PA 503 Week 5 Test Characteristics Problem Set Example

Course	PA 503 Essential Foundations in Clinical Medicine
Week	5
Paper type	Test characteristics problem set
Length	About 800 words, 5 pages
Format	APA 7 student paper
School	Chamberlain University
Program	Master of Physician Assistant Studies (MPAS)
Updated	October 2026

Free sample paper for PA 503 Week 5

Test Characteristics Problem Set: A Chest Radiograph for Lung Cancer in a Former Smoker With Hemoptysis, Worked at Two Pretest Probabilities

Student Name

Chamberlain University

PA 503: Essential Foundations in Clinical Medicine

Instructor Name

Month Day, Year

What this page is doingThe title names the test, the target condition and the two probabilities, so the reader knows the answer will depend on the patient as well as the test.

Test Characteristics Problem Set: A Chest Radiograph for Lung Cancer in a Former Smoker With Hemoptysis, Worked at Two Pretest Probabilities

The Data and Their Sources

Sensitivity: a systematic review of chest radiography for lung cancer in people presenting with symptoms found that the highest-quality primary care studies reported sensitivities of 76.8% and 79.3% (Bradley et al., 2019). This problem set uses 77%.

Specificity: the review did not report a pooled specificity. For this exercise, specificity is set at 90% as a stated teaching assumption, not a measured value.

Pretest probability: a large primary care cohort found that 7.5% of men overall, and 17.1% of men aged 75 to 84, were diagnosed with a respiratory tract cancer within three years of first reporting hemoptysis (Jones et al., 2007). These are used as the two pretest probabilities.

What this page is doingNaming the source of each input, and labeling the specificity as an assumption, keeps the calculation honest about which numbers are measured.

The Two by Two at a Pretest Probability of 7.5%

For 1,000 men like the patient:

Table 1

Chest Radiograph Results at a Pretest Probability of 7.5%

	Cancer present	Cancer absent	Total
Radiograph abnormal	58	93	151
Radiograph normal	17	832	849
Total	75	925	1,000

Note. Note. Built from a sensitivity of 77% (Bradley et al., 2019), an assumed specificity of 90% and a pretest probability of 7.5% (Jones et al., 2007).

Working. Cancer present: 7.5% of 1,000 is 75. True positives: 77% of 75 is 57.75, rounded to 58; false negatives: 75 less 58 is 17. Cancer absent: 925. True negatives: 90% of 925 is 832.5, rounded to 832; false positives: 925 less 832 is 93.

1. Sensitivity, from the table: 58 of 75, or 77.3%.

2. Specificity: 832 of 925, or 89.9%.

3. Positive predictive value: 58 of 151, or 38.4%.

4. Negative predictive value: 832 of 849, or 98.0%.

5. Probability of cancer after a normal radiograph: 17 of 849, or 2.0%.

6. Positive likelihood ratio: sensitivity divided by one less specificity, 0.77 divided by 0.10, or 7.7. Negative likelihood ratio: one less sensitivity divided by specificity, 0.23 divided by 0.90, or 0.26.

The Second Prevalence: 17.1%

For 1,000 men aged 75 to 84 with a first episode of hemoptysis:

Table 2

Chest Radiograph Results at a Pretest Probability of 17.1%

	Cancer present	Cancer absent	Total
Radiograph abnormal	132	83	215
Radiograph normal	39	746	785
Total	171	829	1,000

Note. Note. Same sensitivity and specificity as Table 1, with the higher pretest probability.

7. Positive predictive value: 132 of 215, or 61.4%.

8. Negative predictive value: 746 of 785, or 95.0%.

9. Probability of cancer after a normal radiograph: 39 of 785, or 5.0%.

Test Alone, Test Plus Population

The sensitivity, specificity and likelihood ratios describe the test and stay the same in both tables. The predictive values describe the test in a population and change with pretest probability. A normal radiograph lowers the probability of cancer from 7.5% to 2.0% in the first population, and from 17.1% to 5.0% in the second. In neither case does it reach zero.

What this page is doingSeparating properties of the test from properties of the test in a population is the distinction the problem set is built to check.

Saying What It Means

For the 58-year-old former heavy smoker, a normal chest radiograph would leave a probability of lung cancer around 2%, using the overall figure for men, and probably higher, since heavy smoking raises the patient's risk above the average man with hemoptysis. One case in 50 is not low enough to stop, especially when missing an early cancer has serious consequences. This is why further evaluation with computed tomography is recommended for patients with hemoptysis and risk factors for malignancy despite normal radiographic findings (Earwood & Thompson, 2015). An abnormal radiograph would raise the probability to about 38%, which calls for prompt imaging and referral rather than a diagnosis.

Limits of This Set

The specificity is assumed, so the predictive values and likelihood ratios would change with a measured value. The sensitivity comes from a small number of studies, most at high risk of bias (Bradley et al., 2019). And the pretest probabilities come from a United Kingdom cohort in which smoking history was not used to adjust the figures, so they likely understate the risk for a heavy smoker such as this patient.

