BACKGROUND In 2007, physicians on Yap Island reported an outbreak of illness characterized by rash, conjunctivitis, and arthralgia. Although serum from some patients had IgM antibody against dengue virus, the illness seemed clinically distinct from previously detected dengue. Subsequent testing with the use of consensus primers detected Zika virus RNA in the serum of the patients but no dengue virus or other arboviral RNA. No previous outbreaks and only 14 cases of Zika virus disease have been previously documented. METHODS We obtained serum samples from patients and interviewed patients for information on clinical signs and symptoms. Zika virus disease was confirmed by a finding of Zika virus RNA or a specific neutralizing antibody response to Zika virus in the serum. Patients with IgM antibody against Zika virus who had a potentially cross-reactive neutralizing-antibody response were classified as having probable Zika virus disease. We conducted a household survey to estimate the proportion of Yap residents with IgM antibody against Zika virus and to identify possible mosquito vectors of Zika virus. RESULTS We identified 49 confirmed and 59 probable cases of Zika virus disease. The patients resided in 9 of the 10 municipalities on Yap. Rash, fever, arthralgia, and conjunctivitis were common symptoms. No hospitalizations, hemorrhagic manifestations, or deaths due to Zika virus were reported. We estimated that 73% (95% confidence interval, 68 to 77) of Yap residents 3 years of age or older had been recently infected with Zika virus. Aedes hensilli was the predominant mosquito species identified. CONCLUSIONS This outbreak of Zika virus illness in Micronesia represents transmission of Zika virus outside Africa and Asia. Although most patients had mild illness, clinicians and public health officials should be aware of the risk of further expansion of Zika virus transmission.

https://www.nejm.org/doi/pdf/10.1056/NEJMoa0805715

Zika virus outbreak on Yap Island, Federated States of Micronesia.

There is a simple robust variance estimator for cluster-correlated data. While this estimator is well known, it is poorly documented, and its wide range of applicability is often not understood. The estimator is widely used in sample survey research, but the results in the sample survey literature are not easily applied because of complications due to unequal probability sampling. This brief note presents a general proof that the estimator is unbiased for cluster-correlated data regardless of the setting. The result is not new, but a simple and general reference is not readily available. The use of the method will benefit from a general explanation of its wide applicability.

A Note on Robust Variance Estimation for Cluster‐Correlated Data

This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a potentially large set of prespecified balance conditions that incorporate information about known sample moments. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. The method assures that balance improves on all covariate moments included in the reweighting. It also obviates the need for continual balance checking and iterative searching over propensity score models that may stochastically balance the covariate moments. We demonstrate the use of entropy balancing with Monte Carlo simulations and empirical applications.

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Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies

Many surveys of the U.S. household population are experiencing higher refusal rates. Nonresponse can, but need not, induce nonresponse bias in survey estimates. Recent empirical findings illustrate cases when the linkage between nonresponse rates and nonresponse biases is absent. Despite this, professional standards continue to urge high response rates. Statistical expressions of nonresponse bias can be translated into causal models to guide hypotheses about when nonresponse. causes bias. Alternative designs to measure nonresponse bias exist, providing different but incomplete information about the nature of the bias. A synthesis of research studies estimating nonresponse bias shows the bias often present. A logical question at this moment in history is what advantage probability sample surveys have if they suffer from high nonresponse rates. Since postsurvey adjustment for nonresponse requires auxiliary variables, the answer depends on the nature of the design and the quality of the auxiliary variables.

