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decision_curve_analysis_step_by_step.qmd
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---
title: "Decision Curve Analysis: Step by Step 👣"
author: "Uriah Finkel"
format:
revealjs:
theme: [white, cssrules.scss]
incremental: true
editor: visual
---
## Acknowledgement:
I'd like to thank Dr. Andrew Vickers for his help with this presentation.
You can visit his page on [**mskcc.org/profile/andrew-vickers**](https://www.mskcc.org/profile/andrew-vickers).
$$
\newcommand{\green}[1]{\color{green}{#1}}
\newcommand{\red}[1]{\color{red}{#1}}
$$
## Agenda
- This lecture follows the article [**A simple, step-by-step guide to interpreting decision curve analysis**](https://diagnprognres.biomedcentral.com/articles/10.1186/s41512-019-0064-7).
- Introduction: Motivation behind Decision Curve Analysis and how to draw a Decision Curve.
- How to interpret a Decision Curve: Step by Step guide.
## Code for Decision Curve Analysis 💻
- Standard software is available to run decision curves in R, SAS and Stata on [**decisioncurveanalysis.org**](https://www.mskcc.org/departments/epidemiology-biostatistics/biostatistics/decision-curve-analysis). Python should be with us soon!
- All interactive plots in this presentation were created with [**rtichoke**](https://uriahf.github.io/rtichoke/) R package (I am the author 👋), you are also invited to explore [**rtichoke blog**](https://rtichoke-blog.netlify.app/){.rtichoke_blog} for reproducible examples and some theory.
- For ggplot2 outputs [**dcurves**](https://www.danieldsjoberg.com/dcurves) R package is available on CRAN.
# Introduction
## Which Model is Better? 🤔
#### Select patients for biopsy amongst men with elevated PSA - 🖖 ROC
```{r echo=FALSE}
library(rtichoke)
library(magrittr)
scenario1 <- read.csv("Decision_Curve_Step_by_Step_files/scenario1.csv")
performance_dat <- prepare_performance_data(
probs = list(
"First Model" = scenario1$modela,
"Second Model" = scenario1$modelb
),
reals = list(scenario1$event)
)
performance_dat %>%
plot_roc_curve(
size = 450) %>%
plotly::animation_slider(
currentvalue = list(prefix = "Probability Threshold: ",
font = list(color="black"),
xanchor = "left")
) %>%
plotly::partial_bundle()
```
## Which Model is Better? 🤔
#### Select patients for biopsy amongst men with elevated PSA - ⚖️ Calibration Curve
```{r echo=FALSE}
create_calibration_curve(
probs = list(
"First Model" = scenario1$modela,
"Second Model" = scenario1$modelb
),
reals = list(scenario1$event),
type = "smooth",
histogram_included = FALSE, size = 450
) %>%
plotly::partial_bundle()
```
## Which Model is Better? 🤔
#### Select patients for biopsy amongst men with elevated PSA - 👌 Decision Curve
```{r echo=FALSE}
performance_dat %>%
plot_decision_curve(
# type = "interventions avoided",
size = 450,
min_p_threshold = 0,
max_p_threshold = 0.2
)
```
## Traditional Statistical Metric:
- **Discrimination 🖖**: Model's ability to separate between events and non-events (ROC Curve, AUROC, Sensitivity, Specificity, NPV, PPV, Lift etc).
- **Calibration ⚖️**: Agreement between predicted probabilities and the observed outcomes (Calibration Curve, Calibration in the large, Calibration in the small etc).
- [**Problem**]{style="color: red;"}**🛑** These metrics are not directly informative to clinical value, nor to full decision analytic approaches.
- [**Solution**]{style="color: green;"}**👌** Decision Curve Analysis calculates a clinical "Net Benefit" prediction models or diagnostic tests in comparison to default strategies of treating all or no patients.
