Disease mapping via negative binomial regression M-quantiles

Chambers, Ray; Dreassi, Emanuela; Salvati, Nicola

doi:10.1002/sim.6256

Cited by 29 publications

(54 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is shown that the hierarchical median regression via a Poisson log-normal representation (HQRPLN) more accurately reproduces the regression parameters assumed in the simulation than negative binomial or standard PLN regression. The HQRPLN estimates for contaminated data are competitive with those of classical methods for robust regression using a negative binomial density and M-estimation (Aeberhard et al 2014;Chambers et al 2014), and also with classical methods for median regression for count data (Machado and Santos Silva, 2005). It is also shown that HQRPLN accurately identifies the contaminated observations.…”

Section: Introductionmentioning

confidence: 86%

“…Table 1 contains the resulting regression parameter estimates. It can be seen that negative binomial regression is most vitiated by response outliers, this distortion increasing with C. The Chambers et al (2014) estimates are more robust than negative binomial regression, but not as robust as the Aeberhard et al (2014) estimates or the HQRPLN estimates. Standard Poisson log-normal regression is more robust than the negative binomial regression and the Chambers et al (2014) estimates, but outperformed by the HQRPLN method.…”

Section: Simulated Data Examplementioning

confidence: 94%

“…Thus Chambers et al (2014) consider M-estimation for overdispersed counts using a negative binomial model. They estimate β using the Huber score function (Huber, 1973) and estimating equations 1 n…”

Section: Robust Count Regression Via M-estimation and Bayesian Stratementioning

confidence: 99%

“…The Huber score function uses a cutpoint k to define (absolute) extreme residuals, such as k = 2, with ψ(r) = max(−k, min(k, r)). Chambers et al (2014) use a robust moment estimator for θ = 1/σ, whereas Aeberhard et al (2014) use M-estimation in a form of weighted maximum likelihood, preferring this on efficiency grounds. Bayesian regression methods intended as robust to outliers include ε−contamination priors (Moreno and Pericchi, 1993), modified likelihoods such as weighted likelihoods (Greco et al 2008;Agostinelli and Greco, 2013), and localized regression (Wang and Blei, 2017).…”

Section: Robust Count Regression Via M-estimation and Bayesian Stratementioning

confidence: 99%

“…This reduces the impact of outliers (influential observations) in the response space, providing a better fit for the majority of observations. Chambers et al (2014) extend M-estimation to quantile regression, including count regression. For linear regression the estimating equations become 1 n…”

Section: Quantile Regression: Classical and Bayesian Approachesmentioning

confidence: 99%

See 4 more Smart Citations

Quantile regression for overdispersed count data: a hierarchical method

Congdon

2017

J Stat Distrib App

View full text Add to dashboard Cite

Generalized Poisson regression is commonly applied to overdispersed count data, and focused on modelling the conditional mean of the response. However, conditional mean regression models may be sensitive to response outliers and provide no information on other conditional distribution features of the response. We consider instead a hierarchical approach to quantile regression of overdispersed count data. This approach has the benefits of effective outlier detection and robust estimation in the presence of outliers, and in health applications, that quantile estimates can reflect risk factors. The technique is first illustrated with simulated overdispersed counts subject to contamination, such that estimates from conditional mean regression are adversely affected. A real application involves ambulatory care sensitive emergency admissions across 7518 English patient general practitioner (GP) practices. Predictors are GP practice deprivation, patient satisfaction with care and opening hours, and region. Impacts of deprivation are particularly important in policy terms as indicating effectiveness of efforts to reduce inequalities in care sensitive admissions. Hierarchical quantile count regression is used to develop profiles of central and extreme quantiles according to specified predictor combinations.

show abstract

Section: Introductionmentioning

confidence: 86%

Section: Simulated Data Examplementioning

confidence: 94%

Section: Robust Count Regression Via M-estimation and Bayesian Stratementioning

confidence: 99%

Section: Robust Count Regression Via M-estimation and Bayesian Stratementioning

confidence: 99%

Section: Quantile Regression: Classical and Bayesian Approachesmentioning

confidence: 99%

See 3 more Smart Citations

Quantile regression for overdispersed count data: a hierarchical method

Congdon

2017

J Stat Distrib App

View full text Add to dashboard Cite

show abstract

Generalised M‐quantile random‐effects model for discrete response: An application to the number of visits to physicians

2021

Self Cite

View full text Add to dashboard Cite

In this paper, we extend the linear M‐quantile random intercept model (MQRE) to discrete data and use the proposed model to evaluate the effect of selected covariates on two count responses: the number of generic medical examinations and the number of specialised examinations for health districts in three regions of central Italy. The new approach represents an outlier‐robust alternative to the generalised linear mixed model with Gaussian random effects and it allows estimating the effect of the covariates at various quantiles of the conditional distribution of the target variable. Results from a simulation experiment, as well as from real data, confirm that the method proposed here presents good robustness properties and can be in certain cases more efficient than other approaches.

show abstract

$$\ell _2$$-penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

Krause

Burgard

Morales

2021

Metrika

View full text Add to dashboard Cite

Regional prevalence estimation requires the use of suitable statistical methods on epidemiologic data with substantial local detail. Small area estimation with medical treatment records as covariates marks a promising combination for this purpose. However, medical routine data often has strong internal correlation due to diagnosis-related grouping in the records. Depending on the strength of the correlation, the space spanned by the covariates can become rank-deficient. In this case, prevalence estimates suffer from unacceptable uncertainty as the individual contributions of the covariates to the model cannot be identified properly. We propose an area-level logit mixed model for regional prevalence estimation with a new fitting algorithm to solve this problem. We extend the Laplace approximation to the log-likelihood by an $$\ell _2$$ ℓ 2 -penalty in order to stabilize the estimation process in the presence of covariate rank-deficiency. Empirical best predictors under the model and a parametric bootstrap for mean squared error estimation are presented. A Monte Carlo simulation study is conducted to evaluate the properties of our methodology in a controlled environment. We further provide an empirical application where the district-level prevalence of multiple sclerosis in Germany is estimated using health insurance records.

show abstract

Disease mapping via negative binomial regression M-quantiles

Cited by 29 publications

References 33 publications

Quantile regression for overdispersed count data: a hierarchical method

Quantile regression for overdispersed count data: a hierarchical method

Generalised M‐quantile random‐effects model for discrete response: An application to the number of visits to physicians

$$\ell _2$$-penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

Contact Info

Product

Resources

About