Nonresponse Rates and Nonresponse Bias in Household Surveys

Basics Introduction The problem of missing data Concepts of MCAR, MAR and MNAR Simple solutions that do not (always) work Multiple imputation in a nutshell Goal of the book What the book does not cover Structure of the book Exercises Multiple imputation Historic overview Incomplete data concepts Why and when multiple imputation works Statistical intervals and tests Evaluation criteria When to use multiple imputation How many imputations? Exercises Univariate missing data How to generate multiple imputations Imputation under the normal linear normal Imputation under non-normal distributions Predictive mean matching Categorical data Other data types Classification and regression trees Multilevel data Non-ignorable methods Exercises Multivariate missing data Missing data pattern Issues in multivariate imputation Monotone data imputation Joint Modeling Fully Conditional Specification FCS and JM Conclusion Exercises Imputation in practice Overview of modeling choices Ignorable or non-ignorable? Model form and predictors Derived variables Algorithmic options Diagnostics Conclusion Exercises Analysis of imputed data What to do with the imputed data? Parameter pooling Statistical tests for multiple imputation Stepwise model selection Conclusion Exercises Case studies Measurement issues Too many columns Sensitivity analysis Correct prevalence estimates from self-reported data Enhancing comparability Exercises Selection issues Correcting for selective drop-out Correcting for non-response Exercises Longitudinal data Long and wide format SE Fireworks Disaster Study Time raster imputation Conclusion Exercises Extensions Conclusion Some dangers, some do's and some don'ts Reporting Other applications Future developments Exercises Appendices: Software R S-Plus Stata SAS SPSS Other software References Author Index Subject Index

Flexible Imputation of Missing Data

PART I: Principles of Estimation for Finite Populations and Important Sampling Designs: Survey Sampling in Theory and Practice. Basic Ideas in Estimation from Probability Samples. Unbiased Estimation for Element Sampling Designs. Unbiased Estimation for Cluster Sampling and Sampling in Two or More Stages. Introduction to More Complex Estimation Problems.- PART II: Estimation through Linear Modeling, Using Auxiliary Variables: The Regression Estimator. Regression Estimators for Element Sampling Designs. Regression Estimators for Cluster Sampling and Two-Stage Sampling.- PART III: Further Questions in Design and Analysis of Surveys: Two-Phase Sampling. Estimation for Domains. Variance Estimation. Searching for Optimal Sampling Designs. Further Statistical Techniques for Survey Data.- PART IV: A Broader View of Errors in Surveys: Nonsampling Errors and Extensions of Probability Sampling Theory. Nonresponse. Measurement Errors. Quality Declarations for Survey Data.- Appendix A - D.- References.

Model assisted survey sampling

This article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information. Estimation is equivalent to attaching weights to the survey data. We focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations. We briefly mention an application to the case in which the information consists of known marginal counts in a two- or multi-way table, known as generalized raking. The general regression estimator (GREG) was conceived with multivariate auxiliary information in mind. Ordinarily, this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x. But we note that the GREG can be derived by a different route by focusing instead on the weights. The ordinary sampling weights of the kth observation is 1/πk , where πk is the inclusion probabilit...

Calibration Estimators in Survey Sampling

We propose the name generalized raking for the class of procedures developed in this article, because the classical raking ratio of W. E. Deming is a special case. Generalized raking can be used for estimation in surveys with auxiliary information in the form of known marginal counts in a frequency table in two or more dimensions. An important property of the generalized raking weights is that they reproduce the known marginal counts when applied to the categorical variables that define the frequency table. Our starting point is a class of distance measures and a set of original weights in the form of the standard sampling weights 1/π k , where π k is the inclusion probability of element k. New weights are derived by minimizing the total distance between original weights and new weights. The article makes contributions in three areas: (1) statistical inference conditionally on estimated cell counts, (2) simple calculation of variance estimates for the generalized raking estimators, and (3) presen...