## How to draw a Decision Curve?
::: columns
::: {.column style="font-size: 50%;"}
$${\text{X axis: } {p_{t}} \text{ (Probability Threshold)}}$$
$$\begin{aligned}
{\text{Y axis: }\text{NB Model} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}}
\end{aligned}$$
$$\begin{aligned}
\text{NB Treat None} = 0
\end{aligned}$$
$$\begin{aligned}
\text{NB Treat All} = {\text{Prevalence}} - {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
::: column
```{r echo=FALSE, message=FALSE, warning=FALSE}
dc <- rtichoke::create_decision_curve(
probs = list(scenario1$modela),
reals = list(scenario1$event),
interactive = TRUE, size = 450
) %>%
plotly::partial_bundle()
dc
```
:::
:::
# Step 1 👣: <br>Benefit is [Good]{style="color: green;"}
------------------------------------------------------------------------
::: columns
::: {.column width="50%"}
### [Green]{style="color: green;"} {style="text-align: center; font-size: 150px;"}
::: {style="height:123px; width:100%; clear:both;"}
:::
### **🙂** {style="text-align: center; font-size: 120px;"}
:::
::: {.column width="50%"}
### [Red]{style="color: red;"} {style="text-align: center; font-size: 150px;"}
::: {style="height:123px; width:100%; clear:both;"}
:::
### **🙁** {style="text-align: center; font-size: 120px;"}
:::
:::
------------------------------------------------------------------------
::: columns
::: {.column width="50%"}
### [Green]{style="color: green;"} {style="text-align: center; font-size: 150px;"}
::: {style="height: 0px; width:100%; clear:both;"}
:::
{fig-align="center" width="200"}
:::
::: {.column width="50%"}
### [Red]{style="color: red;"} {style="text-align: center; font-size: 150px;"}
::: {style="height: 49px; width:100%; clear:both;"}
:::
{fig-align="center" width="200"}
:::
:::
## [True Positives]{style="color: green;"} {.smaller}
### Infected and Predicted as Infected - [Good]{style="color: green;"}
[**💊**]{style="font-size: 50px;"} <br> [🤢]{style="font-size: 50px;"}
```{r}
tibble::tribble(
~"type", ~"predicted_positive", ~"predicted_negative",
"Real Positive", "TP", "FN",
"Real Negative", "FP", "TN"
) |>
reactable::reactable(
sortable = FALSE,
fullWidth = FALSE,
borderless = FALSE,
defaultColDef = reactable::colDef(
align = "center",
headerStyle = list(fontWeight = 100)
),
columns = list(
type = reactable::colDef(
name = "",
align = "left",
style = list(fontWeight = 100),
minWidth = 200
),
predicted_positive = reactable::colDef(
name = "Predicted Positive",
style = function(value) {
color <- if (value == "TP") {
"lightgreen"
}
list(fontWeight = 600, background = color)
},
minWidth = 200
),
predicted_negative = reactable::colDef(
name = "Predicted Negative",
style = function(value) {
list(fontWeight = 600)
},
minWidth = 200
)
)
)
```
## [False Positives]{style="color: red;"} {.smaller}
### Not-Infected and Predicted as Infected - [BAD]{style="color: red;"}
[**💊**]{style="font-size: 50px;"} <br> [🤨]{style="font-size: 50px;"}
```{r}
tibble::tribble(
~"type", ~"predicted_positive", ~"predicted_negative",
"Real Positive", "TP", "FN",
"Real Negative", "FP", "TN"
) |>
reactable::reactable(
sortable = FALSE,
fullWidth = FALSE,
borderless = FALSE,
defaultColDef = reactable::colDef(
align = "center",
headerStyle = list(fontWeight = 100)
),
columns = list(
type = reactable::colDef(
name = "",
align = "left",
style = list(fontWeight = 100),
minWidth = 200
),
predicted_positive = reactable::colDef(
name = "Predicted Positive",
style = function(value) {
color <- if (value == "FP") {
"pink"
