All practice questions

A clinical research institute follows a dynamic cohort of patients with heart failure with preserved ejection fraction (HFpEF) to determine the incidence rate of new-onset atrial fibrillation (AF). The total observation period for the study is exactly $4$ years.

Enrollment occurs in three phases:
- $400$ patients are enrolled at the start of the study (Year $0$).
- $200$ patients are enrolled exactly $1$ year into the study.
- $150$ patients are enrolled exactly $2$ years into the study.

During the $4$-year observation period, the following events are recorded:
- $60$ patients from the Year $0$ cohort develop AF exactly $2$ years into the study.
- $30$ patients from the Year $1$ cohort die from non-cardiac causes exactly $2$ years into the study.
- $40$ patients from the Year $2$ cohort are lost to follow-up exactly $2.5$ years into the study.
- $50$ patients from the Year $0$ cohort develop AF exactly $3$ years into the study.

Assume no other patients develop AF, die, or are lost to follow-up, and all remaining patients are followed continuously until the end of the $4$-year study period.

Calculate the incidence rate of atrial fibrillation for this dynamic cohort in cases per $1,000$ person-years. Round your final answer to the nearest whole integer.

A 58-year-old man presents with a 2-month history of progressive dysphagia to solid foods and unintentional weight loss. The physician suspects esophageal cancer. Based on his age, symptoms, and risk factors (chronic smoking and alcohol use), the estimated pretest probability of esophageal cancer is $30\%$. A barium swallow study is ordered as an initial evaluation. In this clinical setting, the barium swallow has a sensitivity of $70\%$ and a specificity of $90\%$ for detecting esophageal malignancy. The barium swallow result is reported as normal (negative).

What is the patient's post-test probability of having esophageal cancer despite the negative barium swallow? (Express your answer as a percentage).

A local public health department is investigating a community outbreak of a highly contagious viral respiratory illness originating from a single elementary school. Initial contact tracing identifies $20$ primary cases, all of whom are students at the school. These $20$ children live in $20$ distinct households. Demographic analysis reveals that the total number of individuals residing in these $20$ households is $105$. Medical record review confirms that among the household members who are not primary cases, $15$ individuals have documented immunity due to recent vaccination and are considered non-susceptible. During the recognized incubation period following exposure to the primary cases, $14$ new cases of the identical respiratory illness develop among the household members.

What is the secondary attack rate (in percentage) of this viral illness among the susceptible household contacts?

A 55-year-old man presents to the emergency department with sudden-onset, tearing chest pain radiating to his back. The physician suspects acute aortic dissection. Based on his history, physical examination, and initial chest x-ray findings, the pre-test probability of an acute aortic dissection is estimated to be $20\%$. The physician orders a rapid D-dimer assay, which for this specific cutoff has a reported sensitivity of $80\%$ and a specificity of $95\%$ for aortic dissection in this clinical setting. The patient's D-dimer result returns negative.

Based on these test characteristics, what is the probability (expressed as a percentage) that this patient actually has an acute aortic dissection despite the negative test result?

A multicenter gastroenterology consortium establishes a prospective registry to evaluate the risk of cholangiocarcinoma in patients with primary sclerosing cholangitis. On January 1, 2020, the team screens 258 patients and excludes 4 who already have evidence of malignancy. The remaining 254 disease-free patients are followed until December 31, 2024.

During this exact 5-year observation period, the following events are recorded among the enrolled cohort:
- 30 patients are diagnosed with cholangiocarcinoma exactly 24 months after enrollment.
- 50 patients are lost to follow-up exactly 36 months after enrollment, with no evidence of malignancy prior to that point.
- 20 patients die from unrelated causes exactly 12 months after enrollment, without developing the cancer.
- The remaining patients complete the full 5-year follow-up period without developing the disease.

Assuming no other patients enter or leave the study, what is the incidence rate of cholangiocarcinoma in this cohort, expressed as cases per $1,000$ person-years?

