Precision, confidence intervals and parameter estimation MCQs With Answer

Introduction

This quiz collection focuses on precision, confidence intervals and parameter estimation tailored for M.Pharm students studying Clinical Pharmacokinetics and Therapeutic Drug Monitoring. It clarifies how measurement error, sample size, and estimation techniques affect the reliability of pharmacokinetic parameters like clearance, volume of distribution and elimination rate constant. You will revisit concepts such as standard error, relative standard error (RSE), confidence interval construction (parametric and nonparametric), the role of Fisher information and bootstrap methods, and practical applications including interval estimation for means, proportions, variances and derived PK parameters. These MCQs emphasize interpretation and methodological choice for robust parameter inference in PK studies.

Q1. What best describes the difference between precision and accuracy in parameter estimation?

• Precision refers to closeness to the true value; accuracy refers to variability among repeated estimates
• Precision refers to variability among repeated estimates; accuracy refers to closeness to the true value
• Precision and accuracy are interchangeable terms in statistical estimation
• Precision measures bias; accuracy measures standard error

Correct Answer: Precision refers to variability among repeated estimates; accuracy refers to closeness to the true value

Q2. Which statement correctly distinguishes standard deviation (SD) from standard error (SE)?

• SD measures sampling variability of the sample mean; SE measures variability in the individual data
• SD measures variability in individual observations; SE measures variability of the sample statistic (e.g., mean)
• SD is always smaller than SE
• SE describes within-subject variability while SD describes between-study variability

Correct Answer: SD measures variability in individual observations; SE measures variability of the sample statistic (e.g., mean)

Q3. The most accurate interpretation of a 95% confidence interval for a population parameter is:

• There is a 95% probability that the true parameter lies inside the calculated interval for this dataset
• If we repeated the study many times and calculated 95% CIs, about 95% of those intervals would contain the true parameter
• 95% of the individual observations fall within this interval
• The parameter is clinically significant with 95% certainty

Correct Answer: If we repeated the study many times and calculated 95% CIs, about 95% of those intervals would contain the true parameter

Q4. Holding variance constant, how does increasing sample size affect the width of a confidence interval for a mean?

• Width increases proportionally to the square root of sample size
• Width decreases and is approximately inversely proportional to the square root of sample size
• Width is independent of sample size
• Width increases linearly with sample size

Correct Answer: Width decreases and is approximately inversely proportional to the square root of sample size

Q5. When constructing a 95% CI for the mean of a small sample from a normally distributed PK measurement with unknown variance, which method is appropriate?

• Use the z-distribution (standard normal) critical value
• Use the t-distribution critical value with n−1 degrees of freedom
• Use a chi-square distribution for the mean
• Use the Poisson approximation

Correct Answer: Use the t-distribution critical value with n−1 degrees of freedom

Q6. For constructing a 95% CI for a population proportion (e.g., fraction of patients achieving therapeutic concentration) when n is moderate, which approach is recommended over the simple normal approximation when proportions are near 0 or 1?

• Use the Clopper–Pearson (exact) interval
• Use the delta method ignoring distributional issues
• Always use the Wald interval (p ± 1.96·SE)
• Use the F-distribution interval

Correct Answer: Use the Clopper–Pearson (exact) interval

Q7. Which distribution is used to construct a confidence interval for a population variance based on a normal sample?

• t-distribution
• Chi-square distribution
• F-distribution
• Exponential distribution

Correct Answer: Chi-square distribution

Q8. In maximum likelihood estimation (MLE), what does the Fisher information quantify?

• The number of parameters in the model
• The amount of information that sample data provide about an unknown parameter, inversely related to the variance of the MLE
• The bias of the estimator only
• The sample size required for hypothesis testing

Correct Answer: The amount of information that sample data provide about an unknown parameter, inversely related to the variance of the MLE

Q9. Which bootstrap confidence interval method adjusts for bias and skewness and is often preferred for PK parameters with asymmetric sampling distributions?

• Percentile bootstrap interval
• Bias-corrected and accelerated (BCa) bootstrap interval
• Standard normal approximation interval
• Clopper–Pearson interval

Correct Answer: Bias-corrected and accelerated (BCa) bootstrap interval

Q10. When estimating a CI for a transformed parameter (e.g., log-transformed clearance), which method uses a first-order Taylor series to approximate variance?