}
list(fontWeight = 600, background = color)
},
minWidth = 200
),
predicted_negative = reactable::colDef(
name = "Predicted Negative",
style = function(value) {
list(fontWeight = 600)
},
minWidth = 200
)
)
)
```
## [False Negatives]{style="color: red;"} {.smaller}
### Infected and Predicted as Not-Infected - [BAD]{style="color: red;"}
<br> [🤢]{style="font-size: 50px;"}
```{r}
tibble::tribble(
~"type", ~"predicted_positive", ~"predicted_negative",
"Real Positive", "TP", "FN",
"Real Negative", "FP", "TN"
) |>
reactable::reactable(
sortable = FALSE,
fullWidth = FALSE,
borderless = FALSE,
defaultColDef = reactable::colDef(
align = "center",
headerStyle = list(fontWeight = 100)
),
columns = list(
type = reactable::colDef(
name = "",
align = "left",
style = list(fontWeight = 100),
minWidth = 200
),
predicted_positive = reactable::colDef(
name = "Predicted Positive",
style = function(value) {
list(fontWeight = 600)
},
minWidth = 200
),
predicted_negative = reactable::colDef(
name = "Predicted Negative",
style = function(value) {
color <- if (value == "FN") {
"pink"
}
list(fontWeight = 600, background = color)
},
minWidth = 200
)
)
)
```
## [True Negatives]{style="color: green;"} {.smaller}
### Not-Infected and Predicted as Not-Infected - [GOOD]{style="color: green;"}
<br> [🤨]{style="font-size: 50px;"}
```{r}
tibble::tribble(
~"type", ~"predicted_positive", ~"predicted_negative",
"Real Positive", "TP", "FN",
"Real Negative", "FP", "TN"
) |>
reactable::reactable(
sortable = FALSE,
fullWidth = FALSE,
borderless = FALSE,
defaultColDef = reactable::colDef(
align = "center",
headerStyle = list(fontWeight = 100)
),
columns = list(
type = reactable::colDef(
name = "",
align = "left",
style = list(fontWeight = 100),
minWidth = 200
),
predicted_positive = reactable::colDef(
name = "Predicted Positive",
style = function(value) {
list(fontWeight = 600)
},
minWidth = 200
),
predicted_negative = reactable::colDef(
name = "Predicted Negative",
style = function(value) {
color <- if (value == "TN") {
"lightgreen"
}
list(fontWeight = 600, background = color)
},
minWidth = 200
)
)
)
```
------------------------------------------------------------------------
## Decision Tree
{fig-align="center"}
## Decision Tree
{fig-align="center"}
## Decision Tree
Probability Threshold is derived from Equivalence between
$$EV_{Treat} = p(Disease) * U_{TP} + p(No Disease) * U_{FP}$$
$$EV_{NoTreat} = p(Disease) * U_{FN} + p(No Disease) * U_{TN}$$
## Decision Tree {style="font-size: 75%;"}
Probability Threshold is derived from Equivalence between
$$EV_{Treat} = EV_{{NoTreat}}$$
$$p(Disease) * U_{TP} + p(No Disease) * U_{FP} =p(Disease) * U_{FN} + p(No Disease) * U_{TN}$$
## Decision Tree {style="font-size: 75%;"}
Probability Threshold is derived from Equivalence between
$$EV_{Treat} = EV_{{NoTreat}}$$
$$p(Disease) * U_{TP} + (1-p(Disease)) * U_{FP} =p(Disease) * U_{FN} + (1-p(Disease)) * U_{TN}$$
## Decision Tree
Probability Threshold is derived from Equivalence between
$$EV_{Treat} = EV_{{NoTreat}}$$
$$p(Disease) * (U_{TP} - U_{FN}) =(1-p(Disease)) * (U_{TN} - U_{FP})$$
## Decision Tree
Probability Threshold is derived from Equivalence between
$$EV_{Treat} = EV_{{NoTreat}}$$
$$\frac{p(Disease)}{(1-p(Disease))} = \frac{(U_{TN} - U_{FP})}{(U_{TP} - U_{FN})}$$
## Decision Tree
Probability Threshold is derived from Equivalence between
$$EV_{💊} = EV_{{No💊}}$$
<!-- $$p(🤢) * U_{💊+🤢} + p(🤨) * U_{💊+🤨} =p(🤢) * U_{💊+🤨} + p(🤨) * U_{🤨}$$ -->
<!-- $$p(🤢) * U_{💊+🤢} + (1-p(🤢)) * U_{💊+🤨} =p(🤢) * U_{💊+🤨} + (1-p(🤢)) * U_{🤨}$$ -->