A multi-center task force is evaluating the diagnostic performance of a novel quantitative serum biomarker, matrix metalloproteinase-9 (MMP-9), for the early detection of severe joint destruction in patients with rheumatoid arthritis.

Extensive population studies reveal the following about the biomarker's distribution:
- In healthy patients without joint destruction, MMP-9 levels are normally distributed with a mean of $40 \text{ ng/mL}$ and a standard deviation of $5 \text{ ng/mL}$.
- In patients with confirmed severe joint destruction, MMP-9 levels are normally distributed with a mean of $60 \text{ ng/mL}$ and a standard deviation of $5 \text{ ng/mL}$.

The current diagnostic threshold for a 'positive' screening result is set at $\geq 50 \text{ ng/mL}$. However, rheumatologists have noted an unacceptably high number of missed diagnoses (false negatives) using this threshold. To improve the test's sensitivity, the task force officially recommends lowering the cutoff threshold to $\geq 45 \text{ ng/mL}$.

Assuming the 68-95-99.7 (empirical) rule applies, by what absolute percentage (percentage points) will the test's specificity decrease as a result of lowering the cutoff from $50 \text{ ng/mL}$ to $45 \text{ ng/mL}$?

A regional health authority is evaluating strategies to reduce the incidence of ventilator-associated pneumonia (VAP) across its intensive care units. A prospective cohort study within the region yields the following incidence data based on patient positioning:

- Incidence of VAP in patients maintained in a supine position: 30 cases per 1,000 ventilator-days
- Incidence of VAP in patients maintained in a semi-recumbent position: 5 cases per 1,000 ventilator-days

Recent clinical audits indicate that, despite existing guidelines, 60% of all mechanically ventilated patients in the region are currently maintained primarily in the supine position.

The health authority plans to implement a strict quality improvement protocol to eliminate the use of the supine position entirely, successfully transitioning all patients to the semi-recumbent position. Assuming the observed association is entirely causal, what percentage of the total current VAP cases in the region can be attributed to the use of the supine position (and thus would be prevented by this initiative)?

Enter your answer as a whole number.

A public health physician is analyzing cholesterol levels in a suburban community. The total serum cholesterol levels of $1,000$ adult residents are recorded and found to follow a perfectly normal distribution. The mean total cholesterol level is $195$ mg/dL, and the standard deviation is $15$ mg/dL.

According to the empirical rule, what is the upper limit of the central range (in mg/dL) that symmetrically encompasses approximately $99.7\%$ of the residents' total cholesterol levels?

A primary care network enters into a partial capitation contract for a panel of $5,000$ adult patients. Under this value-based care model, the network receives a capitation payment of $\$30$ per member per month (PMPM) to provide all comprehensive primary care services.

The network's annual fixed administrative overhead for managing this specific population is $\$400,000$. Previously, patients averaged $2.4$ in-person visits per year, with each visit incurring $\$60$ in variable operational expenses for the network.

To optimize care delivery, the network implements a telehealth triage protocol. The new protocol has a dedicated annual operating cost of $\$120,000$. Following implementation, the average in-person utilization rate decreases to $1.8$ visits per patient per year. The capitation rate, panel size, and variable cost per in-person visit remain unchanged.

What is the annual net financial margin (in dollars) for this patient panel under the new telehealth system?

A physician is critically appraising a multi-page drug advertisement for a novel oral anticoagulant, rivatran, targeted at patients with atrial fibrillation and a high risk of recurrent ischemic stroke.

The headline of the advertisement proclaims in large font: *"Rivatran significantly lowers the risk of recurrent stroke, demonstrating a $20\%$ relative risk reduction compared to standard warfarin therapy!"*

Upon reviewing the fine print in the supplemental prescribing information, the physician examines the following safety and efficacy data from the 3-year pivotal trial:

Based on the data provided, how many patients would need to be treated with rivatran instead of warfarin for 3 years to prevent one recurrent stroke?

