## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 10, Number 1 (2016), 94-117.

### Prevalence and trend estimation from observational data with highly variable post-stratification weights

Yannick Vandendijck, Christel Faes, and Niel Hens

#### Abstract

In observational surveys, post-stratification is used to reduce bias resulting from differences between the survey population and the population under investigation. However, this can lead to inflated post-stratification weights and, therefore, appropriate methods are required to obtain less variable estimates. Proposed methods include collapsing post-strata, trimming post-stratification weights, generalized regression estimators (GREG) and weight smoothing models, the latter defined by random-effects models that induce shrinkage across post-stratum means. Here, we first describe the weight-smoothing model for prevalence estimation from binary survey outcomes in observational surveys. Second, we propose an extension of this method for trend estimation. And, third, a method is provided such that the GREG can be used for prevalence and trend estimation for observational surveys. Variance estimates of all methods are described. A simulation study is performed to compare the proposed methods with other established methods. The performance of the nonparametric GREG is consistent over all simulation conditions and therefore serves as a valuable solution for prevalence and trend estimation from observational surveys. The method is applied to the estimation of the prevalence and incidence trend of influenza-like illness using the 2010/2011 Great Influenza Survey in Flanders, Belgium.

#### Article information

**Source**

Ann. Appl. Stat., Volume 10, Number 1 (2016), 94-117.

**Dates**

Received: December 2014

Revised: July 2015

First available in Project Euclid: 25 March 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1458909909

**Digital Object Identifier**

doi:10.1214/15-AOAS874

**Mathematical Reviews number (MathSciNet)**

MR3480489

**Zentralblatt MATH identifier**

06586138

**Keywords**

Binary data empirical Bayes estimation influenza-like illness nonparametric regression observational survey post-stratification random-effects model

#### Citation

Vandendijck, Yannick; Faes, Christel; Hens, Niel. Prevalence and trend estimation from observational data with highly variable post-stratification weights. Ann. Appl. Stat. 10 (2016), no. 1, 94--117. doi:10.1214/15-AOAS874. https://projecteuclid.org/euclid.aoas/1458909909

#### Supplemental materials

- Additional details and results. The reader is referred to the online Supplementary Material for more information on how the models can be cast in the GLMM framework (Appendix A), for more details on the estimation method (Appendix B), for annotated SAS and R programs (Appendix C), for additional simulation results (Appendix D), and for additional results for different values of $w_{0}$, additional results for smaller sample size and results on model fits and other spline basis functions (Appendix E).Digital Object Identifier: doi:10.1214/15-AOAS874SUPP