Bayesian penalized log-likelihood ratio approach for dose response clinical trial studies

<p>In literature, there are a few unified approaches to test proof of concept and estimate a target dose, including the multiple comparison procedure using modeling approach, and the permutation approach proposed by Klingenberg. We discuss and compare the operating characteristics of these unified approaches and further develop an alternative approach in a Bayesian framework based on the posterior distribution of a penalized log-likelihood ratio test statistic. Our Bayesian approach is much more flexible to handle linear or nonlinear dose–response relationships and is more efficient than the permutation approach. The operating characteristics of our Bayesian approach are comparable to and sometimes better than both approaches in a wide range of dose–response relationships. It yields credible intervals as well as predictive distribution for the response rate at a specific dose level for the target dose estimation. Our Bayesian approach can be easily extended to continuous, categorical, and time-to-event responses. We illustrate the performance of our proposed method with extensive simulations and Phase II clinical trial data examples.</p

Histogram distribution for the samples – (a) Female, (b) Male, (c) 1.5 T and (d) 3 T.

<p>Histogram distribution for the samples – (a) Female, (b) Male, (c) 1.5 T and (d) 3 T.</p

Demographic information for the sample of 295 controls split into both genders and field strengths.

<p>Demographic information for the sample of 295 controls split into both genders and field strengths.</p

Unadjusted means and mean differences (95% confidence interval) of regional cortical thickness by field strength (1.5 T vs. 3 T) for right and left hemispheres in 295 controls using multivariate regression model.

<p>The regions with the significant field strength effect (p<0.05) on cortical thickness are denoted with “*”.</p><p>Note: overall field strength effect on regional cortical thickness is significant with p-value <0.0001 using Pillai's Trace test. ⁺STS  =  superior temporal sulcus.</p

Sample distribution based on image resolution, pulse sequence and scanner manufacturer type.

<p>*Statistical analysis based on scanner type excluded 2 datasets from the sample population.</p

Lateral and medial views of inflated right hemisphere at 1.5 T and 3 T for male vs. female differences in cortical thickness.

<p>The labeled regions are: (A) and (B) precentral, (C) transverse temporal, (D) isthmus cingulate, (E) lingual and (F) cuneus</p

Regional cortical thickness of the 34 segmented regions plotted for the three age groups.

<p>Regional cortical thickness of the 34 segmented regions plotted for the three age groups.</p

L'État français ne doit pas avoir de doute sur le fait qu'une extradition n'emportera pas des conséquences d'une gravité exceptionnelle pour pouvoir y procéder

<p>Note: overall field strength effect on regional cortical thickness is significant with p-value <0.0001 using Pillai's Trace test; Factors ajusted for include: age, gender, resolution, scanner type, sequence, and interactions of field*age, and field*gender. <b>⁺</b>STS  =  superior temporal sulcus.</p