces. A species effect was apparent in Eastern Canada and British Columbia, where teal (A. discors and/or A. carolinensis) were less likely to be infected than mallards (A. platyrhynchos). Risk of AIV infection increased with the density of the breeding population, in both Eastern Canada and the Prairie Provinces, and lower temperatures preceding sampling were associated with a higher probability of AIV infection in Eastern Canada. Our results provide new insights into the ecological and demographic factors associated with AIV infection in waterfowl.

Developing the design of a continuous national health survey for New Zealand

BackgroundA continuously operating survey can yield advantages in survey management, field operations, and the provision of timely information for policymakers and researchers. We describe the key features of the sample design of the New Zealand (NZ) Health Survey, which has been conducted on a continuous basis since mid-2011, and compare to a number of other national population health surveys.MethodsA number of strategies to improve the NZ Health Survey are described: implementation of a targeted dual-frame sample design for better Māori, Pacific, and Asian statistics; movement from periodic to continuous operation; use of core questions with rotating topic modules to improve flexibility in survey content; and opportunities for ongoing improvements and efficiencies, including linkage to administrative datasets.Results and discussionThe use of disproportionate area sampling and a dual frame design resulted in reductions of approximately 19%, 26%, and 4% to variances of Māori, Pacific and Asian statistics respectively, but at the cost of a 17% increase to all-ethnicity variances. These were broadly in line with the survey’s priorities. Respondents provided a high degree of cooperation in the first year, with an adult response rate of 79% and consent rates for data linkage above 90%.ConclusionsA combination of strategies tailored to local conditions gives the best results for national health surveys. In the NZ context, data from the NZ Census of Population and Dwellings and the Electoral Roll can be used to improve the sample design. A continuously operating survey provides both administrative and statistical advantages.

Bark chewing reveals a nutrient limitation of leaves for a specialist folivore

Mineral micronutrients are critical for basic physiological function, and variable availability of minerals over the landscape can influence foraging decisions. Sodium is essential for nerve function and osmotic balance; however, it can be limiting in some environments, such as those at high elevations. Koalas (Phascolarctos cinereus) living in subalpine regions have been observed eating Eucalyptus mannifera bark, an unusual food choice for a folivore. We hypothesized that sodium may be deficient in leaves at high-elevation sites, and that the bark from trees could be a potential sodium source. We compared the mineral content of eucalypt bark and leaves in 3 areas where koalas chew bark and in leaves of a preferred food tree of koalas, E. viminalis, across a range of elevations. Individual chewed trees were rare compared to non-chewed conspecifics and patchily distributed. Bark from chewed E. mannifera trees had significantly higher concentrations of sodium than plant parts from non-chewed neighboring conspecifics and other Eucalyptus species trees. We also found that E. viminalis foliage had significantly less sodium at higher elevations than lowland populations. We propose that koalas have developed the unusual bark-eating behavior to meet sodium requirements in an otherwise sodium-poor landscape. Given the physiological importance of sodium, behavioral adaptations such as these may be critical to the ability of mammalian herbivores to survive in nutrient-deficient landscapes.

Adaptive inference for multi-stage survey data

Multi-level models can be used to account for clustering in data from multi-stage surveys. In some cases, the intraclass correlation may be close to zero, so that it may seem reasonable to ignore clustering and fit a single-level model. This article proposes several adaptive strategies for allowing for clustering in regression analysis of multi-stage survey data. The approach is based on testing whether the PSU-level variance component is zero. If this hypothesis is retained, then variance estimates are calculated ignoring clustering; otherwise, clustering is reflected in variance estimation. A simple simulation study is used to evaluate the various procedures.

A blended link approach to relative risk regression

A binary health outcome may be regressed on covariates using a log link, rather than more typical link functions such as the logit. This allows the exponentiated regression coefficient for each covariate to be interpreted as a relative risk conditional on the remaining covariates. Relative risks are simpler to interpret than the odds ratios which arise with a logit link. There are practical and conceptual challenges in log-link binary regression, mainly due to the requirement that probabilities are less than or equal to 1. Viable probabilities are now usually achieved by the imposition of a constraint on the parameter space, but the log link function is still more work to apply in practice. We propose instead a new smooth link function which is equal to the log up to a cutoff and a linearly scaled logit function above the cutoff. The new approach is conceptually clearer, simpler to implement and generally less biased, and it retains the relative risk interpretation for all but the highest risk individuals. Alternative binary regressions are compared using a simulation study and a diabetic retinopathy dataset.

Statistical Efficiency in Distance Sampling

Distance sampling is a technique for estimating the abundance of animals or other objects in a region, allowing for imperfect detection. This paper evaluates the statistical efficiency of the method when its assumptions are met, both theoretically and by simulation. The theoretical component of the paper is a derivation of the asymptotic variance penalty for the distance sampling estimator arising from uncertainty about the unknown detection parameters. This asymptotic penalty factor is tabulated for several detection functions. It is typically at least 2 but can be much higher, particularly for steeply declining detection rates. The asymptotic result relies on a model which makes the strong assumption that objects are uniformly distributed across the region. The simulation study relaxes this assumption by incorporating over-dispersion when generating object locations. Distance sampling and strip transect estimators are calculated for simulated data, for a variety of overdispersion factors, detection functions, sample sizes and strip widths. The simulation results confirm the theoretical asymptotic penalty in the non-overdispersed case. For a more realistic overdispersion factor of 2, distance sampling estimation outperforms strip transect estimation when a half-normal distance function is correctly assumed, confirming previous literature. When the hazard rate model is correctly assumed, strip transect estimators have lower mean squared error than the usual distance sampling estimator when the strip width is close enough to its optimal value (± 75% when there are 100 detections; ± 50% when there are 200 detections). Whether the ecologist can set the strip width sufficiently accurately will depend on the circumstances of each particular study.

Oxygen exchange during the reaction of POCl3 and water

To investigate O exchange during the reaction of POCl3 and water, natural abundance POCl3 was reacted with water highly enriched in 18O, and the resulting H3PO4 was isolated as KH2PO4. This reaction was conducted with and without tetrahydrofuran (THF) as a solvent, and was controlled in THF and violent in its absence. Approximately 5 × 10–4 M aqueous solutions of the KH2PO4 were analyzed using electrospray ionization mass spectrometry, to estimate the proportions of the mass-clumped 16,17,18O isotope analogues of [H2PO4]–. During analysis, ~29 % of [H2PO4]– dehydrated to [PO3]–, for which the proportions of the O isotope analogues were also measured. These proportions were compared with those predicted for O exchange at either four or three positions on the P atom of POCl3. The data strongly support O exchange at all four positions, whether or not THF was used to moderate conditions during the reaction. This result clears the way for safe, predictable synthesis of heavy-O labelled orthophosphate from POCl3 and 18O enriched water for evaluation as an environmental and biochemical tracer.