Change unit increase from 1 to 10 when calculating odds ratios in r-CodePudding

I used the package questionr to calculate the odds ratios for a logistic regression model with two variables, var1 and var2. I used the code:

odds.ratio(mymodel, level=0.95)

This returned odds ratios with 95% CIs; however, I would like to report odds ratios for a 10-unit increase versus a 1-unit increase. Is there a package in r capable of doing this?

CodePudding user response：

If anyone else is searching for this in the future...just discovered the oddsratio package, which has the incr (increment) argument.

CodePudding user response：

The odds ratio (as reported in questionr) shows you the odds of a positive outcome when the independent variable is 1, divided by the odds of a positive outcome when the independent variable is 0. However, by extension, when the independent variable is two, we can square the odds ratio to find the odds ratio of a two-point increase, and so on.

This means that you can raise the odds ratio (and its confidence intervals) to the power of 10 to get the odds ratio for a 10-point increase.

Let's demonstrate with a simple logistic regression:

set.seed(1)

iv <- sample(100)
dv <- rbinom(100, 1, iv/100)
df <- data.frame(dv, iv)

model <- glm(dv ~ iv, data = df, family = binomial)

model
#> 
#> Call:  glm(formula = dv ~ iv, family = binomial, data = df)
#> 
#> Coefficients:
#> (Intercept)           iv  
#>    -2.46465      0.04997  
#> 
#> Degrees of Freedom: 99 Total (i.e. Null);  98 Residual
#> Null Deviance:       138.6 
#> Residual Deviance: 102.9     AIC: 106.9

Now we can see the odds ratio easily using questionr:

questionr_or <- questionr::odds.ratio(model)
#> Waiting for profiling to be done...

questionr_or
#>                   OR    2.5 % 97.5 %         p    
#> (Intercept) 0.085039 0.025954 0.2354 9.833e-06 ***
#> iv          1.051241 1.032145 1.0741 7.070e-07 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

This shows us the odds ratio for a 1-point increase. If we want a 10-point increase, we just raise these coefficients by a power of 10:

questionr_or[2, 1:3]^10
#>          OR    2.5 %   97.5 %
#> iv 1.648257 1.372168 2.043965

You will see that this gives the same result as the incr argument being set to 10 in the or_glm function from oddsratio:

oddsratio::or_glm(df, model, incr = list(iv = 10))
#>   predictor oddsratio ci_low (2.5) ci_high (97.5) increment
#> 1        iv     1.648        1.372          2.044        10

^{Created on 2021-10-21 by the reprex package (v2.0.0)}