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.