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Introduction to BayesianReasoning

Gorka Navarrete

2023-11-14

Bayesian reasoning

Bayesian reasoning in medical contexts

This package includes a few functions to plot and help understand Positive and Negative Predictive Values, and their relationship with Sensitivity, Specificity and Prevalence.

The Positive Predictive Value of a medical test is the probability that a positive result will mean having the disease. Formally p(Disease|+)
The Negative Predictive Value of a medical test is the probability that a negative result will mean not having the disease. Formally p(Healthy|-)

The BayesianReasoning package has three main functions:

PPV_heatmap(): Plot heatmaps with PPV or NPV values for the given test and disease parameters.
PPV_diagnostic_vs_screening(): Plots the difference between the PPV of a test in a diagnostic context (very high prevalence; or a common study sample, e.g. ~50% prevalence) versus a screening context (lower prevalence).
min_possible_prevalence(): Calculates how high should the prevalence of a disease be to reach a desired PPV given certain test parameters.

If you want to install the package can use: remotes::install_github("gorkang/BayesianReasoning"). Please report any problems you find in the Issues Github page.

There is a shiny app implementation with most of the main features available.

PPV_heatmap()

Plot heatmaps with PPV or NPV values for a given specificity and a range of Prevalences and FP or FN (1 - Sensitivity). The basic parameters are:

min_Prevalence: Min prevalence in y axis. “min_Prevalence out of y”
max_Prevalence: Max prevalence in y axis. “1 out of max_Prevalence”
Sensitivity: Sensitivity of the test
max_FP: FP is 1 - specificity. The x axis will go from FP = 0% to max_FP
Language: “es” for Spanish or “en” for English


PPV_heatmap(min_Prevalence = 1,
            max_Prevalence = 1000, 
            Sensitivity = 100, limits_Specificity = c(90, 100),
            Language = "en")

NPV

You can also plot an NPV heatmap with PPV_NPV = “NPV”.


PPV_heatmap(PPV_NPV = "NPV",
            min_Prevalence = 800, max_Prevalence = 1000, 
            Specificity = 95, limits_Sensitivity = c(90, 100),
            Language = "en")

Area overlay

You can add different types of overlay to the plots.

For example, an area overlay showing the point PPV for a given prevalence and FP or FN:


PPV_heatmap(min_Prevalence = 1, max_Prevalence = 1200, 
            Sensitivity = 81, 
            limits_Specificity = c(94, 100),
            label_subtitle = "Prenatal screening for Down Syndrome by Age",
            overlay = "area",
            overlay_labels = "40 y.o.",
            overlay_position_FP = 4.8,
            overlay_prevalence_1 = 1,
            overlay_prevalence_2 = 68)

The area plot overlay can show more details about how the calculation of PPV/NPV is performed:


PPV_heatmap(min_Prevalence = 1, max_Prevalence = 1200, 
            Sensitivity = 81, 
            limits_Specificity = c(94, 100),
            label_subtitle = "Prenatal screening for Down Syndrome by Age", 
            overlay_extra_info = TRUE,
            overlay = "area",
            overlay_labels = "40 y.o.",
            overlay_position_FP = 4.8,
            overlay_prevalence_1 = 1,
            overlay_prevalence_2 = 68)

Line overlay

Also, you can add a line overlay highlighting a range of prevalences and FP. This is useful, for example, to show how the PPV of a test changes with age:


PPV_heatmap(min_Prevalence = 1, max_Prevalence = 1800, 
            Sensitivity = 90, 
            limits_Specificity = c(84, 100),
            label_subtitle = "PPV of Mammogram for Breast Cancer by Age",
            overlay = "line", 
            overlay_labels = c("80 y.o.", "70 y.o.", "60 y.o.", "50 y.o.", "40 y.o.", "30 y.o.", "20  y.o."),
            overlay_position_FP = c(6.5, 7, 8, 9, 12, 14, 14),
            overlay_prevalence_1 = c(1, 1, 1, 1, 1, 1, 1),
            overlay_prevalence_2 = c(22, 26, 29, 44, 69, 227, 1667))

Another example. In this case, the FP is constant across age:


PPV_heatmap(min_Prevalence = 1, max_Prevalence = 2000, Sensitivity = 81, 
            limits_Specificity = c(94, 100),
            label_subtitle = "Prenatal screening for Down Syndrome by Age",
            overlay = "line",
            overlay_labels = c("40 y.o.", "30 y.o.", "20 y.o."),
            overlay_position_FP = c(4.8, 4.8, 4.8),
            overlay_prevalence_1 = c(1, 1, 1),
            overlay_prevalence_2 = c(68, 626, 1068))

PPV_diagnostic_vs_screening()

In scientific studies developing a new test for the early detection of a medical condition, it is quite common to use a sample where 50% of participants has a medical condition and the other 50% are normal controls. This has the unintended effect of maximizing the PPV of the test.

This function shows a plot with the difference between the PPV of a diagnostic context (very high prevalence; or a common study sample, e.g. ~50% prevalence) versus that of a screening context (lower prevalence).


PPV_diagnostic_vs_screening(max_FP = 10, 
                            Sensitivity = 100, 
                            prevalence_screening_group = 1000, 
                            prevalence_diagnostic_group = 2)

min_possible_prevalence()

Imagine you would like to use a test in a population and want to have a 98% PPV. That is, IF a positive result comes out in the test, you would like a 98% certainty that it is a true positive.

How high should the prevalence of the disease be in that group?

min_possible_prevalence(Sensitivity = 100, 
                        FP_test = 0.1, 
                        min_PPV_desired = 98)

To reach a PPV of 98 when using a test with 100 % Sensitivity and 0.1 % False Positive Rate, you need a prevalence of at least 1 out of 21

Another example, with a very good test, and lower expectations:

min_possible_prevalence(Sensitivity = 99.9, 
                        FP_test = .1, 
                        min_PPV_desired = 70)

To reach a PPV of 70 when using a test with 99.9 % Sensitivity and 0.1 % False Positive Rate, you need a prevalence of at least 1 out of 429

plot_cutoff()

Since v0.4.2 you can also plot the distributions of sick and healthy individuals and learn about how a cutoff point changes the True Positives, False Positives, True Negatives, False Negatives, Sensitivity, Specificity, PPV and NPV.


PLOTS = plot_cutoff(prevalence = 0.2,
                    cutoff_point = 33, 
                    mean_sick = 35, 
                    mean_healthy = 20, 
                    sd_sick = 3, 
                    sd_healthy = 5
                    )

PLOTS$final_plot

Then, with remove_layers_cutoff_plot() you can remove specific layers, to help you understand some of these concepts.


# Sensitivity
remove_layers_cutoff_plot(PLOTS$final_plot, delete_what = c("FP", "TN")) + ggplot2::labs(subtitle = "Sensitivity = TP/(TP+FN)")


# Specificity
remove_layers_cutoff_plot(PLOTS$final_plot, delete_what = c("FN", "TP")) + ggplot2::labs(subtitle = "Specificity = TN/(TN+FP)")


# PPV
remove_layers_cutoff_plot(PLOTS$final_plot, delete_what = c("TN", "FN")) + ggplot2::labs(subtitle = "PPV = TP/(TP+FP)")


# NPV
remove_layers_cutoff_plot(PLOTS$final_plot, delete_what = c("TP", "FP")) + ggplot2::labs(subtitle = "NPV = TN/(TN+FN)")

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.