# CoronaVirus_Disease_2019_prevalence: Who should be inspected? In BayesianFROC: FROC Analysis by Bayesian Approaches

## Description

Even if we test all people, the result is true with very low probabilties.

## Usage

 1 CoronaVirus_Disease_2019_prevalence(pre, se, sp) 

## Arguments

 pre Prevalence of population se Sensitivity of a diagnostic test sp Specificity of a diagnostic test

## Details

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 Diagnosis \ truth Diseased Non-diseased ----------------------- ----------------------- ------------- Positive se*n (N-n)(1-sp) Negative (1-se)*n (N-n)sp ----------------------- ----------------------- ------------- n N-n

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For example,

if prevalence is 0.0001,

population is 10000,

specificity = 0.8,

sensitivity = 0.9,

then the table is the following.

We can calculates the probability of the event that positive-diagnosis correctly detects the diseased patient is

\frac{9}{1998 + 9} = 9/(1998+9) = 0.00448

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 Diagnosis \ truth Diseased Non-diseased ----------------------- ----------------------- ------------- Positive 9 1998 Negative 1 7992 ----------------------- ----------------------- ------------- n = 10 N-n=10000-10

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## Value

same as  CoronaVirus_Disease_2019()

Prob(Truth = diseased | Diagnosis = Positive) = \frac{Se\times pre}{Se \times pre + (1-pre)\times(1-sp)}

where we denotes the conditional probability measure of an event A given the assumed occurrence of G as an usual manner

P(A|G):= \frac{P(A \cap G)}{P(G)}.

 CoronaVirus_Disease_2019()
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 CoronaVirus_Disease_2019_prevalence(0.0001, 0.9,0.8) CoronaVirus_Disease_2019_prevalence(0.03,0.9,0.8) CoronaVirus_Disease_2019_prevalence(0.3,0.9,0.8) #======================================================================================== # If Sensitivity and Specificity is larger, then, the probability is also larger #======================================================================================== x <- stats::runif(1111,0,1) y <- CoronaVirus_Disease_2019_prevalence(0.1,x,x) dark_theme(4) plot(x,y) x <- stats::runif(1111,0,1) y <- CoronaVirus_Disease_2019_prevalence(0.01,x,x) dark_theme(4) plot(x,y) x <- stats::runif(1111,0,1) y <- CoronaVirus_Disease_2019_prevalence(0.001,x,x) dark_theme(4) plot(x,y) #======================================================================================== # linear case: # # If prevalence is 0.5 # and sensitivity = specificity # then, the probability is exactly same as sensitivity = specificity # #======================================================================================== x <- stats::runif(1111,0,1) y <- CoronaVirus_Disease_2019_prevalence(0.5,x,x) dark_theme(4) plot(x,y) sum(x==y)==length(x) # Because the last is true, the probablity is same as sensitivity # when the prevalence is 0.5. #======================================================================================== # If the prevalence is larger, then, the probability is also larger #======================================================================================== x <- stats::runif(1111,0,1) y <- CoronaVirus_Disease_2019_prevalence(x,0.9,0.9) dark_theme(4) plot(x,y)