Definition and calculation of odds ratio US Medical PG Practice Questions and MCQs
Practice US Medical PG questions for Definition and calculation of odds ratio. These multiple choice questions (MCQs) cover important concepts and help you prepare for your exams.
Definition and calculation of odds ratio 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 odds ratio 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 odds ratio US Medical PG Question 2: Group of 100 medical students took an end of the year exam. The mean score on the exam was 70%, with a standard deviation of 25%. The professor states that a student's score must be within the 95% confidence interval of the mean to pass the exam. Which of the following is the minimum score a student can have to pass the exam?
- A. 45%
- B. 63.75%
- C. 67.5%
- D. 20%
- E. 65% (Correct Answer)
Definition and calculation of odds ratio Explanation: ***65%***
- To find the **95% confidence interval (CI) of the mean**, we use the formula: Mean ± (Z-score × Standard Error). For a 95% CI, the Z-score is approximately **1.96**.
- The **Standard Error (SE)** is calculated as SD/√n, where n is the sample size (100 students). So, SE = 25%/√100 = 25%/10 = **2.5%**.
- The 95% CI is 70% ± (1.96 × 2.5%) = 70% ± 4.9%. The lower bound is 70% - 4.9% = **65.1%**, which rounds to **65%** as the minimum passing score.
*45%*
- This value is significantly lower than the calculated lower bound of the 95% confidence interval (approximately 65.1%).
- It would represent a score far outside the defined passing range.
*63.75%*
- This value falls below the calculated lower bound of the 95% confidence interval (approximately 65.1%).
- While close, this score would not meet the professor's criterion for passing.
*67.5%*
- This value is within the 95% confidence interval (65.1% to 74.9%) but is **not the minimum score**.
- Lower scores within the interval would still qualify as passing.
*20%*
- This score is extremely low and falls significantly outside the 95% confidence interval for a mean of 70%.
- It would indicate performance far below the defined passing threshold.
Definition and calculation of odds ratio 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 odds ratio 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 odds ratio US Medical PG Question 4: A researcher is trying to determine whether a newly discovered substance X can be useful in promoting wound healing after surgery. She conducts this study by enrolling the next 100 patients that will be undergoing this surgery and separating them into 2 groups. She decides which patient will be in which group by using a random number generator. Subsequently, she prepares 1 set of syringes with the novel substance X and 1 set of syringes with a saline control. Both of these sets of syringes are unlabeled and the substances inside cannot be distinguished. She gives the surgeon performing the surgery 1 of the syringes and does not inform him nor the patient which syringe was used. After the study is complete, she analyzes all the data that was collected and performs statistical analysis. This study most likely provides which level of evidence for use of substance X?
- A. Level 3
- B. Level 1 (Correct Answer)
- C. Level 4
- D. Level 5
- E. Level 2
Definition and calculation of odds ratio Explanation: ***Level 1***
- The study design described is a **randomized controlled trial (RCT)**, which is considered the **highest level of evidence (Level 1)** in the hierarchy of medical evidence.
- Key features like **randomization**, **control group**, and **blinding (double-blind)** help minimize bias and strengthen the validity of the findings.
*Level 2*
- Level 2 evidence typically comprises **well-designed controlled trials without randomization** (non-randomized controlled trials) or **high-quality cohort studies**.
- While strong, they do not possess the same level of internal validity as randomized controlled trials.
*Level 3*
- Level 3 evidence typically includes **case-control studies** or **cohort studies**, which are observational designs and carry a higher risk of bias compared to RCTs.
- These studies generally do not involve randomization or intervention assignment by the researchers.
*Level 4*
- Level 4 evidence is usually derived from **case series** or **poor quality cohort and case-control studies**.
- These studies provide descriptive information or investigate associations without strong control for confounding factors.
*Level 5*
- Level 5 evidence is the **lowest level of evidence**, consisting of **expert opinion** or **animal research/bench research**.
- This level lacks human clinical data or systematic investigative rigor needed for higher evidence levels.
Definition and calculation of odds ratio US Medical PG Question 5: You are reading through a recent article that reports significant decreases in all-cause mortality for patients with malignant melanoma following treatment with a novel biological infusion. Which of the following choices refers to the probability that a study will find a statistically significant difference when one truly does exist?
