Definition and calculation of relative risk US Medical PG Practice Questions and MCQs
Practice US Medical PG questions for Definition and calculation of relative risk. These multiple choice questions (MCQs) cover important concepts and help you prepare for your exams.
Definition and calculation of relative risk US Medical PG Question 1: You have been asked to quantify the relative risk of developing bacterial meningitis following exposure to a patient with active disease. You analyze 200 patients in total, half of which are controls. In the trial arm, 30% of exposed patients ultimately contracted bacterial meningitis. In the unexposed group, only 1% contracted the disease. Which of the following is the relative risk due to disease exposure?
- A. (30 * 99) / (70 * 1)
- B. [30 / (30 + 70)] / [1 / (1 + 99)] (Correct Answer)
- C. [70 / (30 + 70)] / [99 / (1 + 99)]
- D. [[1 / (1 + 99)] / [30 / (30 + 70)]]
- E. (70 * 1) / (30 * 99)
Definition and calculation of relative risk Explanation: ***[30 / (30 + 70)] / [1 / (1 + 99)]***
- This formula correctly calculates the **relative risk (RR)**. The numerator represents the **incidence rate in the exposed group** (30% of 100 exposed patients = 30 cases out of 100), and the denominator represents the **incidence rate in the unexposed group** (1% of 100 unexposed patients = 1 case out of 100).
- Relative risk is the ratio of the **risk of an event** in an **exposed group** to the **risk of an event** in an **unexposed group**.
*[(30 * 99) / (70 * 1)]*
- This formula is for calculating the **odds ratio (OR)**, specifically using a 2x2 table setup where 30 represents exposed cases, 70 represents exposed non-cases, 1 represents unexposed cases, and 99 represents unexposed non-cases.
- The odds ratio is a measure of association between an exposure and an outcome, representing the **odds of an outcome** given exposure compared to the odds of the outcome without exposure.
*[70 / (30 + 70)] / [99 / (1 + 99)]*
- This formula calculates the **relative risk of *not* developing the disease**, which is the inverse of what the question asks for.
- It compares the proportion of exposed individuals who *do not* contract the disease to the proportion of unexposed individuals who *do not* contract the disease.
*[[1 / (1 + 99)] / [30 / (30 + 70)]]*
- This formula calculates the **inverse of the relative risk**, which is not what the question asks for.
- It would represent the ratio of the incidence in the unexposed group to the incidence in the exposed group.
*[(70 * 1) / (30 * 99)]*
- This is an **incorrect variation** of the odds ratio calculation, with the terms in the numerator and denominator swapped compared to the standard formula.
- Therefore, it does not represent the relative risk or a correctly calculated odds ratio.
Definition and calculation of relative risk US Medical PG Question 2: A 25-year-old man with a genetic disorder presents for genetic counseling because he is concerned about the risk that any children he has will have the same disease as himself. Specifically, since childhood he has had difficulty breathing requiring bronchodilators, inhaled corticosteroids, and chest physiotherapy. He has also had diarrhea and malabsorption requiring enzyme replacement therapy. If his wife comes from a population where 1 in 10,000 people are affected by this same disorder, which of the following best represents the likelihood a child would be affected as well?
- A. 0.01%
- B. 2%
- C. 0.5%
- D. 1% (Correct Answer)
- E. 50%
Definition and calculation of relative risk Explanation: ***Correct Option: 1%***
- The patient's symptoms (difficulty breathing requiring bronchodilators, inhaled corticosteroids, and chest physiotherapy; diarrhea and malabsorption requiring enzyme replacement therapy) are classic for **cystic fibrosis (CF)**, an **autosomal recessive disorder**.
- For an autosomal recessive disorder with a prevalence of 1 in 10,000 in the general population, **q² = 1/10,000**, so **q = 1/100 = 0.01**. The carrier frequency **(2pq)** is approximately **2q = 2 × (1/100) = 1/50 = 0.02**.
- The affected man is **homozygous recessive (aa)** and will always pass on the recessive allele. His wife has a **1/50 chance of being a carrier (Aa)**. If she is a carrier, she has a **1/2 chance of passing on the recessive allele**.
- Therefore, the probability of an affected child = **(Probability wife is a carrier) × (Probability wife passes recessive allele) = 1/50 × 1/2 = 1/100 = 1%**.
*Incorrect Option: 0.01%*
- This percentage is too low and does not correctly account for the carrier frequency in the population and the probability of transmission from a carrier mother.