Generalized Raking Procedures in Survey Sampling

Foundations of inference in survey sampling

Preface. Chapter 1: Introduction. Chapter 2: The Survey and Its Imperfections. 2.1 The survey objective. 2.2 Sources of error in a survey. Chapter 3: General Principles to Assist Estimation. 3.1 Introduction. 3.2 The importance of auxiliary information. 3.3 Desirable features of an auxiliary vector. Chapter 4: The Use of Auxiliary Information under Ideal Conditions. 4.1 Introduction. 4.2 The Horvitz-Thompson estimator. 4.3 The generalized regression estimator. 4.4 Variance and variance estimation. 4.5 Examples of the generalized regression estimator. Chapter 5: Introduction to Estimation in the Presence of Nonresponse. 5.1 General background. 5.2 Errors caused by sampling and nonresponse. Appendix: Variance and mean squared error under nonresponse. Chapter 6: Weighting of Data in the Presence of Nonresponse. 6.1 Traditional approaches to weighting. 6.2 Auxiliary vectors and auxiliary information. 6.3 The calibration approach: some terminology. 6.4 Point estimation under the calibration approach. 6.5 Calibration estimators for domains. 6.6 Comments on the calibration approach. 6.7 Alternative sets of calibrated weights. 6.8 Properties of the calibrated weights. Chapter 7: Examples of Calibration Estimators. 7.1 Examples of familiar estimators for data with nonresponse. 7.2 The simplest auxiliary vector. 7.3 One-way classification. 7.4 A single quantitative auxiliary variable. 7.5 One-way classification combined with a quantitative variable. 7.6 Two-way classification. 7.7 A Monte Carlo simulation study. Chapter 8 The Combined Use of Sample Information and Population Information. 8.1 Options for the combined use of information. 8.2 An example of calibration with information at both levels. 8.3 A Monte Carlo simulation study of alternative calibration procedures. 8.4 Two-step procedures in practice. Chapter 9 Analysing the Bias due to Nonresponse. 9.1 Simple estimators and their nonresponse bias. 9.2 Finding an efficient grouping. 9.3 Further illustrations of the nonresponse bias. 9.4 A general expression for the bias of the calibration estimator. 9.5 Conditions for near-unbiasedness. 9.6 A review of concepts, terms and ideas. Appendix: Proof of Proposition 9.1. Chapter 10: Selecting the Most Relevant Auxiliary Information. 10.1 Discussion. 10.2 Guidelines for the construction of an auxiliary vector. 10.3 The prospects for near-zero bias with traditional estimators. 10.4 Further avenues towards a zero bias. 10.5 A further tool for reducing the bias. 10.6 The search for a powerful auxiliary vector. 10.7 Empirical illustrations of the indicators. 10.8 Literature review. Chapter 11: Variance and Variance Estimation. 11.1 Variance estimation for the calibration estimator. 11.2 An estimator for ideal conditions. 11.3 A useful relationship. 11.4 Variance estimation for the two-step A and two-step B procedures. 11.5 A simulation study of the variance estimation technique. 11.6 Computational aspects of point and variance estimation. Appendix: Properties of two-phase GREG estimator. Chapter 12: Imputation. 12.1 What is imputation? 12.2 Terminology. 12.3 Multiple study variables. 12.4 The full imputation approach. 12.5 The combined approach. 12.6 The full weighting approach. 12.7 Imputation by statistical rules. 12.8 Imputation by expert judgement or historical data. Chapter 13: Variance Estimation in the Presence of Imputation. 13.1 Issues in variance estimation under the full imputation approach. 13.2 An identity of combined and fully weighted approaches. 13.3 More on the risk of underestimating the variance. 13.4 A broader view of variance estimation for the combined approach. 13.5 Other issues arising with regard to item nonresponse. 13.6 Further comments on imputation. Appendix: Proof of Proposition 13.1. Chapter 14: Estimation Under Nonresponse and Frame Imperfections. 14.1 Introduction. 14.2 Estimation of the persister total. 14.3 Direct estimation of the target population total. 14.4 A case study. References. Index.

Carl-Erik Särndal

Papers

Model assisted survey sampling

Calibration Estimators in Survey Sampling

Generalized Raking Procedures in Survey Sampling

Foundations of inference in survey sampling

Estimation in Surveys with Nonresponse