Calibration Plot

library(predtools)
library(magrittr)
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#>     filter, lag
#> The following objects are masked from 'package:base':
#>
#>     intersect, setdiff, setequal, union
library(ggplot2)

What is calibration plot?

Calibration plot is a visual tool to assess the agreement between predictions and observations in different percentiles (mostly deciles) of the predicted values.

calibration_plot function constructs calibration plots based on provided predictions and observations columns of a given dataset. Among other options implemented in the function, one can evaluate prediction calibration according to a grouping factor (or even from multiple prediction models) in one calibration plot.

A step-by-step guide.

Imagine the variable y indicates risk of disease recurrence in a unit of time. We have a prediction model that quantifies this risk given a patient’s age, disease severity level, sex, and whether the patient has a comorbidity.

The package comes with two exemplary datasets. dev_data and val_data. We use the dev_data as the development sample and the val_data as the external validation sample.

data(dev_data)
data(val_data)

dev_data has 500 rows. val_data has 400 rows.

Here are the first few rows of dev_data:

age severity sex comorbidity y
55 0 0 1 1
52 1 0 0 0
63 0 0 1 0
61 1 1 1 1
58 0 1 0 0
54 1 0 0 1
45 0 0 0 0

We use the development data to fit a logistic regression model as our risk prediction model:

summary(reg)
#>
#> Call:
#> glm(formula = y ~ sex + age + severity + comorbidity, family = binomial(link = "logit"),
#>     data = dev_data)
#>
#> Deviance Residuals:
#>     Min       1Q   Median       3Q      Max
#> -1.2904  -0.8272  -0.6373   1.1570   2.1050
#>
#> Coefficients:
#>              Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.728929   0.565066  -3.060  0.00222 **
#> sex          0.557178   0.223631   2.492  0.01272 *
#> age          0.005175   0.010654   0.486  0.62717
#> severity    -0.557335   0.227587  -2.449  0.01433 *
#> comorbidity  1.091936   0.209944   5.201 1.98e-07 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#>     Null deviance: 602.15  on 499  degrees of freedom
#> Residual deviance: 560.41  on 495  degrees of freedom
#> AIC: 570.41
#>
#> Number of Fisher Scoring iterations: 4

Given this, our risk prediction model can be written as:

$$\bf{ logit(p)=-1.7289+0.5572*sex+0.0052*age-0.5573*severity+1.0919*comorbidity}$$.

Now, we can create the calibration plot in development and validation datasets by using calibration_plot function.

dev_data$pred <- predict.glm(reg, type = 'response') val_data$pred <- predict.glm(reg, newdata = val_data, type = 'response')

calibration_plot(data = dev_data, obs = "y", pred = "pred", title = "Calibration plot for development data")
#> $calibration_plot calibration_plot(data = val_data, obs = "y", pred = "pred", y_lim = c(0, 0.6), title = "Calibration plot for validation data", group = "sex") #>$calibration_plot
#> Warning: Removed 1 rows containing missing values (geom_point). 