<!-- $$p(🤢) * (U_{💊+🤢} - U_{💊+🤨}) =(1-p(🤢)) * (U_{🤨} - U_{💊+🤨})$$ -->
$$\frac{p(🤢)}{(1-p(🤢))} = \frac{(U_{🤨} - U_{💊+🤨})}{(U_{💊+🤢} - U_{🤢})}$$
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Sensitivity } = \frac{\green{\bf{TP}}}{\text{TP + FN}}
\end{aligned}$$
$$\begin{aligned}
\text{Specificity} = \frac{\green{\bf{TN}}}{\text{TN + FP}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{TP + FN}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Net Benefit} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Sensitivity } = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\text{Specificity} = \frac{\green{\bf{TN}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positive}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Net Benefit} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Sensitivity } = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\text{Specificity} = \frac{\green{\bf{TN}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positive}}{\text{N}}
\end{aligned}$$
$$\begin{aligned}
{\text{1 - Prevalence}} = \frac{\text{Real Negatives}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Net Benefit} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Sensitivity } = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\text{Specificity} = \frac{\green{\bf{TN}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positive}}{\text{N}}
\end{aligned}$$
$$\begin{aligned}
{\text{1 - Prevalence}} = \frac{\text{Real Negatives}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\text{Net Benefit} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
$$\tiny{\begin{aligned}
\text{Net Benefit} = {\text{Sensitivity}} * {\text{Prevalence}} - {\text{(1 - Specificity)}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Sensitivity}} = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\red{\bf{1 - Specificity}} = \frac{\bf{\red{FP}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positives}}{\text{N}}
\end{aligned}$$
$$\begin{aligned}
{\text{1 - Prevalence}} = \frac{\text{Real Negatives}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Net Benefit}} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
$$\tiny{\begin{aligned}
\green{\bf{Net Benefit}} = {\green{\bf{Sensitivity}}} * {\text{Prevalence}} - {\red{\bf{(1 - Specificity)}}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Sensitivity}} = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\red{\bf{1 - Specificity}} = \frac{\bf{\red{FP}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positives}}{\text{N}}
\end{aligned}$$
$$\begin{aligned}
{\text{1 - Prevalence}} = \frac{\text{Real Negatives}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Net Benefit}} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
$$\tiny{\begin{aligned}
\green{\bf{Net Benefit}} = {\green{\bf{Sensitivity}}} * {\text{Prevalence}} - {\red{\bf{(1 - Specificity)}}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
$$\tiny{\begin{aligned}
\text{Net Benefit Treat All} = {\green{\bf{1}}} * {\text{Prevalence}} - {\red{\bf{(1 - 0)}}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Sensitivity}} = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\red{\bf{1 - Specificity}} = \frac{\bf{\red{FP}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positives}}{\text{N}}
\end{aligned}$$
$$\begin{aligned}
{\text{1 - Prevalence}} = \frac{\text{Real Negatives}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Net Benefit}} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
