Biostatistics Interview Questions and Answers

A p-value is the probability, under the null hypothesis and the statistical model being used, of obtaining a result at least as extreme as the observed result.

A small p-value indicates that the observed data would be relatively unusual if the null hypothesis were true.

A p-value summarizes evidence against a specified null hypothesis, whereas a confidence interval provides a range of parameter values that are compatible with the data under the statistical procedure used to construct the interval.

A confidence interval is often more informative because it communicates both the estimated effect and its uncertainty.

In repeated sampling, if we repeatedly applied the same confidence-interval procedure under the same conditions, approximately 95% of the resulting intervals would contain the true parameter.

For a particular calculated interval, it is better not to say that there is a 95% probability that the fixed parameter lies inside that specific interval under the standard frequentist interpretation.

Statistical significance usually means that the result provides sufficient evidence against a prespecified null hypothesis according to a chosen significance level, such as 0.05.

Statistical significance does not necessarily imply clinical importance. Effect size, confidence intervals, clinical relevance, study design, and patient context must also be considered.

Yes.

With a sufficiently large sample size, even a very small treatment difference can produce a small p-value.

For example, a treatment might reduce an outcome by 0.5 units with a very narrow confidence interval excluding zero. The result can be statistically significant but too small to matter clinically.

A Type I error occurs when we reject a true null hypothesis. Its probability is controlled by the significance level, usually denoted \(\alpha\).

A Type II error occurs when we fail to reject a false null hypothesis. Its probability is commonly denoted \(\beta\).

Statistical power is:

Power is the probability of detecting a specified effect when that effect truly exists, under the assumptions of the statistical design.

Power generally increases with:

• Larger sample size
• Larger true effect size
• Lower variability
• Higher significance level
• More informative study design

For a fixed design, reducing sample size generally reduces power.

The standard deviation describes variability among individual observations. The standard error describes uncertainty in an estimated quantity, such as a sample mean.

For a simple sample mean:

As sample size increases, the standard error of the mean generally decreases.

The normal distribution is a continuous symmetric distribution characterized by its mean and variance.

In a normal distribution, the mean, median, and mode coincide.

Approximately 68%, 95%, and 99.7% of observations lie within one, two, and three standard deviations of the mean, respectively, under the ideal normal model.

The Central Limit Theorem states, under appropriate conditions, that the sampling distribution of a properly standardized sample mean approaches a normal distribution as sample size increases, even when the underlying population distribution is not normal.

This is one reason normal-based inference can be useful for means even when individual observations are not normally distributed.

Parametric methods generally make assumptions about the distribution or structure of the data and estimate parameters of that model.

Nonparametric methods typically make fewer distributional assumptions and often operate on ranks or other distribution-free quantities.

Examples include the two-sample t-test as a parametric method and the Wilcoxon rank-sum test as a commonly used nonparametric alternative.

The choice depends on the estimand, data structure, distributional assumptions, and study design.

A two-sample t-test compares means under its model assumptions. A Wilcoxon rank-sum test compares distributions through ranks and can be useful when a rank-based analysis is appropriate.

I would not select the method solely because the sample size is "small" or because the data fail a normality test. I would first consider the scientific question and the characteristics of the outcome.

No.

Correlation describes statistical association. Causal inference requires additional assumptions and study-design or analytical conditions that support a causal interpretation.

Randomization is particularly important in clinical trials because it helps balance measured and unmeasured prognostic factors in expectation.

A confounder is a variable that creates a misleading or distorted association between an exposure and an outcome because of its relationship with the exposure and outcome.

For example, in an observational study, age could be associated with both a treatment exposure and an outcome. Failure to account for age could distort the estimated treatment association.

Randomization assigns participants to treatment groups using a chance-based mechanism.

Its major purpose is to reduce systematic differences between treatment groups and provide a foundation for causal inference under the trial's assumptions.

Randomization does not guarantee that every prognostic variable will be perfectly balanced in a finite sample.

Stratified randomization helps maintain balance between treatment groups within important prespecified factors, such as disease stage, geographic region, or prior therapy.

The stratification factors should generally be clinically justified and carefully aligned with the analysis strategy.

Blinding reduces the potential for knowledge of treatment assignment to influence behavior, assessment, reporting, or other aspects of the trial.

Depending on the study, participants, investigators, outcome assessors, sponsors, or statisticians may be blinded.

The primary endpoint is the prespecified outcome that is central to evaluating the main objective of the trial.

Secondary endpoints address additional important objectives.

The distinction matters because the primary endpoint generally drives the sample-size justification and the main confirmatory inference.

An estimand precisely describes the treatment effect of interest.

It specifies the population, treatment conditions, endpoint or variable, handling of intercurrent events, and summary measure used to quantify the effect.

The estimand helps align the scientific question, trial design, data collection, statistical analysis, and interpretation.

The intention-to-treat principle generally evaluates randomized participants according to the treatment strategy to which they were assigned, regardless of subsequent adherence or treatment changes, according to the prespecified analysis.

It helps preserve the benefits of randomization and provides an estimate related to the treatment strategy assigned by the trial.

An ITT-oriented analysis generally follows randomized treatment assignment. A per-protocol analysis focuses on participants who sufficiently adhered to specified protocol requirements.

Per-protocol analyses can be subject to selection bias because protocol adherence after randomization is not generally random.

A safety population is generally defined according to participants who received at least a specified amount of study treatment, often at least one dose, with the exact definition prespecified in the statistical analysis plan.