A Check on the Rounding

Rounding the cells to whole people changes the derived figures slightly: sensitivity from the table is 77.3% rather than 77.0%, and specificity 89.9% rather than 90.0%. These differences do not change any interpretation, but they are reported so that a reader recomputing from the table gets the same answers as the text. Any reader who prefers to keep fractional people in the cells will find the predictive values change only in the first decimal place.

What this page is doingReporting the effect of rounding lets a reader recompute every figure from the tables and get the same answers.

References

Bradley, S. H., Abraham, S., Callister, M. E., Grice, A., Hamilton, W. T., Lopez, R. R., Shinkins, B., & Neal, R. D. (2019). Sensitivity of chest X-ray for detecting lung cancer in people presenting with symptoms: A systematic review. British Journal of General Practice, 69(689), e827-e835. https://doi.org/10.3399/bjgp19X706853

Earwood, J. S., & Thompson, T. D. (2015). Hemoptysis: Evaluation and management. American Family Physician, 91(4), 243-249.

Jones, R., Latinovic, R., Charlton, J., & Gulliford, M. C. (2007). Alarm symptoms in early diagnosis of cancer in primary care: Cohort study using General Practice Research Database. BMJ, 334(7602), 1040. https://doi.org/10.1136/bmj.39171.637106.AE

PA 503 Week 5 instructions, in plain terms

In the fifth week you work a test characteristics problem set. Set up a two-by-two table with the true and false results in the correct cells and totals in the margins, since most later figures come from it. Calculate sensitivity, specificity, predictive values and likelihood ratios, showing each step. Then repeat the predictive values at a second prevalence to show how they change while sensitivity and specificity do not. Separate characteristics of the test from what the test means for a particular patient. Name the source of each input, and label any assumed value. Finish by explaining in plain words what a result would mean for the patient in the case.

How this PA 503 Week 5 example is built

The problem set takes sensitivity of 77% from a systematic review of chest radiography in symptomatic patients, assumes a specificity of 90% for teaching and uses primary care cohort figures of 7.5% and 17.1% as pretest probabilities. The first table gives 58 true positives, 17 false negatives, 93 false positives and 832 true negatives per 1,000. Answers show a positive predictive value of 38.4%, a negative predictive value of 98.0%, likelihood ratios of 7.7 and 0.26, and a post-test probability of 2.0% after a normal film. The second table raises those to 61.4%, 95.0% and 5.0%. Interpretation explains why computed tomography still follows a normal film.

Reading the PA 503 Week 5 grading rubric

Rows and columns swapped at the outset is the expensive error, because everything after it computes cleanly and is wrong, and a marker who spots it stops reading. Reporting a characteristic of the test as though it answered the patient's question loses heavily too, such as treating sensitivity as the chance of cancer after a positive film. Missing working, unlabeled assumptions, a single prevalence and no plain interpretation also cost points. Strong sets build the table correctly, show each calculation, repeat at a second prevalence, separate test properties from predictive values, name sources and explain what the result means for the patient. A brief note on rounding effects shows care that markers notice.

PA 503 Week 5 help: mistakes that cost points

Test characteristics problems are mostly arithmetic, but the setup and interpretation decide the grade. If you share the problem your instructor assigned, we can help you set up the two-by-two table correctly, show each step and repeat the calculation at a second prevalence. Plain-language interpretation of each figure, the part most often skipped, is something we can write with you. The calculations stay yours. If your problem supplies likelihood ratios rather than sensitivity and specificity, we can help you work from those to post-test probabilities using odds, with each step shown. We can also show how the predictive values shift if the assumed specificity is changed, so you can see how much the answer depends on it.

Get a PA-503 Week 5 example written to your instructions

Send the item list from your problem set, any figures it supplies and the rounding convention your section publishes, and a custom example comes back worked to them within 24 to 48 hours, the first one free. Where a real test is named, include it, and the calculations are built on its published characteristics rather than on a stand-in.

More PA 503 papers and MPAS samples

PA 503 Week 5 questions, answered

Do we need likelihood ratios?

Some sections require them and others treat them as an extension. Where they appear they tend to replace predictive value as the interpretation tool, because they belong to the test alone and can be applied to any starting probability. Send the item list from your own set and the example computes exactly what is asked, in the order it is asked.

How much rounding is acceptable?

Declare it once and hold it. Two decimal places for proportions and whole percents for the interpretation is common and rarely queried. What costs marks is drifting between items, which makes the two prevalences look further apart or closer together than the arithmetic actually says. If your section states a convention, that one wins.

What if no figures are supplied at all?

Then the example runs realistic invented figures through the same working, with each number labeled as constructed so nothing reads as a published statistic. None of the method changes. If your assignment names a real test or a documented characteristic, send it and the calculations are built on that value instead.

Where can I find a free PA 503 Week 5 sample paper?

This page holds a complete PA 503 Week 5 problem set on chest radiography for lung cancer at two pretest probabilities.

What risk remains after a normal film in the PA 503 Week 5 sample?

About 2.0% at a pretest probability of 7.5%, and 5.0% at 17.1%, which is why further imaging follows in high-risk patients.