$$\tiny{\begin{aligned}
\green{\bf{Net Benefit}} = {\green{\bf{Sensitivity}}} * {\text{Prevalence}} - {\red{\bf{(1 - Specificity)}}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
$$\tiny{\begin{aligned}
\text{Net Benefit Treat All} = {\text{Prevalence}} - {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Sensitivity}} = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\red{\bf{1 - Specificity}} = \frac{\bf{\red{FP}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positives}}{\text{N}}
\end{aligned}$$
$$\begin{aligned}
{\text{1 - Prevalence}} = \frac{\text{Real Negatives}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Net Benefit}} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
$$\tiny{\begin{aligned}
\green{\bf{Net Benefit}} = {\green{\bf{Sensitivity}}} * {\text{Prevalence}} - {\red{\bf{(1 - Specificity)}}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
$$\tiny{\begin{aligned}
\text{Net Benefit Treat All} = {\text{Prevalence}} - {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
$$\tiny{\begin{aligned}
\text{Net Benefit Treat None} = {\green{\bf{0}}} * {\text{Prevalence}} - {\red{\bf{(1 - 1)}}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
:::
## Step 1 👣: Benefit is [Good]{style="color: green;"}
::: columns
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Sensitivity}} = \frac{\green{\bf{TP}}}{\text{Real Positives}}
\end{aligned}$$
$$\begin{aligned}
\red{\bf{1 - Specificity}} = \frac{\bf{\red{FP}}}{\text{Real Negatives}}
\end{aligned}$$
$$\begin{aligned}
{\text{Prevalence}} = \frac{\text{Real Positives}}{\text{N}}
\end{aligned}$$
$$\begin{aligned}
{\text{1 - Prevalence}} = \frac{\text{Real Negatives}}{\text{N}}
\end{aligned}$$
:::
::: {.column style="font-size: 50%;"}
$$\begin{aligned}
\green{\bf{Net Benefit}} = \frac{\green{\bf{TP}}}{\text{N}} - \frac{\red{\bf{FP}}}{\text{N}} * {\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}$$
:::
$$\tiny{\begin{aligned}
\green{\bf{Net Benefit}} = {\green{\bf{Sensitivity}}} * {\text{Prevalence}} - {\red{\bf{(1 - Specificity)}}} * {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
$$\tiny{\begin{aligned}
\text{Net Benefit Treat All} = {\text{Prevalence}} - {\text{(1 - Prevalence)}} *{\frac{{p_{t}}}{{1 - p_{t}}}}
\end{aligned}}$$
$$\tiny{\begin{aligned}
\text{Net Benefit Treat None} = 0
\end{aligned}}$$
:::
# Step 2 👣: <br>Preference Differ
## Step 2 👣: Preference Differ
::: columns
::: {.column style="font-size: 50%;"}
Low Probability Threshold means that I'm worried about the **outcome**:
- I'm worried about **Prostate Cancer** 🦀
- I'm worried about **Heart Disease** 💔
- I'm worried about **Infection** 🤢
:::
::: column
```{r echo=FALSE}
library('plotly')
# Create figure
dc %>% # Add trace
plotly::layout(
images = list(
list(
# Add images
source = "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/91402b30-6488-4c64-9fd5-5a1dc9ea8bd6/deypsl5-59796e39-aec1-426e-befe-8b460e6648ef.png/v1/fill/w_567,h_538,strp/mr__worry_by_enzothemii_deypsl5-fullview.png?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOjdlMGQxODg5ODIyNjQzNzNhNWYwZDQxNWVhMGQyNmUwIiwiaXNzIjoidXJuOmFwcDo3ZTBkMTg4OTgyMjY0MzczYTVmMGQ0MTVlYTBkMjZlMCIsIm9iaiI6W1t7ImhlaWdodCI6Ijw9NTM4IiwicGF0aCI6IlwvZlwvOTE0MDJiMzAtNjQ4OC00YzY0LTlmZDUtNWExZGM5ZWE4YmQ2XC9kZXlwc2w1LTU5Nzk2ZTM5LWFlYzEtNDI2ZS1iZWZlLThiNDYwZTY2NDhlZi5wbmciLCJ3aWR0aCI6Ijw9NTY3In1dXSwiYXVkIjpbInVybjpzZXJ2aWNlOmltYWdlLm9wZXJhdGlvbnMiXX0.Q5L0SXP17MyiaymICWE9uhQZmB_SODDWzxJPmk0pcLk",
xref = "x",