• Profile likelihood method
• Delta method
• Bootstrap percentile method
• Exact binomial method

Correct Answer: Delta method

Q11. Which estimation method explicitly incorporates prior knowledge and produces a posterior distribution for parameters?

• Ordinary least squares (OLS)
• Maximum likelihood estimation (MLE)
• Bayesian estimation
• Method of moments

Correct Answer: Bayesian estimation

Q12. In population PK fitting, why might weighted least squares (WLS) be preferred over ordinary least squares (OLS)?

• WLS assumes homoscedastic residuals while OLS handles heteroscedasticity
• WLS gives equal weight to all residuals unlike OLS
• WLS accounts for heteroscedastic error structures (e.g., variance proportional to predicted concentration), improving parameter precision
• WLS is only applicable for categorical outcomes

Correct Answer: WLS accounts for heteroscedastic error structures (e.g., variance proportional to predicted concentration), improving parameter precision

Q13. Relative standard error (RSE) reported for an estimated PK parameter is defined as:

• Standard error divided by the sample size
• Standard error divided by the estimate, often expressed as a percentage
• Standard deviation of observations divided by the estimate
• Estimate divided by standard error

Correct Answer: Standard error divided by the estimate, often expressed as a percentage

Q14. For nonlinear PK models with skewed parameter sampling distributions, which confidence interval approach based on the likelihood is particularly useful?

• Delta method interval
• Profile likelihood confidence interval
• Simple Wald interval using asymptotic normality
• Clopper–Pearson interval

Correct Answer: Profile likelihood confidence interval

Q15. If a 95% CI for the difference in mean AUC between two formulations does not include zero, what does this imply?

• The difference is statistically significant at approximately the 5% level
• The formulations are equivalent
• The sample size was too small
• The CI is invalid because it excludes zero

Correct Answer: The difference is statistically significant at approximately the 5% level

Q16. To achieve a desired half-width (d) of a 95% CI for a normal mean with known variance σ², the required sample size n is approximately:

• n = (1.96·σ / d)²
• n = (σ / d)²
• n = (1.96·d / σ)²
• n = 1.96·σ·d

Correct Answer: n = (1.96·σ / d)²

Q17. In population PK models, shrinkage of individual parameter estimates toward the population mean most directly reduces which property of the individual estimates?

• Their bias relative to the population mean
• Their variability across individuals, potentially masking true between-subject variability
• Their computational complexity
• Their estimation using non-linear mixed effects methods

Correct Answer: Their variability across individuals, potentially masking true between-subject variability

Q18. What is the primary difference between a confidence interval and a prediction interval in the PK context?

• Confidence intervals and prediction intervals are identical concepts
• A confidence interval estimates uncertainty around the population mean parameter; a prediction interval estimates the range for a future individual observation including residual variability
• Confidence intervals predict individual outcomes; prediction intervals estimate parameter means
• Prediction intervals are narrower than confidence intervals because they account for individual variability

Correct Answer: A confidence interval estimates uncertainty around the population mean parameter; a prediction interval estimates the range for a future individual observation including residual variability

Q19. When estimating the elimination half-life (t1/2) from the terminal slope (λz) of log-linear concentration-time data, the standard error of t1/2 can be derived using which approach?

• Apply the delta method to the transformation t1/2 = ln(2)/λz using the variance of the slope
• Directly use the chi-square distribution for t1/2
• Use the Clopper–Pearson interval on t1/2
• Half-life has no sampling variability and requires no SE

Correct Answer: Apply the delta method to the transformation t1/2 = ln(2)/λz using the variance of the slope

Q20. When empirical sampling distributions are irregular or sample size is small, which choice is generally preferred for constructing CIs for PK parameters?

• Rely exclusively on asymptotic normal (Wald) intervals
• Use nonparametric or bootstrap-based intervals to better reflect sampling distribution shape
• Use the delta method without checking assumptions
• Always double the standard error to be conservative

Correct Answer: Use nonparametric or bootstrap-based intervals to better reflect sampling distribution shape

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