*Incorrect Option: 2%*
- This represents approximately the carrier frequency (1/50 ≈ 2%), but does not account for the additional 1/2 probability that a carrier mother would pass on the recessive allele.
*Incorrect Option: 0.5%*
- This value would be correct if the carrier frequency were 1/100 instead of 1/50, which does not match the given population prevalence.
*Incorrect Option: 50%*
- **50%** would be the risk if both parents were carriers of an autosomal recessive disorder (1/4 chance = 25% for affected, but if we know one parent passes the allele, conditional probability changes). More accurately, 50% would apply if the disorder were **autosomal dominant** with one affected parent, which is not the case here.
Definition and calculation of relative risk US Medical PG Question 3: A medical research study is evaluating an investigational novel drug (medication 1) as compared with standard therapy (medication 2) in patients presenting to the emergency department with myocardial infarction (MI). The study enrolled a total of 3,000 subjects, 1,500 in each study arm. Follow-up was conducted at 45 days post-MI. The following are the results of the trial:
Endpoints Medication 1 Medication 2 P-Value
Primary: death from cardiac causes 134 210 0.03
Secondary: hyperkalemia 57 70 0.4
What is the relative risk of death from a cardiac cause, expressed as a percentage? (Round to the nearest whole number.)
- A. 64% (Correct Answer)
- B. 42%
- C. 72%
- D. 36%
- E. 57%
Definition and calculation of relative risk Explanation: ***64%***
- The **relative risk (RR)** is calculated as the event rate in the exposed group divided by the event rate in the unexposed (control) group.
- For cardiac death, the event rate for Medication 1 is 134/1500 = 0.0893, and for Medication 2 is 210/1500 = 0.14. Therefore, RR = 0.0893 / 0.14 = 0.6378.
- Expressing as a percentage: 0.6378 × 100 = 63.78%, which rounds to **64%**.
- This indicates that Medication 1 has 64% of the risk of cardiac death compared to Medication 2, representing a **36% relative risk reduction**.
*42%*
- This option is incorrect as it does not reflect the accurate calculation of **relative risk** using the provided event rates.
- A calculation error or conceptual misunderstanding of the relative risk formula would lead to this value.
*72%*
- This percentage is higher than the calculated relative risk, suggesting an incorrect application of the formula or a misinterpretation of the event rates.
- It does not represent the ratio of risk between the two medication groups for cardiac death.
*36%*
- This value represents the **relative risk reduction** (100% - 64% = 36%), not the relative risk itself.
- This is a common error where students confuse relative risk with relative risk reduction.
*57%*
- While closer to the correct answer, this value is not the precise result when rounding to the nearest whole number.
- Small calculation discrepancies or rounding at intermediate steps could lead to this slightly different percentage.
Definition and calculation of relative risk US Medical PG Question 4: A recent study examined trends in incidence and fatality of ischemic stroke in a representative sample of Scandinavian towns. The annual incidence of ischemic stroke was calculated to be 60 per 2,000 people. The 1-year case fatality rate for ischemic stroke was found to be 20%. The health department of a town in southern Sweden with a population of 20,000 is interested in knowing the 1-year mortality conferred by ischemic stroke. Based on the study's findings, which of the following estimates the annual mortality rate for ischemic stroke per 20,000?
- A. 600 people
- B. 400 people
- C. 120 people (Correct Answer)
- D. 60 people
- E. 12 people
Definition and calculation of relative risk Explanation: ***120 people***
- The annual incidence of ischemic stroke is 60 per 2,000 people. For a population of 20,000, the annual number of new stroke cases would be (60/2,000) * 20,000 = **600 cases**.
- With a 1-year case fatality rate of 20%, the annual mortality from ischemic stroke is 20% of these 600 cases, which is 0.20 * 600 = **120 people**.
*600 people*
- This number represents the estimated **annual incidence of ischemic stroke** in a town of 20,000 people, not the mortality rate.
- It is calculated as (60/2,000) * 20,000 = 600, before applying the case fatality rate.
*400 people*
- This number is not directly derived from the provided incidence and fatality rates for a population of 20,000.
- It might represent a miscalculation of either incidence or mortality.
*60 people*
- This is the **incidence of ischemic stroke** per 2,000 people, not the mortality rate for a larger population of 20,000.
- It does not account for the total population size or the case fatality rate.
*12 people*
- This would be the mortality if the incidence was extremely low or the case fatality rate was significantly lower than 20% for a population of 20,000.
- It is a significant underestimate based on the given data.