yref = "y",
x = 0.05,
y = -0.015,
sizex = 0.13,
sizey = 0.13,
layer = "below"
)#,
# list(
# # Add images
# source = "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/91402b30-6488-4c64-9fd5-5a1dc9ea8bd6/deypsl5-59796e39-aec1-426e-befe-8b460e6648ef.png/v1/fill/w_567,h_538,strp/mr__worry_by_enzothemii_deypsl5-fullview.png?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOjdlMGQxODg5ODIyNjQzNzNhNWYwZDQxNWVhMGQyNmUwIiwiaXNzIjoidXJuOmFwcDo3ZTBkMTg4OTgyMjY0MzczYTVmMGQ0MTVlYTBkMjZlMCIsIm9iaiI6W1t7ImhlaWdodCI6Ijw9NTM4IiwicGF0aCI6IlwvZlwvOTE0MDJiMzAtNjQ4OC00YzY0LTlmZDUtNWExZGM5ZWE4YmQ2XC9kZXlwc2w1LTU5Nzk2ZTM5LWFlYzEtNDI2ZS1iZWZlLThiNDYwZTY2NDhlZi5wbmciLCJ3aWR0aCI6Ijw9NTY3In1dXSwiYXVkIjpbInVybjpzZXJ2aWNlOmltYWdlLm9wZXJhdGlvbnMiXX0.Q5L0SXP17MyiaymICWE9uhQZmB_SODDWzxJPmk0pcLk",
# xref = "x",
# yref = "y",
# x = 0.85,
# y = -0.015,
# sizex = 0.13,
# sizey = 0.13,
# layer = "below"
# )
)
) %>%
plotly::layout(xaxis = list(range = list(-0.2, 1)),
yaxis = list(range = list(-0.1, 0.34))) %>%
plotly::layout(width=500,
height=500) %>%
plotly::layout(
shapes = list(
list(
type = "line",
y0 = 0.24,
y1 = 1,
yref = "paper",
x0 = 0.1,
x1 = 0.1,
line = list(color = "black", dash="dot")
))
) %>%
plotly::partial_bundle()
```
:::
:::
## Step 2 👣: Preference Differ
::: columns
::: {.column style="font-size: 50%;"}
High Probability Threshold means that I'm worried about the **Intervention**:
- I'm worried about **Biopsy** 💉
- I'm worried about **Statins** 💊
- I'm worried about **Antibiotics** 💊
:::
::: column
```{r echo=FALSE}
# Create figure
dc %>% # Add trace
plotly::layout(
images = list(
list(
source = "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/91402b30-6488-4c64-9fd5-5a1dc9ea8bd6/deypsl5-59796e39-aec1-426e-befe-8b460e6648ef.png/v1/fill/w_567,h_538,strp/mr__worry_by_enzothemii_deypsl5-fullview.png?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOjdlMGQxODg5ODIyNjQzNzNhNWYwZDQxNWVhMGQyNmUwIiwiaXNzIjoidXJuOmFwcDo3ZTBkMTg4OTgyMjY0MzczYTVmMGQ0MTVlYTBkMjZlMCIsIm9iaiI6W1t7ImhlaWdodCI6Ijw9NTM4IiwicGF0aCI6IlwvZlwvOTE0MDJiMzAtNjQ4OC00YzY0LTlmZDUtNWExZGM5ZWE4YmQ2XC9kZXlwc2w1LTU5Nzk2ZTM5LWFlYzEtNDI2ZS1iZWZlLThiNDYwZTY2NDhlZi5wbmciLCJ3aWR0aCI6Ijw9NTY3In1dXSwiYXVkIjpbInVybjpzZXJ2aWNlOmltYWdlLm9wZXJhdGlvbnMiXX0.Q5L0SXP17MyiaymICWE9uhQZmB_SODDWzxJPmk0pcLk",
xref = "x",
yref = "y",
x = 0.85,
y = -0.015,
sizex = 0.13,
sizey = 0.13,
layer = "below"
)
)
) %>%
plotly::layout(xaxis = list(range = list(-0.2, 1)),
yaxis = list(range = list(-0.1, 0.34))) %>%
plotly::layout(width=500,
height=500) %>%
plotly::layout(
shapes = list(
list(
type = "line",
y0 = 0.24,
y1 = 1,
yref = "paper",
x0 = 0.9,
x1 = 0.9,
line = list(color = "black", dash="dot")
))
) %>%
plotly::partial_bundle()
```
:::
:::
# Step 3 👣:<br>Unit of Preference = Threshold Probability
## Step 3 👣: Unit of Preference = Threshold Probability
::: columns
::: {.column style="font-size: 50%;"}
[**Remember:**]{style="color: red;"} almost always (specially in Health Care) -
Sensitivity does not have the same importance as Specificity and having 1 TP does not have the same clinical utility as having 1 FP.
A good example for a bad practice in evaluating performance of prediction model is the Youden's J statistics:
$${\displaystyle J={\frac {\green{\bf{TP}}}{{\green{\bf{TP}}}+{\red{\bf{FN}}}}}+{\frac {\green{\bf{TN}}}{{\green{\bf{TN}}}+{\red{\bf{FP}}}}}-1}$$ Maximizing Youden's J statistic might lead to a Probability Threshold that will do more harm than good, even if the prediction model is accurate!
