Question

A recent nationwide study investigated the value of the prostate-specific antigen (PSA) blood test for the detection of prostate cancer among 100,000 men 50 years of age and older. Of the 686 men who tested positive on the PSA test, a total of 281 were ultimately diagnosed with prostate cancer, either by immediate needle biopsy or during 12 months of watchful waiting. An additional 45 men who tested negative on the PSA test were ultimately diagnosed with prostate cancer during 12 months of follow-up.1) Set up the 2X2 contingency table for the data.
2) What is the sensitivity of the PSA test? Interpret the result.3) What is the specificity of the PSA test? Interpret the result.4) What is the positive predictive value (PPV) of the PSA test? Interpret the result.5) What is the negative predictive value (NPV) of the PSA test? Interpret the result.6)A screening test is available to identify individuals with a genetic mutation that puts them at greater risk for stroke. The test is extremely expensive and is not covered by most insurance plans, so those choosing to have the test usually have to pay for it out-of-pocket. However, it has been determined that the screening test is very valuable because the annual incidence of stroke among those who have been screened is nearly half that of the general population.7) One major benefit of mammography screening for breast cancer is that the disease is often diagnosed in the presymptomatic phase of the disease, before it is detectable by any other means, and breast cancers diagnosed in such early stages respond better to treatment. Another benefit of screening is that women diagnosed with breast cancer by way of mammography have better survival rates than women diagnosed by other means.8) The prognosis for neuroblastoma, a tumor that occurs in young children, varies greatly by patient. Some tumors are slow-growing and may even heal spontaneously. Others tumors are fast-growing and aggressive. A urine screening test for neuroblastoma is currently available that detects metabolites produced by the tumor. It has been suggested that such screening is highly valuable PH20001 Essentials of Epidemiology 2 because the case-fatality rate of neuroblastoma among children diagnosed with the urine test is much lower than it is for those who were not screened.9) Suppose that a new screening test has recently been developed to aid in the early identification of individuals with rheumatoid arthritis. However, the value of the test has not yet been established. In an effort to test the effectiveness of the new test in predicting a future diagnosis of rheumatoid arthritis, investigators enroll a group of volunteer participants, record their test result, and follow them forward for the development of the condition. It is subsequently determined that the new screening test is highly effective in predicting a definitive diagnosis of rheumatoid arthritis because the incidence of the condition among those who screened positive was much higher than that of the general population.10) There are at least a dozen types of human papillomaviruses (HPV) that are considered high-risk and cause approximately 5% of all cancers world-wide. However, high-risk HPV infections are common and most occur without any symptoms and resolve on their own within 1-2 years. In 2003, cervical HPV screening tests became available and are now approved for use in combination with a Pap test among women over the age of 30. Such tests can detect infection of several high-risk HPV types before cell changes become evident. Some argue that HPV screening tests should be approved for universal use among women of all ages because the incidence of high-risk HPV infections has increased dramatically over the past decade.

Answer 1

Answer:

Step-by-step explanation:

Remember:

Any medical test used to detect certain sicknesses have several probabilities associated with their results.

Positive (test is +) ⇒ P(+)

True positive (test is + and the patient is sick) ⇒ P(+ ∩ S)

False-positive (test is + but the patient is healthy) ⇒P(+ ∩ H)

Negative (test is -) ⇒ P(-)

True negative (test is - and the patient is healthy) ⇒ P(- ∩ H)

False-negative (test is - but the patient is sick) ⇒ P(- ∩ S)

You can arrange them in a contingency table as:

Probabilities  Positive ; Negative

           Sick     + ∩ S    ;    - ∩ S        S          

      Healthy    + ∩ H    ;   - ∩ H        H

                            +              -            1

The sensibility of the test is defined as the capacity of the test to detect the sickness in sick patients (true positive rate).

⇒ P(+/S) = P(+ ∩ S)

                    P(S)

The specificity of the test is the capacity of the test to have a negative result when the patients are truly healthy (true negative rate)

⇒ P(-/H) = P(- ∩ H)

                    P(H)

1) You are studying the value of the prostate-specific antigen (PSA) blood test for the detection of prostate cancer on men of 50 years of age and older.

Total 100000 men

686 men tested positive

281 of the men that tested positive had cancer

45 men that tested negative had cancer

Total - positive cases: 100000 - 686 = 99314 tested negative

              ;  Positive   ;   Negative   ;   Total

Sick        ;     281       ;      45           ;    326

Healthy  ;     405      ;    99269      ;   99674

Total       ;    686       ;    99314       ;  100000  

2)

Sensitivity of the test is

P(+/S) = P(+ ∩ S) =  0.00281 = 0.86

                P(S)        0.00326

Where:

P(+ ∩ S) = 281/100000 = 0.00281

P(S) = 326/100000 = 0.00326

The test has an 86% probability of detecting PSA in sick patients.

3)

Specificity of the test is

P(-/H) = P(- ∩ H) = 0.99269 = 0.995

                P(H)       0.99674

Where:

P(- ∩ H)= 99269/100000= 0.99269

P(H)= 99674/100000= 0.99674

The test has a 99.5% probability of not detecting PSA in healthy patients.

4)

Positive predictive value (PPV)

It's defined as the probability of being sick when the test is positive:

P(S/+)= P(S ∩ +) = 0.00281 = 0.04

                P(+)       0.0686

Where

P(+)= 686/100000= 0.0686

There is a 4% probability of having cancer if the test is positive.

5)

Negative predictive value (NPV)

P(H/-)= P(H ∩ -) = 0.99269 = 0.999

               P(-)        0.99314

Where:

P(-)= 99314/100000= 0.99314

There is a 99.9% probability of being healthy if the test is negative.

6 to 10 are all examples of medical tests.

I hope this helps!