Definition and calculation of relative risk US Medical PG Question 5: A 45-year-old man comes to the clinic concerned about his recent exposure to radon. He heard from his co-worker that radon exposure can cause lung cancer. He brings in a study concerning the risks of radon exposure. In the study, there were 300 patients exposed to radon, and 18 developed lung cancer over a 10-year period. To compare, there were 500 patients without radon exposure and 11 developed lung cancer over the same 10-year period. If we know that 0.05% of the population has been exposed to radon, what is the attributable risk percent for developing lung cancer over a 10 year period after radon exposure?
- A. 3.8%
- B. 0.31%
- C. 2.2%
- D. 6.0%
- E. 63.3% (Correct Answer)
Definition and calculation of relative risk Explanation: ***63.3%***
- The **attributable risk percent (ARP)** quantifies the proportion of disease in the exposed group that is attributable to the exposure. It is calculated as [(Incidence in exposed - Incidence in unexposed) / Incidence in exposed] * 100.
- In this case, **Incidence in exposed (radon)** = 18/300 = 0.06 or 6%. **Incidence in unexposed** = 11/500 = 0.022 or 2.2%. Therefore, ARP = [(0.06 - 0.022) / 0.06] * 100 = (0.038 / 0.06) * 100 = **63.3%**.
*3.8%*
- This value represents the difference in the **absolute risk** or incidence between the exposed and unexposed groups (6% - 2.2% = 3.8%).
- It does not represent the proportion of disease in the exposed group that is due to the exposure.
*0.31%*
- This value is not derived from the given data using standard epidemiological formulas for attributable risk percent.
- It is possibly a miscalculation or an irrelevant measure in this context.
*2.2%*
- This value represents the **incidence of lung cancer in the unexposed group** (11/500 = 0.022 or 2.2%).
- It is a component of the ARP calculation but not the ARP itself.
*6.0%*
- This value represents the **incidence of lung cancer in the radon-exposed group** (18/300 = 0.06 or 6%).
- It is used in the numerator and denominator for calculating the attributable risk percent but is not the final ARP.
Definition and calculation of relative risk US Medical PG Question 6: A researcher is designing an experiment to examine the toxicity of a new chemotherapeutic agent in mice. She splits the mice into 2 groups, one of which she exposes to daily injections of the drug for 1 week. The other group is not exposed to any intervention. Both groups are otherwise raised in the same conditions with the same diet. One month later, she sacrifices the mice to check for dilated cardiomyopathy. In total, 52 mice were exposed to the drug, and 50 were not exposed. Out of the exposed group, 13 were found to have dilated cardiomyopathy on necropsy. In the unexposed group, 1 mouse was found to have dilated cardiomyopathy. Which of the following is the relative risk of developing cardiomyopathy with this drug?
- A. 12.5 (Correct Answer)
- B. 25.0
- C. 13.7
- D. 16.3
- E. 23.0
Definition and calculation of relative risk Explanation: ***Correct Option: 12.5***
- The **relative risk (RR)** is calculated as the **risk in the exposed group divided by the risk in the unexposed group**: RR = [a/(a+b)] / [c/(c+d)]
- **Risk in exposed group** = 13/52 = 0.25 (25%)
- **Risk in unexposed group** = 1/50 = 0.02 (2%)
- **RR = 0.25 / 0.02 = 12.5**
- This indicates that mice exposed to the chemotherapeutic agent are **12.5 times more likely** to develop dilated cardiomyopathy compared to unexposed mice
- An **RR > 1** indicates increased risk with exposure, supporting the drug's cardiotoxicity
*Incorrect Option: 25.0*
- This value results from **miscalculating the unexposed group risk** (e.g., using 0.01 instead of 0.02 as the denominator)
- If the unexposed risk was halved incorrectly: 0.25 / 0.01 = 25.0
- This overestimates the relative risk by a factor of 2
*Incorrect Option: 13.7*
- This value does not result from the correct **relative risk formula**
- May arise from an **arithmetic error** or confusion with other epidemiological measures
- The correct calculation of 13/52 ÷ 1/50 does not yield this result
*Incorrect Option: 16.3*
- This might result from **miscounting the number of subjects** in either group or confusing **relative risk with odds ratio**
- The **odds ratio** would be calculated as (13/39) / (1/49) = 16.3
- Remember: **Relative risk uses total exposed/unexposed as denominators**, while odds ratio uses non-diseased counts
*Incorrect Option: 23.0*
- This value suggests a **fundamental error** in applying the relative risk formula
- Could result from using incorrect numerators or denominators (e.g., 13/1 instead of proper risk calculation)
- Significantly overestimates the true relative risk of 12.5
Definition and calculation of relative risk US Medical PG Question 7: A research group wants to assess the safety and toxicity profile of a new drug. A clinical trial is conducted with 20 volunteers to estimate the maximum tolerated dose and monitor the apparent toxicity of the drug. The study design is best described as which of the following phases of a clinical trial?