:::
::: column
```{r echo=FALSE, message=FALSE, warning=FALSE, paged.print=FALSE}
perf_dat <- rtichoke::prepare_performance_data(
probs = list(scenario1$modela),
reals = list(scenario1$event)
)
j_idx <- perf_dat %>%
dplyr::mutate(j_idx = sensitivity + specificity - 1) %>%
dplyr::filter(j_idx == max(j_idx)) %>%
dplyr::mutate(sensitivity = sensitivity + 0.02,
FPR = FPR - 0.02) %>%
dplyr::select(sensitivity, FPR)
perf_dat %>%
rtichoke::plot_roc_curve(interactive = TRUE, size = 450) %>%
plotly::add_annotations(
text = "Youden's J Index",
data = j_idx,
x =~ FPR,
y =~ sensitivity
)
```
:::
:::
## Step 3 👣: Unit of Preference = Threshold Probability
::: columns
::: {.column style="font-size: 50%;"}
[**Remember:**]{style="color: red;"} almost always (specially in Health Care) -
Sensitivity does not have the same importance as Specificity and having 1 TP does not have the same clinical utility as having 1 FP.
A good example for a bad practice in evaluating performance of prediction model is the Youden's J statistics:
$${\displaystyle \green{\bf{J}}={\green{\bf{Sens}}}-{\red{\bf{(1 - Spec)}}}}$$
$${\displaystyle \green{\bf{NB}}={\green{\bf{Sens}}} * {\text{Prev}}-{\red{\bf{(1 - Spec)}}}* {\text{(1 - Prev)}}*{\frac{{p_{t}}}{{1 - p_{t}}}}}$$
:::
::: column
```{r echo=FALSE, message=FALSE, warning=FALSE, paged.print=FALSE}
perf_dat <- rtichoke::prepare_performance_data(
probs = list(scenario1$modela),
reals = list(scenario1$event)
)
j_idx <- perf_dat %>%
dplyr::mutate(j_idx = sensitivity + specificity - 1) %>%
dplyr::filter(j_idx == max(j_idx)) %>%
dplyr::mutate(sensitivity = sensitivity + 0.02,
FPR = FPR - 0.02) %>%
dplyr::select(sensitivity, FPR)
perf_dat %>%
rtichoke::plot_roc_curve(interactive = TRUE, size = 450) %>%
plotly::add_annotations(
text = "Youden's J Index",
data = j_idx,
x =~ FPR,
y =~ sensitivity
)
```
:::
:::
## Step 3 👣: Unit of Preference = Threshold Probability
::: columns
::: {.column style="font-size: 50%;"}
I wouldn't give more than 4 antibiotics in order to help 1 infected patient.
If a patient's risk was above 20% I will give him antibiotics, otherwise I won't.
The risk of 20% is an odds of 1:4, so in using a threshold probability of 20%, the doctor is telling us "missing an infected patiant is 4 times worse than giving antibiotics to a healthy patient."
$$p_t = \frac{1}{1 + 4} = 0.2$$ $$\frac{p_t}{1 - p_t} = \frac{0.2}{1 - 0.2} = \frac{1}{4}$$
:::
::: column
```{r echo=FALSE, message=FALSE, warning=FALSE, paged.print=FALSE}
dc_performance_data <- rtichoke::prepare_performance_data(
probs = list(scenario1$modela),
reals = list(scenario1$event)
) %>%
rtichoke:::add_hover_text_to_performance_data("one model",
curve = "decision") %>%
dplyr::mutate(
slider_text =
glue::glue("Pt: {stringr::str_pad(probability_threshold, 8, 'right')} \\
Odds: 1:{round((1 - probability_threshold) / probability_threshold, digits = 2)}")
)
basic_dc <- rtichoke:::create_reference_lines_for_plotly(
curve = "decision",
performance_table_type = "one model",
prevalence = rtichoke:::get_prevalence_from_performance_data(
dc_performance_data),
performance_data = dc_performance_data) %>%