All practice questions

A 45-year-old man weighing $80 \text{ kg}$ is admitted to the intensive care unit with severe sepsis. He requires immediate intravenous administration of an antibiotic. The target peak plasma concentration ($C_p$) for this drug is $12 \text{ mg/L}$. Pharmacokinetic data indicates that the volume of distribution ($V_d$) for this antibiotic is $0.5 \text{ L/kg}$. What is the appropriate intravenous loading dose (in mg) required to achieve the desired target plasma concentration for this patient?

An infectious disease specialist is evaluating a male patient with multidrug-resistant bacteremia to design an appropriate antimicrobial dosing regimen.

Patient details:
- Age: $68$ years
- Weight: $72 \text{ kg}$
- Serum creatinine: $2.0 \text{ mg/dL}$ (stable over the past week)

The team plans to start a novel continuous intravenous antibiotic. Pharmacokinetic data indicates that this drug is excreted exclusively by glomerular filtration, and its clearance is directly equal to the patient's creatinine clearance. The target steady-state plasma concentration ($C_{ss}$) required for bactericidal efficacy is $15 \text{ mg/L}$.

Assuming the Cockcroft-Gault equation is $\text{CrCl} = \frac{(140 - \text{Age}) \times \text{Weight in kg}}{72 \times \text{Serum Creatinine in mg/dL}} \times (0.85 \text{ if female})$, what continuous intravenous infusion rate (in $\text{mg/hr}$) is required to achieve the target steady-state concentration?

A 60-kg woman is hospitalized for a severe, refractory asthma exacerbation. She is placed on a continuous intravenous infusion of aminophylline at a rate of 30 mg/hr. No initial loading dose was administered prior to starting the infusion.

Aminophylline has a known systemic clearance of 0.05 L/kg/hr and an elimination half-life of 6.93 hours in this patient population (assume $\ln(2) = 0.693$). The drug follows first-order kinetics and distributes into a single pharmacokinetic compartment.

After exactly 6.93 hours of continuous infusion, the patient's work of breathing abruptly increases, and an arterial blood gas analysis indicates impending respiratory failure. The intensivist decides to administer an immediate intravenous bolus (loading dose) of aminophylline to rapidly achieve the exact steady-state concentration that the current infusion rate is targeting.

What is the required intravenous bolus dose in milligrams?

An $80\text{-kg}$, 65-year-old male is transferred to the intensive care unit due to septic shock. The critical care team decides to rapidly initiate broad-spectrum antibiotic therapy, which includes a novel antimicrobial, Drug X. The clinical pharmacist provides the following pharmacokinetic parameters for Drug X in critically ill adults:

- Volume of distribution ($V_d$): $0.5 \text{ L/kg}$
- Systemic clearance ($Cl$): $2.0 \text{ L/hr}$
- Oral bioavailability ($F$): $80\%$

The target peak plasma concentration ($C_p$) required for therapeutic efficacy against the suspected pathogen is $20 \text{ mg/L}$. To rapidly achieve this target level, an intravenous loading dose is ordered.

What intravenous loading dose (in mg) should be administered to this patient?

A prospective cohort study is conducted to evaluate the incidence of major adverse cardiovascular events (MACE) in patients receiving a novel lipid-lowering therapy. The investigators enroll $1,000$ patients who are free of cardiovascular disease at baseline. The study follows these patients for exactly $4$ years. During the study period, the following events are recorded:

- $200$ patients experience a MACE at exactly the end of Year $1$.
- $100$ patients are lost to follow-up (without experiencing a MACE) at exactly the end of Year $2$.
- The remaining $700$ patients complete the full $4$-year follow-up without experiencing a MACE.

Based on these data, what is the incidence rate of MACE per $1,000$ person-years in this cohort?

A clinical study investigates a newly developed oral medication aimed at reducing the incidence of recurrent urinary tract infections (UTIs) in postmenopausal women. The investigation includes $1,000$ participants who are randomly allocated in equal numbers to either the new medication or a placebo. Over a $12$-month period, $150$ out of the $500$ participants taking the placebo develop a recurrent UTI. Meanwhile, $100$ out of the $500$ participants taking the new oral medication develop a recurrent UTI.

What is the number needed to treat (NNT) to prevent one recurrent UTI in this population?

