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Improved estimation in negative binomial regression.

ABSTRACT: Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn affects inference on mean parameters. This article proposes inference for negative binomial regression based on adjustments of the score function aimed at mean or median bias reduction. The resulting estimating equations generalize those available for improved inference in generalized linear models and can be solved using a suitable extension of iterative weighted least squares. Simulation studies confirm the good properties of the new methods, which are also found to solve in many cases numerical problems of maximum likelihood estimation. The methods are illustrated and evaluated using two case studies: an Ames salmonella assay data set and data on epileptic seizures. Inference based on adjusted scores turns out to generally improve on maximum likelihood, and even on explicit bias correction, with median bias reduction being overall preferable.

SUBMITTER: Kenne Pagui EC

PROVIDER: S-EPMC9314673 | biostudies-literature | 2022 Jun

REPOSITORIES: biostudies-literature

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Improved estimation in negative binomial regression.

Kenne Pagui Euloge Clovis EC Salvan Alessandra A Sartori Nicola N

Statistics in medicine 20220311 13

Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn affects inference on mean parameters. This article proposes inference for negative binomial regression based on adjustments of the score function aimed at mean or median bias reduction. The resulting estimating equations generalize those available for improved inf ...[more]

PMID: 35277866

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Project description:BackgroundIt is difficult to detect the outbreak of emergency infectious disease based on the exiting surveillance system. Here we investigate the utility of the Baidu Search Index, an indicator of how large of a keyword is in Baidu's search volume, in the early warning and predicting the epidemic trend of COVID-19.MethodsThe daily number of cases and the Baidu Search Index of 8 keywords (weighted by population) from December 1, 2019 to March 15, 2020 were collected and analyzed with times series and Spearman correlation with different time lag. To predict the daily number of COVID-19 cases using the Baidu Search Index, Zero-inflated negative binomial regression was used in phase 1 and negative binomial regression model was used in phase 2 and phase 3 based on the characteristic of independent variable.ResultsThe Baidu Search Index of all keywords in Wuhan was significantly higher than Hubei (excluded Wuhan) and China (excluded Hubei). Before the causative pathogen was identified, the search volume of "Influenza" and "Pneumonia" in Wuhan increased with the number of new onset cases, their correlation coefficient was 0.69 and 0.59, respectively. After the pathogen was public but before COVID-19 was classified as a notifiable disease, the search volume of "SARS", "Pneumonia", "Coronavirus" in all study areas increased with the number of new onset cases with the correlation coefficient was 0.69 ~ 0.89, while "Influenza" changed to negative correlated (rs: -0.56 ~ -0.64). After COVID-19 was closely monitored, the Baidu Search Index of "COVID-19", "Pneumonia", "Coronavirus", "SARS" and "Mask" could predict the epidemic trend with 15 days, 5 days and 6 days lead time, respectively in Wuhan, Hubei (excluded Wuhan) and China (excluded Hubei). The predicted number of cases would increase 1.84 and 4.81 folds, respectively than the actual number of cases in Wuhan and Hubei (excluded Wuhan) from 21 January to 9 February.ConclusionThe Baidu Search Index could be used in the early warning and predicting the epidemic trend of COVID-19, but the search keywords changed in different period. Considering the time lag from onset to diagnosis, especially in the areas with medical resources shortage, internet search data can be a highly effective supplement of the existing surveillance system.

Project description:BackgroundThe odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR.MethodsWe propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial.ResultsIn simulation studies, confidence intervals for the OR were 56-65% as wide (geometric model), 75-79% as wide (Poisson model), and 61-69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression.ConclusionsMore precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions.

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Improved estimation in negative binomial regression.

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Improved estimation in negative binomial regression.

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