- A. Phase 0
- B. Phase III
- C. Phase V
- D. Phase II
- E. Phase I (Correct Answer)
Definition and calculation of relative risk Explanation: ***Phase I***
- **Phase I clinical trials** involve a small group of healthy volunteers (typically 20-100) to primarily assess **drug safety**, determine a safe dosage range, and identify side effects.
- The main goal is to establish the **maximum tolerated dose (MTD)** and evaluate the drug's pharmacokinetic and pharmacodynamic profiles.
*Phase 0*
- **Phase 0 trials** are exploratory studies conducted in a very small number of subjects (10-15) to gather preliminary data on a drug's **pharmacodynamics and pharmacokinetics** in humans.
- They involve microdoses, not intended to have therapeutic effects, and thus cannot determine toxicity or MTD.
*Phase III*
- **Phase III trials** are large-scale studies involving hundreds to thousands of patients to confirm the drug's **efficacy**, monitor side effects, compare it to standard treatments, and collect information that will allow the drug to be used safely.
- These trials are conducted after safety and initial efficacy have been established in earlier phases.
*Phase V*
- "Phase V" is not a standard, recognized phase in the traditional clinical trial classification (Phase 0, I, II, III, IV).
- This term might be used in some non-standard research contexts or for post-marketing studies that go beyond Phase IV surveillance, but it is not a formal phase for initial drug development.
*Phase II*
- **Phase II trials** involve several hundred patients with the condition the drug is intended to treat, focusing on **drug efficacy** and further evaluating safety.
- While safety is still monitored, the primary objective shifts to determining if the drug works for its intended purpose and at what dose.
Definition and calculation of relative risk US Medical PG Question 8: A medical research study is beginning to evaluate the positive predictive value of a novel blood test for non-Hodgkin’s lymphoma. The diagnostic arm contains 700 patients with NHL, of which 400 tested positive for the novel blood test. In the control arm, 700 age-matched control patients are enrolled and 0 are found positive for the novel test. What is the PPV of this test?
- A. 400 / (400 + 0) (Correct Answer)
- B. 700 / (700 + 300)
- C. 400 / (400 + 300)
- D. 700 / (700 + 0)
- E. 700 / (400 + 400)
Definition and calculation of relative risk Explanation: ***400 / (400 + 0) = 1.0 or 100%***
- The **positive predictive value (PPV)** is calculated as **True Positives / (True Positives + False Positives)**.
- In this scenario, **True Positives (TP)** are the 400 patients with NHL who tested positive, and **False Positives (FP)** are 0, as no control patients tested positive.
- This gives a PPV of 400/400 = **1.0 or 100%**, indicating that all patients who tested positive actually had the disease.
*700 / (700 + 300)*
- This calculation does not align with the formula for PPV based on the given data.
- The denominator `(700+300)` suggests an incorrect combination of various patient groups.
*400 / (400 + 300)*
- The denominator `(400+300)` incorrectly includes 300, which is the number of **False Negatives** (patients with NHL who tested negative), not False Positives.
- PPV focuses on the proportion of true positives among all positive tests, not all diseased individuals.
*700 / (700 + 0)*
- This calculation incorrectly uses the total number of patients with NHL (700) as the numerator, rather than the number of positive test results in that group.
- The numerator should be the **True Positives** (400), not the total number of diseased individuals.
*700 / (400 + 400)*
- This calculation uses incorrect values for both the numerator and denominator, not corresponding to the PPV formula.
- The numerator 700 represents the total number of patients with the disease, not those who tested positive, and the denominator incorrectly sums up values that don't represent the proper PPV calculation.
Definition and calculation of relative risk US Medical PG Question 9: A randomized controlled trial was initiated to evaluate a novel DPP-4 inhibitor for blood glucose management in diabetic patients. The study used a commonly prescribed sulfonylurea as the standard of care treatment. 2,000 patients were enrolled in the study with 1,000 patients in each arm. One of the primary outcomes was the development of diabetic nephropathy during treatment. This outcome occurred in 68 patients on the DPP-4 inhibitor and 134 patients on the sulfonylurea. What is the relative risk reduction (RRR) for patients using the DPP-4 inhibitor compared with the sulfonylurea?
