Mixed-Effects Negative Binomial Regression with Interval Censoring: A Simulation Study and Application to Precipitation and All-Cause Mortality Rates among Black South Africans over 1997-2013 Público

Landon, Christian (Spring 2019)

Permanent URL: https://etd.library.emory.edu/concern/etds/cv43nx88x?locale=pt-BR


In research using epidemiological surveillance data, counts of health outcomes are often censored in order to protect privacy when the nonzero number of health outcomes occurring in specific times and places is small. Several common approaches to modeling such censored, hierarchically structured, over-dispersed count data neglect either the uncertainty in true counts from the censoring process, or the hierarchical structure of the spatiotemporally clustered data. Mixed-effects interval-censored negative binomial regression has potential to address these methodological issues directly. In this study, we conducted simulations to contrast the performance of mixed-effects interval-censored negative binomial regression against three other approaches, to illustrate how the extent of censoring, between-cluster variation, sample size, and strength of the true association can affect the findings from this method and comparison methods.

We assessed the bias in parameter estimates and standard errors, 95% confidence interval coverage, statistical power, and type I error rates of our model and the alternative approaches. The simulated data was generated under a hierarchical negative binomial process to which a mixed-effects negative binomial model was fit (Model 1). Then interval-censoring was imposed on the dataset and the interval-censored mixed-effects negative binomial regression was applied (Model 2). Next, we applied a condition on the dataset wherein the censored values were all deterministically imputed at a fixed value in the middle of the range of plausible counts. Under this condition that had some misclassification of the true counts, we applied mixed-effects negative binomial regression. Lastly, we then fitted fixed-effects negative binomial regression models that accounted for the interval-censoring, but neglected the hierarchy (Model 4). Building upon this, we applied the four modeling approaches to a real-world uncensored dataset of monthly mortality rates among black South Africans over 1997-2013, to examine the estimates of association of precipitation with mortality across Models 1-4, applying artificial censoring and deterministic imputation to mirror the simulations. Overall, in the simulated data, Models 1, 2, and 4 performed well in all measures. However, Model 3 performed increasingly poorly as the true effect size increased with the other parameters in the model. In the South Africa dataset, Models 1, 2, and 3 obtained similar estimates suggesting an inverse association of precipitation with mortality in black South Africans, while Model 4 gave a divergent finding. In conclusion, interval-censored mixed effects negative binomial regression should be considered as an analytical option when outcome data have both clustering and interval censoring.

Table of Contents



Statistical Analysis of Simulated Data. 4

Simulation Summaries. 5


Mortality Data. 6

Standardized Precipitation Index. 7

Model Specification and Statistical Analysis. 7


Simulation Study. 8

Precipitation and Mortality Rates among Black South Africans. 10



References. 15

Tables. 18

Table 1: Simulation Design and Sample Size. 18

Table 2. Model Descriptions and Forms. 19

Figures. 20

Appendix. 22

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