I am trying to familiarize myself with constructing and interpreting confidence curves, but am not sure my interpretation of these curves is correct. I would appreciate any feedback - including corrections to my interpretations if they are warranted. Note that I provided my own interpretations for the first two examples in this post, which were inspired by the article **P value functions: An underused method to present research results and to promote quantitative reasoning** by Infanger and SchmidtāTrucksĆ¤ss (https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8293) However, the 3rd example needs an interpretation.

**Example 1:**

This example concerns a binary logistic regression model where Y = whether or not the study subject finds a phone reminder useful and X = gender and the interest is in inference about the gender effect. (Y is coded so that 1 stands for useful and 0 for not useful; X is coded as 0 for males and 1 for females; males are treated as the reference.)

The point estimate for the odds ratio of finding the phone reminder useful is 1.97 and the associate 95% confidence interval is 1.19 to 3.26. The confidence curve is shown below.

Would an interpretation like the one below work for **Example 1**?

*The ratio of odds of finding the phone reminder useful for females relative to males was estimated to be 1.97 (95% confidence interval: 1.19 to 3.26; p = 0.008). Since this estimated ratio and the associated P-value function both lie above 1 (which corresponds to equal odds), the study provides evidence that females have higher odds of finding the phone reminder useful compared to males. Furthermore, the 95% confidence interval indicates that the study was most compatible at the 95% confidence level with females having odds of finding the phone reminder useful that were anywhere from 19% to 226% higher than those for males.*

**Example 2:**

This example concerns a binary logistic regression model where Y = whether or not the study subject finds a phone reminder useful and X = whether or not study subject was assessed by a physician before a threshold date. (Y is coded as before so that 1 stands for useful and 0 for not useful; X is coded as 0 if assessment date falls before the threshold date and 1 otherwise).

The point estimate for the odds ratio of finding the phone reminder useful is 1.26 and the associate 95% confidence interval is 0.77 to 2.06. The confidence curve is shown below.

Would an interpretation like the one below work for **Example 2**?

*The ratio of odds of finding the phone reminder useful for those assessed by a physician after the threshold date relative to those assessed before it was estimated to be 1.26 (95% confidence interval: 0.77 to 2.06; p = 0.363). Since this estimated ratio and most of the associated P-value function lie above 1 (which corresponds to equal odds), the study provides evidence that those assessed by a physician after the threshold date have higher odds of finding the phone reminder useful compared to those assessed before that date. However, the study cannot dismiss, with a high amount of confidence, the possibility that those assessed by a physician after the threshold date have lower odds of finding the phone reminder useful. In particular, the 95% confidence interval indicates that the study was most compatible at the 95% confidence level with subjects assessed by a physician after the threshold date having odds of finding the phone reminder useful that were anywhere from 23% lower to 106% higher than those corresponding to subjects assessed before that date.*

For the last statement in the above, I used that (0.77 - 1) x 100% = -23% and (2.06 - 1) x 100% = 106%.

**Example 3:**

This example concerns a binary logistic regression model where Y = whether or not the study subject finds a phone reminder useful and X = whether or not the study subject lives alone in their home. (Y is coded as before so that 1 stands for useful and 0 for not useful; X is coded as 0 for alone and 1 for not alone; alone is treated as the reference.)

The point estimate for the odds ratio of finding the phone reminder useful is 1.09 and the associate 95% confidence interval is 0.56 to 2.03. The confidence curve is shown below.

I searched the literature but couldnāt find any explicit example of interpretation of a confidence curve that covers this type of scenario, so here I am stumped as to how to report the results. (All examples I could find are along the lines captured by my Examples 1 and 2.) I would really appreciate if someone could offer a valid interpretation for this specific scenario.

**Note**

The above plots were created with the **concurve** package in R, which includes a *curve_gen()* function. Here is the generic R code I used to create them:

```
install.packages("remotes")
remotes::install_cran("pbmcapply", force = TRUE)
remotes::install_cran("concurve", force = TRUE)
library(concurve)
library(pbmcapply)
model <- glm(Y ~ X,
data = mydata,
family=binomial(link="logit"))
summary(model)
round(exp(coef(model)),2)
round(exp(confint(model)),2)
model_con <- curve_gen(model = model,
var = "X",
method="glm",
steps = 100,
table = TRUE)
model_con
model_consonance <- model_con[[1]]
model_consonance$lower.limit <- exp(model_consonance$lower.limit)
model_consonance$upper.limit <- exp(model_consonance$upper.limit)
model_consonance_curve <-
ggcurve(model_consonance,
measure = "ratio",
type="c",
nullvalue = TRUE)
```

When I downloaded the Github version of the **concurve** package, it wouldnāt show the vertical line corresponding to the null value (i.e., OR = 1), so I had to force the line to be shown using the R code below:

```
library(ggplot2)
model_consonance_curve +
geom_vline(xintercept = 1, linetype=3, colour="red", size=1.5)
```

Also, note that I manually exponentiated the endpoints of the confidence limits produced by *curve_gen()* to get what I think should have been plotted in the confidence curve, rather than the default plotted by the **concurve** package.