A pediatric researcher is analyzing the birth weights of full-term neonates born at 39 weeks of gestation at a large regional hospital. The dataset, which includes 5,000 infants, follows a normal distribution. The analysis reveals a mean birth weight of $3,400$ g and a variance of $90,000 \text{ g}^2$. For a secondary analysis, the researcher needs to identify the birth weight threshold for the lowest $2.5\%$ of the cohort. Based on the empirical rule, what is the maximum birth weight (in grams) that would fall into the lowest $2.5\%$ of this distribution?

A large epidemiological study is investigating a novel serum biomarker, alpha-7-glycoprotein (A7G), to predict incident heart failure in adults over age $50$. The A7G levels in the study population ($N = 10,000$) are determined to follow a normal distribution. Preliminary statistical analysis reveals that $16\%$ of the participants have an A7G level greater than $45 \text{ mg/L}$, while $2.5\%$ of the participants have an A7G level less than $21 \text{ mg/L}$.

Based on these findings, what is the variance of the A7G levels in this study population? (Provide your answer as a numeric value)

A clinical pharmacologist is analyzing the steady-state trough concentrations of a newly approved monoclonal antibody targeted for severe refractory eosinophilic asthma. In a post-marketing surveillance cohort of $5,000$ adult patients, the serum trough concentrations follow a normal, symmetric bell-shaped distribution.

The variance of the steady-state trough concentrations in this population is calculated to be $9.0 \text{ (mcg/mL)}^2$. Furthermore, statistical analysis reveals that the $84^\text{th}$ percentile for the trough concentration is $17.0 \text{ mcg/mL}$.

The clinical trial protocol dictates that any patient with a trough concentration falling at or below the $2.5^\text{th}$ percentile is at extremely high risk for subtherapeutic exposure and should undergo immediate dose escalation.

Below what trough concentration (in $\text{mcg/mL}$) will a patient qualify for this dose escalation?

A medical resident is presenting a recent multicenter, randomized controlled trial at journal club. The trial evaluated a novel medication, neprastatin, for the prevention of acute exacerbations in patients with severe chronic obstructive pulmonary disease (COPD). The study enrolled 5,000 patients, with 2,500 randomly assigned to receive daily neprastatin and 2,500 assigned to receive a placebo. At the end of the 2-year follow-up period, the published abstract states that 150 patients in the placebo group experienced an acute COPD exacerbation, compared to 100 patients in the neprastatin group.

Based on the results presented in the abstract, what is the number needed to treat (NNT) with neprastatin to prevent one acute COPD exacerbation?

An epidemiologic surveillance system monitors the time to complete resolution of symptoms in a cohort of $20,000$ healthcare workers who contracted a novel upper respiratory viral infection. The symptom resolution times are normally distributed, demonstrating a mean of $18$ days and a variance of $4$ days $^2$.

Based on the empirical (68-95-99.7) rule, what is the expected number of healthcare workers whose symptoms resolved in either less than $14$ days or more than $24$ days?

A recent multi-center, randomized, double-blind clinical trial evaluated the efficacy of a novel monoclonal antibody for the prevention of episodic migraines. The published abstract includes the following data regarding the primary endpoint:

Based on these reported event rates, what is the number needed to treat (NNT) to prevent one additional patient from progressing to chronic migraine?

A multicenter rheumatology research network is analyzing demographic data for a newly defined phenotype of large-vessel vasculitis. The registry includes $2,500$ confirmed cases. The investigators perform a descriptive analysis of the age of initial symptom onset. The resulting histogram demonstrates a normal distribution. According to the registry's statistical report, the $2.5^\text{th}$ percentile for age of symptom onset is $29$ years, and the $84^\text{th}$ percentile is $53$ years.

Based on the empirical characteristics of normal distributions, what is the mean age of symptom onset (in years) for this patient cohort?

A gastroenterology research team is evaluating colonic transit times in a cohort of healthy volunteers using a radiopaque marker technique. The distribution of transit times in this population is determined to be normally distributed. The researchers report a mean transit time of $36 \text{ hours}$ and a variance of $16 \text{ hours}^2$. Based on these descriptive statistics, a volunteer whose colonic transit time sits exactly at the $84^{\text{th}}$ percentile has a transit time of how many hours?

A physician is evaluating a promotional brochure for a novel cardioprotective agent, 'Cardio-X.' The advertisement's headline prominently asserts: "Reduces the risk of major adverse cardiovascular events (MACE) by 50%!"