- A. 23%
- B. 49% (Correct Answer)
- C. 33%
- D. 59%
- E. 43%
Definition and calculation of relative risk Explanation: ***49%***
- To calculate **relative risk reduction (RRR)**, first determine the **event rate (ER)** for each group.
- ER (DPP-4 inhibitor) = 68/1000 = 0.068. ER (Sulfonylurea) = 134/1000 = 0.134.
- Next, calculate the **absolute risk reduction (ARR)**: ARR = ER (Sulfonylurea) - ER (DPP-4 inhibitor) = 0.134 - 0.068 = 0.066.
- Finally, calculate RRR: RRR = ARR / ER (Sulfonylurea) = 0.066 / 0.134 ≈ 0.4925 or **49%**.
*23%*
- This value is incorrect and does not result from the proper application of the **relative risk reduction (RRR)** formula.
- A common mistake is to reverse the subtrahend and minuend in the numerator or denominator.
*33%*
- This value is incorrect and does not result from the proper application of the **relative risk reduction (RRR)** formula.
- Incorrect calculations in either the numerator or denominator of the **RRR formula** would lead to this incorrect result.
*59%*
- This value is incorrect and is likely the result of an error in calculating either the **absolute risk reduction (ARR)** or dividing it by the wrong **event rate**.
- Always ensure the correct event rates are used for the control group and the intervention group.
*43%*
- This value is incorrect and does not align with the correct calculation of **relative risk reduction (RRR)**.
- Errors in setting up the formula or executing the division could lead to this result.
Definition and calculation of relative risk US Medical PG Question 10: A 42-year-old woman presents to the physician because of an abnormal breast biopsy report following suspicious findings on breast imaging. Other than being concerned about her report, she feels well. She has no history of any serious illnesses and takes no medications. She does not smoke. She consumes wine 1–2 times per week with dinner. There is no significant family history of breast or ovarian cancer. Vital signs are within normal limits. Physical examination shows no abnormal findings. The biopsy shows lobular carcinoma in situ (LCIS) in the left breast. Which of the following is the most appropriate next step in management?
- A. Careful observation + routine mammography (Correct Answer)
- B. Left mastectomy + axillary dissection + local irradiation
- C. Lumpectomy + routine screening
- D. Lumpectomy + breast irradiation
- E. Breast irradiation + tamoxifen
Definition and calculation of relative risk Explanation: ***Careful observation + routine mammography***
- **Lobular carcinoma in situ (LCIS)** is considered a **non-obligate precursor** to invasive carcinoma, meaning it indicates an increased risk for developing invasive breast cancer in either breast (approximately 1-2% per year), but it is not itself invasive.
- Management typically involves **careful surveillance** with routine clinical exams and **mammography**, as this is the most appropriate initial approach for classic LCIS.
- Surgical excision is often unnecessary due to LCIS's diffuse nature and the fact that it serves as a risk marker rather than a direct precancerous lesion requiring removal.
*Left mastectomy + axillary dissection + local irradiation*
- This aggressive approach is reserved for **invasive breast cancer** and would be excessive for LCIS, which is a non-invasive lesion and a marker of increased risk rather than an immediate threat.
- **Axillary dissection** is performed to stage nodal involvement in invasive cancer, which is not applicable here as LCIS does not metastasize.
*Lumpectomy + routine screening*
- While a **lumpectomy (excision)** may be considered for **pleomorphic LCIS** or when there is diagnostic uncertainty, it is not the standard initial management for classic LCIS.
- Classic LCIS is often multifocal and bilateral, making localized excision less effective as a risk-reduction strategy.
*Lumpectomy + breast irradiation*
- **Radiation therapy** is typically used to reduce local recurrence risk after **lumpectomy for invasive breast cancer** or **ductal carcinoma in situ (DCIS)**.
- For LCIS, irradiation is generally not recommended as it is non-invasive and does not benefit from local radiation treatment.
*Breast irradiation + tamoxifen*
- **Tamoxifen** is a selective estrogen receptor modulator (SERM) that can be **offered for risk reduction** in women with LCIS, potentially reducing the risk of invasive breast cancer by approximately 50%.
- However, tamoxifen is typically discussed as an **additional preventive option** after initial diagnosis and counseling, not as the immediate next step.
- **Breast irradiation** is not indicated for LCIS, as it is non-invasive and does not require local radiation treatment, making this combination inappropriate.
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