- A. Type II error
- B. Type I error
- C. Confidence interval
- D. p-value
- E. Power (Correct Answer)
Definition and calculation of odds ratio Explanation: ***Power***
- **Power** is the probability that a study will correctly reject the null hypothesis when it is, in fact, false (i.e., will find a statistically significant difference when one truly exists).
- A study with high power minimizes the risk of a **Type II error** (failing to detect a real effect).
*Type II error*
- A **Type II error** (or **beta error**) occurs when a study fails to reject a false null hypothesis, meaning it concludes there is no significant difference when one actually exists.
- This is the **opposite** of what the question describes, which asks for the probability of *finding* a difference.
*Type I error*
- A **Type I error** (or **alpha error**) occurs when a study incorrectly rejects a true null hypothesis, concluding there is a significant difference when one does not actually exist.
- This relates to the **p-value** and the level of statistical significance (e.g., p < 0.05).
*Confidence interval*
- A **confidence interval** provides a range of values within which the true population parameter is likely to lie with a certain degree of confidence (e.g., 95%).
- It does not directly represent the probability of finding a statistically significant difference when one truly exists.
*p-value*
- The **p-value** is the probability of observing data as extreme as, or more extreme than, that obtained in the study, assuming the null hypothesis is true.
- It is used to determine statistical significance, but it is not the probability of detecting a true effect.
Definition and calculation of odds ratio US Medical PG Question 6: A physician attempts to study cirrhosis in his state. Using a registry of admitted patients over the last 10 years at the local hospital, he isolates all patients who have been diagnosed with cirrhosis. Subsequently, he contacts this group of patients, asking them to complete a survey assessing their prior exposure to alcohol use, intravenous drug abuse, blood transfusions, personal history of cancer, and other medical comorbidities. An identical survey is given to an equal number of patients in the registry who do not carry a prior diagnosis of cirrhosis. Which of the following is the study design utilized by this physician?
- A. Randomized controlled trial
- B. Case-control study (Correct Answer)
- C. Cross-sectional study
- D. Cohort study
- E. Meta-analysis
Definition and calculation of odds ratio Explanation: ***Case-control study***
- This study design **identifies subjects based on their outcome (cases with cirrhosis, controls without cirrhosis)** and then retrospectively investigates their past exposures.
- The physician selected patients with cirrhosis (cases) and patients without cirrhosis (controls), then assessed their prior exposures to risk factors like alcohol use and intravenous drug abuse.
*Randomized controlled trial*
- This design involves randomly assigning participants to an **intervention group** or a **control group** to assess the effect of an intervention.
- There is no intervention being tested or randomization occurring in this study; it is observational.
*Cross-sectional study*
- A cross-sectional study measures the **prevalence of disease and exposure at a single point in time** in a defined population.
- This study collects retrospective exposure data and compares two distinct groups (cases and controls), rather than assessing prevalence at one time point.
*Cohort study*
- A cohort study **follows a group of individuals over time** to see if their exposure to a risk factor is associated with the development of a disease.
- This study starts with the outcome (cirrhosis) and looks backward at exposures, which is the opposite direction of a cohort study.
*Meta-analysis*
- A meta-analysis is a statistical method that **combines the results of multiple independent studies** to produce a single, more powerful estimate of treatment effect or association.
- This is an original research study collecting new data, not a systematic review or synthesis of existing studies.
Definition and calculation of odds ratio US Medical PG Question 7: 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 odds ratio 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 odds ratio US Medical PG Question 8: You submit a paper to a prestigious journal about the effects of coffee consumption on mesothelioma risk. The first reviewer lauds your clinical and scientific acumen, but expresses concern that your study does not have adequate statistical power. Statistical power refers to which of the following?
- A. The probability of detecting an association when no association exists.
- B. The probability of not detecting an association when an association does exist.
- C. The probability of detecting an association when an association does exist. (Correct Answer)
- D. The first derivative of work.
- E. The square root of the variance.
Definition and calculation of odds ratio Explanation: ***The probability of detecting an association when an association does exist.***
- **Statistical power** is defined as the probability that a study will correctly reject a false null hypothesis, meaning it will detect a true effect or association if one exists.
- A study with **adequate statistical power** is less likely to miss a real effect.
*The probability of detecting an association when no association exists.*
- This describes a **Type I error** or **false positive**, often represented by **alpha (α)**.
- It is the probability of incorrectly concluding an effect or association exists when, in reality, there is none.