Seeking to understand the true clinical impact before prescribing it to a patient, the physician reviews the primary 5-year randomized controlled trial data included in the fine print.

The trial included 5,000 patients randomized equally into a treatment group and a placebo group. The results table is as follows:

Based on the trial data provided, what is the number needed to treat (NNT) with Cardio-X to prevent one death from any cause over the 5-year period? (Enter the numerical value)

A hospital's Pharmacy and Therapeutics committee is evaluating a proposal to add a novel anticoagulant, *Thrombostat*, to the formulary for stroke prevention in patients with nonvalvular atrial fibrillation. The committee reviews the primary outcome data from the pivotal, double-blind, randomized controlled trial.

The trial enrolled $8000$ patients, who were randomized in a $1:1$ ratio to receive either *Thrombostat* or standard-of-care warfarin. Over a 2-year follow-up period, the incidence of the primary endpoint (ischemic stroke) was recorded as follows:

Based on these study results, what is the number needed to treat (NNT) with *Thrombostat* instead of warfarin to prevent one ischemic stroke over 2 years?

A medical researcher is evaluating the relationship between the class of oral antidiabetic medication prescribed and the incidence of major adverse cardiovascular events (MACE) in a retrospective cohort of 1,250 patients with type 2 diabetes. The medication classes are categorized as SGLT2 inhibitors ($n = 450$), GLP-1 receptor agonists ($n = 600$), and DPP-4 inhibitors ($n = 200$). The cardiovascular outcomes over the study period are classified into three mutually exclusive categories: myocardial infarction ($n = 150$), ischemic stroke ($n = 100$), and no MACE ($n = 1,000$).

The researcher plans to use a Pearson chi-square test to determine if the choice of medication is independent of cardiovascular outcomes. A key assumption of this test is that no more than 20% of the expected cell frequencies are less than 5.

Under the null hypothesis of no association, what is the expected count of patients who were prescribed a GLP-1 receptor agonist and subsequently experienced a myocardial infarction? (Enter your answer as a whole number).

A research team is investigating the relationship between preoperative smoking status and the incidence of post-operative respiratory complications in patients undergoing elective abdominal surgery. The researchers categorize $500$ patients into three groups: current smokers ($n=100$), former smokers ($n=150$), and never smokers ($n=250$). During the $30$-day post-operative period, the following number of patients developed respiratory complications:

- Current smokers: $15$
- Former smokers: $10$
- Never smokers: $5$

The researchers plan to perform a Chi-square test of independence to analyze this categorical data. Assuming the null hypothesis of no association is true, what is the expected count of current smokers who develop post-operative respiratory complications?

A multicenter clinical trial is designed to evaluate the efficacy of newly formulated lipid-lowering regimens in patients with familial hypercholesterolemia. The study randomizes 360 patients equally into 6 distinct treatment arms: high-intensity statin monotherapy, statin plus ezetimibe, statin plus a PCSK9 inhibitor, statin plus bempedoic acid, PCSK9 inhibitor monotherapy, and a placebo group.

After 12 weeks, an initial one-way analysis of variance (ANOVA) reveals a statistically significant difference in the mean percentage reduction of LDL cholesterol across the groups ($p = 0.004$). The investigators plan to conduct post-hoc pairwise comparisons using independent $t$-tests to identify which specific groups differ from one another. To control the family-wise Type I error rate at $\alpha = 0.05$, they apply a Bonferroni correction by dividing the overall $\alpha$ by the total number of unique pairwise comparisons.

How many unique pairwise comparisons can be made among the treatment arms in this study?

A 68-year-old woman is admitted to the hospital with a complicated intra-abdominal infection. She is started on a newly approved intravenous antimicrobial agent. The standard maintenance dose of this medication for patients with normal renal function (defined as a creatinine clearance of $100 \text{ mL/min}$) is $600 \text{ mg}$ administered every 24 hours. Pharmacokinetic data indicate that in healthy individuals, $60\%$ of the drug is eliminated unchanged in the urine, while the remaining $40\%$ undergoes hepatic metabolism. The patient's basic metabolic panel reveals an elevated serum creatinine, and her creatinine clearance is estimated to be $25 \text{ mL/min}$. Assuming linear pharmacokinetics and normal hepatic function, what should be the new daily maintenance dose in $\text{mg}$ to achieve the same steady-state average drug concentration as a patient with normal renal function?