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Prospective Detection of Outbreaks
Published in Leonhard Held, Niel Hens, Philip O’Neill, Jacco Wallinga, Handbook of Infectious Disease Data Analysis, 2019
Benjamin Allévius, Michael Höhle
to the historical values. In the previous expression, s denotes the time points of the historic values and is the over-dispersion parameter. If the dispersion parameter in the quasi-Poisson is estimated to be smaller than one, then a Poisson model (i.e. ) is used instead. Based on the estimated GLM model, we compute the upper of limit of a one-sided prediction interval for by where , because the current observation is not used as part of the estimation. We know that asymptotically , where denotes the inverse of the observed Fisher information. Therefore, is normally distributed with variance . Through the use of the delta method, we find that .
Examples of Homework Questions
Published in Albert Vexler, Alan D. Hutson, Statistics in the Health Sciences, 2018
Fisher information ı(.): Let where is unknown. Calculate ı(μ).Let where is unknown. Calculate ı(σ2).Let where is unknown. Calculate ı(λ).
Some Statistical Procedures for Biomarker Measurements Subject to Instrumental Limitations
Published in Albert Vexler, Alan D. Hutson, Xiwei Chen, Statistical Testing Strategies in the Health Sciences, 2017
Albert Vexler, Alan D. Hutson, Xiwei Chen
Perkins et al. (2013) developed asymptotically consistent, efficient estimators for the mean vector and covariance matrix of multivariate normally distributed biomarkers affected by LOD. An approximation for the Fisher information and covariance matrix was developed for the maximum likelihood estimations (MLEs). The method was applied to a receiver operating characteristic curve (see Chapter 8 for details) setting, generating an MLE for the area under the curve for the best linear combination of multiple biomarkers and accompanying confidence interval. Simulation studies were conducted to confirm the good performance of point and confidence interval estimates with bias and root mean squared error and coverage probability presented. The MLEs were shown to be consistent. It was demonstrated that properly addressing LODs can lead to optimal biomarker combinations with increased discriminatory ability. The method was applied to experimental animal, primate, and human studies of association between dioxin and PCBs and endometriosis (Louis et al. 2005) to illustrate how the underlying distribution of multiple biomarkers with LOD can be assessed and display increased discriminatory ability over naïve methods.
A multivariate zero-inflated binomial model for the analysis of correlated proportional data
Published in Journal of Applied Statistics, 2022
Dianliang Deng, Yiguang Sun, Guo-Liang Tian
In this subsection, the Fisher scoring algorithm is derived to calculate the MLEs of the parameters 16]). However, the Fisher scoring algorithm requires more complex calculation than EM algorithm for deriving the expected Fisher information matrix. Moreover, the expected Fisher information matrix could not be tractable for the complicated models. Since the estimation under multivariate zero-inflated binomial distribution is multi-parameter case, the Fisher scoring algorithm should be studied. Now, based on the equation (6), the score vector is
Improving the utility of the European Health Literacy Survey Questionnaire: a computerized adaptive test for patients with stroke
Published in Disability and Rehabilitation, 2022
Yi-Jing Huang, Gong-Hong Lin, Ya-Chen Lee, Tzu-Yi Wu, Wen-Hsuan Hou, Ching-Lin Hsieh
A MATLAB program was written to simulate the assessment procedures of the CAT-EHL using the item parameters and patient responses on the HLS-EU-Q retrieved from the Rasch validation study [9]. A total of 10 simulation analyses were performed using the 10 candidate stopping rules. Adaptive assessments were simulated using the maximum Fisher information and the maximum a posteriori estimation. The maximum Fisher information was used to select items that were tailored to each patient’s ability. The maximum a posteriori estimation was adopted to estimate each patient’s ability on the basis of a 12-dimensional Rasch partial credit model. The CAT-EHL selected the most informative item from the item bank in each assessment. After entering the patient’s response to the item, the CAT-EHL estimated the patient’s ability and the reliability. The CAT-EHL then determined whether the preset stopping rule was achieved in all domains. The assessment procedures were repeated until the preset stopping rule was achieved in all domains. Furthermore, a minimum of one item per domain had to be administered. Therefore, at least 12 items were required to complete the CAT-EHL. The average reliability of patient ability estimates and the average number of items required for administration were calculated at the end of each simulation analysis. The average reliability of the item bank was also calculated, which indicated that the reliability was highest when patients completed all the items in the item bank.
Inference on a progressive type I interval-censored truncated normal distribution
Published in Journal of Applied Statistics, 2020
Chandrakant Lodhi, Yogesh Mani Tripathi
We have organized the rest of this paper as follows. In Section 2, we compute maximum likelihood estimates of unknown parameters μ and τ using an EM algorithm. We further use this method to obtain asymptotic intervals from the observed Fisher information matrix. In this section, we also provide midpoint and probability plot estimates of both parameters under progressively type I interval-censored data. Bayes estimates of unknown parameters are derived with respect to squared error and linex loss functions in Section 3 using the importance sampling procedure. We further obtain highest posterior density (HPD) intervals using the importance sampling. A simulation study is conducted in Section 4 to compare the performance of proposed methods of estimation. A real data set is analyzed in Section 5 for illustration purposes. In Section 6, we discuss inspection times and optimal censoring plans under progressive type I interval censoring. Some concluding remarks are given in Section 7.