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A physical examination was used to screen for breast cancer in 2,500 women with biopsy-proven adenocarcinoma of the breast and in 5,000 age- and race-matched control women. The results of the physical examination were positive (i.e., a mass was palpated) in 1,800 cases and in 800 control women, all of whom showed no evidence of cancer at biopsy.The sensitivity of the physical examination was: ______

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VericaVujicic

Answer:

72%

Explanation:

There are two main caracteristics of the test: sensitivity and specificity.

Sensitivity (Sn) is ability of the test to correctly count those with the disease. Specificity (Sp) is ability of the test to correctly identify those without the disease.

To calculate Sn and Sp, there has to be true information on number of diseased and desease-free patients which in this case, we do have according to biopsy results.

2500 patients has carcinoma

5000 patients are disease-free individuals

According to the physical examination, there are 1800 patients with carcinoma (among 2500 with biopsy-established carcinoma, these are true positive) and 800 patients with carcinoma among those 5000 which do not have a disease, according to biopsy results (these are false positive). True negative will be the rest of the disease-free patients (5000-800) and false negative are remaining patients out of 2500 certainly positive (2500-1800).

A table can be made:

                 Disease

                 +         -

Test  +    TP       FP  

          -    FN       TN

TP - true positive

FP - false positive

FN - false negative

TN - true negative

Sn and Sp are calculated:

Sn= [tex]\frac{TP}{TP+FN}[/tex]      Sp=[tex]\frac{TN}{TN+FP}[/tex]

In this case we have:

                                          Carcinoma

                                             +            -

Physical examination  +    1800     800  

                                      -    700       4200

Sn=[tex]\frac{1800}{1800+700}=0,72=72%[/tex]%

Sp=[tex]\frac{4200}{4200+800}=0,84=84%[/tex]%

Cancer is a condition in which unusual cells multiplies rapidly and uncontrollably that damages body tissues and organs.

  • Cancer can be estimated by the test having specificity and sensitivity.

  • Sensitivity (Sn) is a characteristic of a test to determine the number of patients having the illness.

  • Specificity (Sp) is a true negative measure that tells about the patient that does not have the illness.

To determine sensitivity and specificity there should be correct information on the number of patients having disease and patients without the disease.

  • Number of patients having carcinoma: 2500

  • The number of disease-free patients is: 5000

According to the examination, 1800 carcinoma patients are true positive. 800 patients among the 5000 are false positive.

  • True negative will be the disease-free patients: 5000-800= 4200

  • The remaining patients are the false negative: 2500-1800=700

The above data can be shown as:

                                  Disease

                                    +           -

                 Test +        TP       FP

                          -        FN      TN

(Where, TP: true positive, FP: false positive, FN: false negative and TN: true negative)

To calculate Sn and Sp the formula used is:

       [tex]Sn=\dfrac{TP}{TP+FN}[/tex]                      [tex]Sp= \dfrac{TN}{TN+FP}[/tex]

In the above case,

                                            Carcinoma

                                             +            -

Physical examination  +    1800       800  

                                      -     700        4200

So according to the formula and the data Sn and Sp can be calculated as:

[tex]Sn= \dfrac{1800}{1800+700} = 0.72[/tex]      = 72%

[tex]Sp= \dfrac{4200}{4200+800} = 0.84[/tex]       = 84%

Therefore, the sensitivity is 72% and specificity is 84%.

To learn more about sensitivity and specificity follow the given link:

https://brainly.com/question/14785231

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