Abstract
This study was inspired by the need to estimate pointwise confidence intervals (CIs) for a nonlinear dose-response model from a dose-finding clinical trial. Profile likelihood based CI for a nonlinear dose response model is often recommended. However, it is still not commonly used in dose-finding studies because it cannot generally be calculated explicitly. Most previous research has mainly focused on the performance of the profile likelihood based CI method compared with other common approaches. However, there are still no reports on computing profile likelihood based pointwise CIs for an entire dose-response curve. Based on a previous dose-finding trial with binary-response data, this present study proposed to calculate profile likelihood based pointwise CIs by using the bisection method with proper calculation order for doses in the curve plus crude search when the expected response is close to a boundary. The convergence could be improved by applying appropriate starting values for the optimization procedure with straightforward programming techniques. The algorithm worked well in most cases based on the simulation study and it can be applied more generally to other dose-response models, and other type of data like normally distributed response. It would indeed be great to be able to use profile likelihood approaches more routinely when constructing pointwise CIs for nonlinear dose-response models.
Highlights
In dose-finding studies, together with parameter estimates from the fitted dose-response model, the pointwise confidence intervals (CIs) of the expected response for doses on the entire curve that characterize the uncertainty of the fitted model are always needed to provide essential information for identifying the optimal dose (s)
The disadvantages of the normal-based pointwise Wald-type CIs were obvious in our example, which has been discussed in previous reports as follows: the lower confidence limits of a dose nearby placebo are negative [2,4]; pointwise CIs are non-monotone as function of dose [4]; coverage rates are not correct for some doses [3,4,15], especially for doses between two observed doses
We have addressed the computation of profile likelihood based pointwise CIs for a nonlinear 4-parameter logistic model with binomially distributed data based on a phase 2 dose-finding trial
Summary
In dose-finding studies, together with parameter estimates from the fitted dose-response model, the pointwise confidence intervals (CIs) of the expected response for doses on the entire curve that characterize the uncertainty of the fitted model are always needed to provide essential information for identifying the optimal dose (s). Because the pointwise CIs can be estimated sequentially, the monotonicity of confidence limits can be taken into account to facilitate the calculation when setting the lower and upper bound of the initial search interval of a dose.
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