Binary Endpoint
A study, conducted in mice, tested a potentially harmful drug at the following doses: 0, 200, 350, or 800 units of a chemical. There were 200 mice, with 50 mice in each dose group. The window below displays some data from the study in the ToxTools Case-editor, where data may be opened, entered, or edited. 

Tumor Data as displayed in the Case-Editor

The Summary Information and Parameter Estimates output displays the binary response rates (percent with lung tumors) at the different dose levels, which increase from 6% at the control level to 24% at the highest dose level.

From the ToxTools Model-fit menu, which features a rich class of dose-response models, the Probit model was chosen to arrive at the model dialog box, where one selects variables to fit the model. Here, dose was chosen as the predictor variable.

Model Dialog Box for Probit Fit

The following window displays tabular output for both summary information on the data, as well as results for the Probit model fit. The results show a significant dose effect.

Summary Information and Parameter Estimates

From the ToxTools Plot menu, which features exploratory as well as fitted plot displays, a graph of the fitted model and observed response values may be viewed. The plot below shows the fitted Probit model with observed tumor percents versus dose. 

Fitted plot for the Probit Model

One may be interested in seeing if the trend in the response rates is statistically significant. The Test menu below shows the different options available in ToxTools for trend and pairwise tests, which are easy to compute.

Menu For Trend Tests

For binary trend tests, both asymptotic and exact tests may be performed. The model dialog for a trend test and the corresponding results are shown below. 

Model Dialog for a Trend Test

Output for trend test

The results show a significant trend. To complement the trend tests, ToxTools also includes pairwise tests, which compares each non-zero dose group to the zero (or control) group.

Here, the tumor rates from the both the 200 and 300 dose groups are not significantly different from those in the control group, while the response from the 800 dose group is significantly different from those in the control group.