A physician is evaluating a promotional brochure for a newly approved biologic agent for the prevention of cardiovascular events in high-risk patients. The brochure prominently features a bar graph illustrating a $40\%$ relative risk reduction (RRR) in the primary composite endpoint (nonfatal myocardial infarction, nonfatal stroke, and cardiovascular death) over a 4-year period compared to placebo.

To better understand the data, the physician reviews the trial methodology in the accompanying package insert. In the clinical trial, the absolute risk of the primary composite endpoint in the placebo group was $20\%$ over 4 years. The medication was also associated with an increased incidence of injection-site reactions, with a calculated number needed to harm (NNH) of 25 over 4 years.

The physician is considering prescribing this biologic agent to a 55-year-old man with hyperlipidemia. Using a validated cardiovascular risk calculator, the physician estimates that this specific patient's absolute risk for experiencing the primary composite endpoint without the biologic treatment is $5\%$ over the next 4 years.

Assuming the relative risk reduction of the medication remains constant across different baseline risk levels, what is the calculated number needed to treat (NNT) to prevent one primary composite endpoint event over 4 years for a population with this patient's specific baseline risk profile?

A cross-sectional study is conducted to evaluate the intraocular pressure (IOP) in a population of $5,000$ healthy adults over the age of $40$. The collected IOP measurements are determined to follow a normal distribution with a mean of $15$ mm Hg. The researchers note that approximately $800$ participants ($16\%$ of the cohort) have an IOP greater than $18$ mm Hg.

Based on these findings, what is the variance of the intraocular pressure in this population?

A randomized, double-blind clinical trial evaluates the efficacy of a novel Janus kinase (JAK) inhibitor for the treatment of moderate-to-severe atopic dermatitis. A total of $428$ patients are randomized into one of four treatment arms: JAK inhibitor 15 mg, JAK inhibitor 30 mg, an active comparator (dupilumab), and placebo. The primary outcome is the absolute reduction in the Eczema Area and Severity Index (EASI) score from baseline to week 16. The data for this continuous variable are determined to be normally distributed, and Levene's test confirms homogeneity of variances across the groups.

Researchers perform a one-way analysis of variance (ANOVA) to evaluate whether there is a statistically significant difference in the mean EASI score reduction among the treatment groups. The $F$-statistic is calculated by dividing the between-group mean square by the within-group mean square.

What is the within-group (denominator) degrees of freedom for this statistical test?

An internist is discussing a newly approved direct oral anticoagulant with a 72-year-old male patient who has non-valvular atrial fibrillation. The patient brings in a direct-to-consumer print advertisement he found in a magazine. The headline reads, "Cut your risk of a stroke by a third!"

To provide accurate counseling, the internist reads the detailed prescribing information included in the advertisement's inset. The data stems from a 2-year randomized clinical trial that enrolled a total of 8,000 patients. Half of the patients received standard warfarin therapy, and the other half received the new medication. Over the 2-year follow-up period, 240 patients in the warfarin group experienced an ischemic stroke, compared to 160 patients in the new medication group.

Based on the data provided in the advertisement's inset, what is the number needed to treat (NNT) with the new medication for 2 years to prevent one additional stroke compared to warfarin?

An internal medicine specialist is analyzing the published results of a multi-center randomized controlled trial to decide if a new antithrombotic drug should be added to the hospital formulary. The study compared the new drug against standard care over a $3$-year period.

The following event frequencies were observed in the trial:

*Note: Relative risk changes are calculated against the standard care baseline.

To assess the overall clinical utility, the specialist evaluates a composite outcome of "total major clinical events," defined as the sum of ischemic strokes and major bleeding episodes.

Calculate the net number of total major clinical events PREVENTED for every $10,000$ patients treated with the new antithrombotic instead of standard care over the $3$-year period.

