Dose-Time-Response Modeling Using Negative Binomial Distribution |
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| Authors: | Munmun Roy M. M. Islam M. A. Matin |
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| Affiliation: | 1. Statistics Department, Head Office, Bangladesh Bank , Dhaka , Bangladesh;2. Department of Mathematical Sciences , Ball State University , Muncie , Indiana , USA;3. Department of Statistics , Jahangirnagar University , Savar , Dhaka , Bangladesh |
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| Abstract: | People exposed to certain diseases are required to be treated with a safe and effective dose level of a drug. In epidemiological studies to find out an effective dose level, different dose levels are applied to the exposed and a certain number of cures is observed. Negative binomial distribution is considered to fit overdispersed Poisson count data. This study investigates the time effect on the response at different time points as well as at different dose levels. The point estimation and confidence bands for ED 100p (t) and LT 100p (d) are formulated in closed form for the proposed dose-time-response model with the negative binomial distribution. Numerical illustrations are carried out in order to check the performance level of the proposed model. |
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| Keywords: | Delta method ED 100p (t) Fieller's theorem GLM LT 100p (d) |
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