*The probability of not detecting an association when an association does exist.*
- This refers to a **Type II error** or **false negative**, represented by **beta (β)**.
- **Statistical power** is calculated as **1 - β**, so this option describes the complement of power.
*The first derivative of work.*
- The first derivative of work with respect to time represents **power** in physics, which is the rate at which work is done.
- This option is a **distractor** from physics and is unrelated to statistical power in research.
*The square root of the variance.*
- The **square root of the variance** is the **standard deviation**, a measure of the dispersion or spread of data.
- This is a statistical concept but is not the definition of statistical power.
Definition and calculation of odds ratio US Medical PG Question 9: A survey was conducted in a US midwestern town in an effort to assess maternal mortality over the past year. The data from the survey are given in the table below:
Women of childbearing age 250,000
Maternal deaths 2,500
Number of live births 100, 000
Number of deaths of women of childbearing age 7,500
Maternal death is defined as the death of a woman while pregnant or within 42 days of termination of pregnancy from any cause related to or aggravated by, the pregnancy. Which of the following is the maternal mortality rate in this midwestern town?
- A. 1,000 per 100,000 live births
- B. 33 per 100,000 live births
- C. 3,000 per 100,000 live births
- D. 33,300 per 100,000 live births
- E. 2,500 per 100,000 live births (Correct Answer)
Definition and calculation of odds ratio Explanation: ***2,500 per 100,000 live births***
- The maternal mortality rate is calculated as the number of **maternal deaths** per 100,000 **live births**. The given data directly provide these values.
- Calculation: (2,500 maternal deaths / 100,000 live births) × 100,000 = **2,500 per 100,000 live births**.
*1,000 per 100,000 live births*
- This value is incorrect as it does not align with the provided numbers for maternal deaths and live births in the calculation.
- It might result from a miscalculation or using incorrect numerator/denominator values from the dataset.
*33 per 100,000 live births*
- This value is significantly lower than the correct rate and suggests a substantial error in calculation or an incorrect understanding of how the maternal mortality rate is derived.
- It could potentially result from dividing the number of live births by maternal deaths, which is the inverse of the correct formula.
*3,000 per 100,000 live births*
- This option is close to the correct answer but slightly higher, indicating a possible calculation error, for instance, including non-maternal deaths or other causes of deaths in the numerator.
- The definition of maternal death is specific to pregnancy-related or aggravated causes, so extraneous deaths would inflate the rate.
*33,300 per 100,000 live births*
- This figure results from incorrectly calculating the proportion of maternal deaths among all deaths of women of childbearing age: (2,500 / 7,500) × 100,000 = 33,333.
- This is a conceptual error as the maternal mortality rate should use live births as the denominator, not total deaths of women of childbearing age.
Definition and calculation of odds ratio US Medical PG Question 10: In 2013 the national mean score on the USMLE Step 1 exam was 227 with a standard deviation of 22. Assuming that the scores for 15,000 people follow a normal distribution, approximately how many students scored above the mean but below 250?
- A. 5,100 (Correct Answer)
- B. 4,500
- C. 6,000
- D. 3,750
- E. 6,750
Definition and calculation of odds ratio Explanation: ***5,100***
- To solve this, first calculate the **z-score** for 250: (250 - 227) / 22 = 1.045.
- Using a **z-table**, the area under the curve from the mean (z=0) to z=1.045 is approximately 0.353. Multiplying this by 15,000 students gives approximately **5,295 students**, which is closest to 5,100.
*4,500*
- This answer would imply a smaller proportion of students between the mean and 250 (around 30%), which is lower than the calculated z-score of 1.045 suggests.
- It does not accurately reflect the area under the **normal distribution curve** for the given range.
*6,000*
- This option would mean that approximately 40% of students scored in this range, which would correspond to a z-score much higher than 1.045 or a different standard deviation.
- This calculation overestimates the number of students within the specified range.
*3,750*
- This value represents 25% of the total students (15,000 * 0.25), indicating that only a quarter of the distribution lies in this range.
- This significantly underestimates the proportion of students scoring between the mean and 250 for the given standard deviation.
*6,750*
- This option reflects approximately 45% of the total student population (15,000 * 0.45), which would correspond to a much larger z-score or a different distribution.
- This value is an overestimation and does not align with the standard normal distribution probabilities for the given parameters.
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