An infectious disease specialist is consulting on a 48-year-old male inpatient with a severe systemic infection. The patient's body mass is $75 \text{ kg}$. The physician decides to start a continuous intravenous infusion of a narrow-therapeutic-index antibiotic. The established target steady-state serum concentration is $15 \text{ mg/L}$. Pharmacokinetic data for this drug indicate a volume of distribution of $0.8 \text{ L/kg}$ and an elimination half-life of $13.86 \text{ hours}$. Assuming first-order elimination kinetics, what maintenance infusion rate (in $\text{mg/hr}$) is required to sustain the target concentration?

Emergency medical services bring a 52-year-old man to the emergency department after he was found unresponsive in a park. He has a known history of severe alcohol use disorder. On physical examination, his temperature is $36.5^\circ\text{C}$ ($97.7^\circ\text{F}$), blood pressure is $110/70 \text{ mmHg}$, pulse is $98/\text{min}$, and respiratory rate is $16/\text{min}$. He is uncooperative and confused but moves all extremities spontaneously.

Initial laboratory studies reveal the following:

A toxicology screen is negative for acetaminophen and salicylates. His blood ethanol level is undetectable. The laboratory reports a measured serum osmolality of $324 \text{ mOsm/kg H}_2\text{O}$.

Based on the provided laboratory results, what is the patient's calculated osmolar gap?

A 45-year-old man weighing $80 \text{ kg}$ is admitted to the hospital with a severe skin and soft tissue infection. The physician decides to initiate therapy with a novel oral antimicrobial agent. To ensure immediate therapeutic effect, a loading dose is required. The target peak plasma concentration for this medication is $15 \text{ mg/L}$. The drug has a known volume of distribution of $0.6 \text{ L/kg}$ and an oral bioavailability of $75\%$.

What is the required oral loading dose in mg to achieve the desired peak plasma concentration?

A 64-year-old man is evaluated in the intensive care unit for a progressive decline in urine output. Three days ago, he underwent an emergent exploratory laparotomy for a perforated duodenal ulcer. His postoperative course was complicated by hypotension requiring vasopressor support for 24 hours, but he is currently hemodynamically stable. His urine output over the last 8 hours has been 120 mL.

Laboratory studies are obtained and reveal the following:

Serum chemistry
Sodium: $140$ mEq/L
Potassium: $4.8$ mEq/L
Chloride: $105$ mEq/L
Bicarbonate: $20$ mEq/L
BUN: $42$ mg/dL
Creatinine: $2.0$ mg/dL (baseline was $0.9$ mg/dL)

Urine studies
Sodium: $70$ mEq/L
Creatinine: $50$ mg/dL
Osmolality: $310$ mOsm/kg $H_2O$

Based on these laboratory results, what is the patient's fractional excretion of sodium (FENa)? Give your answer as a percentage.

A 27-year-old woman with a history of type 1 diabetes mellitus presents to the emergency department with abdominal pain, nausea, and severe, intractable vomiting for the past 48 hours. She stopped taking her insulin yesterday due to an inability to tolerate oral intake. On physical examination, her pulse is 118/min, blood pressure is 98/60 mm Hg, and respiratory rate is 18/min. Her mucous membranes are dry.

Arterial blood gas on room air reveals:
pH: $7.38$
$pCO_2$: $42 \text{ mm Hg}$

Serum laboratory results are as follows:
Sodium: $140 \text{ mEq/L}$
Potassium: $3.1 \text{ mEq/L}$
Chloride: $88 \text{ mEq/L}$
Bicarbonate: $24 \text{ mEq/L}$
Glucose: $610 \text{ mg/dL}$
Blood urea nitrogen: $42 \text{ mg/dL}$
Creatinine: $1.8 \text{ mg/dL}$

To evaluate for the presence of a mixed acid-base disorder, the physician calculates the delta-adjusted bicarbonate (also known as the expected bicarbonate derived from the delta gap). Assuming a baseline normal anion gap of $12 \text{ mEq/L}$, what is this patient's delta-adjusted bicarbonate (in mEq/L)?