Safety analyses may therefore use a population different from the primary efficacy population.

A hazard ratio compares the instantaneous event rates between two groups under the assumptions of the fitted survival model.

For example, a hazard ratio of 0.70 can be described as an estimated 30% relative reduction in the hazard in one group compared with the reference group, assuming the proportional-hazards interpretation is appropriate.

A Kaplan-Meier estimator estimates the survival function while accounting for right-censored observations.

The curve represents the estimated probability of remaining event-free beyond a given time.

Censoring indicates that the event has not been observed for that participant during the period in which they were followed.

Right censoring occurs when the event time is not observed beyond a certain point, but we know that the event has not occurred up to that point.

Common examples include a participant completing follow-up without an event, being lost to follow-up, or reaching an administrative study cutoff before experiencing the event.

The proportional-hazards assumption means that the hazard ratio between groups is constant over time, or more precisely that the ratio of hazards does not depend on time under the model.

If proportional hazards is substantially violated, a single hazard ratio may not adequately summarize the treatment effect.

Logistic regression is commonly used when the outcome is binary.

The model relates predictors to the log odds of the outcome:

Exponentiating a coefficient gives an odds ratio associated with a one-unit increase in the corresponding predictor, holding other model variables constant.

An odds ratio of 2 means the odds of the outcome are estimated to be twice as large in one group compared with the reference group, under the model.

It does not mean that the probability of the outcome is twice as large.

Important assumptions depend on the inferential goal, but commonly include appropriate functional form, independent errors where applicable, constant error variance, and assumptions concerning the distribution of errors for certain types of inference.

For a clinical trial, I would also consider randomization, covariate measurement, treatment coding, missing data, influential observations, and whether the model corresponds to the scientific question.

An interaction means that the association or treatment effect depends on the level of another variable.

For example, a treatment could have a different estimated effect in younger and older participants.

An interaction is sometimes described as effect modification, although the exact interpretation depends on the model and estimand.

ANCOVA can compare treatment groups while adjusting for prespecified baseline covariates.

For example, a continuous endpoint measured at Week 12 might be analyzed using treatment group as a factor and baseline measurement as a covariate.

Covariate adjustment can improve precision when the baseline covariate is strongly associated with the outcome.

Mixed-effects models are useful for correlated or hierarchical observations.

In longitudinal clinical trials, repeated measurements from the same participant are correlated. A mixed model can account for this dependence through random effects and/or an appropriate covariance structure.

When many hypotheses are tested, the probability of obtaining at least one apparently significant result by chance can increase.

Therefore, confirmatory clinical trials may use multiplicity-control procedures such as hierarchical testing, gatekeeping, alpha spending, or other prespecified strategies.

A two-sided test considers departures from the null hypothesis in either direction.

A one-sided test focuses on a prespecified direction.

The choice should be determined before examining the data and justified by the scientific question and study design. One should not choose a one-sided test after seeing the observed treatment effect simply to obtain a smaller p-value.

MCAR means the probability of missingness does not depend on observed or unobserved data.

MAR means missingness can depend on observed information, conditional on which the missingness mechanism does not depend on the missing values themselves.

MNAR generally refers to missingness that depends on unobserved or missing information even after accounting for observed data.

These mechanisms are conceptual assumptions that guide sensitivity analysis and modeling rather than variables that can usually be proven directly from the observed dataset.

I would first understand why the data are missing and whether missingness is related to treatment, outcome history, adverse events, progression, or other variables.

I would then follow the prespecified estimand and SAP, use an analysis method appropriate to the outcome and missing-data assumptions, and perform sensitivity analyses when warranted.

I would avoid automatically assuming that simple methods such as last observation carried forward are unbiased.

Multiple imputation replaces missing values with multiple plausible values drawn from an imputation model.

Each completed dataset is analyzed separately, and the results are combined using rules that account for both within-imputation and between-imputation variability.

A sensitivity analysis evaluates whether conclusions are robust to reasonable alternative assumptions, analytical choices, or data-handling strategies.

For example, a primary missing-data analysis might be complemented by alternative assumptions representing less favorable outcomes after discontinuation.

The required inputs depend on the design and endpoint but can include:

• Primary endpoint
• Target treatment effect
• Type I error rate
• Desired power
• Variability or event rate
• Allocation ratio
• Follow-up duration
• Accrual assumptions
• Expected dropout or non-evaluable rate

For time-to-event studies, the number of events is often more fundamental than the total number randomized.

Increasing sample size generally reduces the standard error of an estimate and increases precision.

It also generally increases statistical power for detecting a specified nonzero effect.

However, a larger sample does not automatically eliminate bias or make a poorly designed study valid.

Effect size quantifies the magnitude of an observed or estimated difference or association.

It provides information that a p-value alone does not.

In clinical research, the effect size should be interpreted together with its confidence interval and clinical relevance.

A standardized mean difference expresses a difference between means relative to a measure of variability.

It can be useful when outcomes are measured on different scales, although the clinical interpretation can be less intuitive than the original measurement scale.

A meta-analysis statistically combines results from multiple studies to estimate an overall effect, provided that combining the studies is scientifically and statistically appropriate.

Important considerations include heterogeneity, study quality, effect-measure compatibility, publication bias, and the choice of fixed-effect or random-effects methodology.

I-squared describes the proportion of observed variability in effect estimates that is attributed to between-study heterogeneity rather than sampling variability, under the framework of the meta-analysis.

It should not be interpreted in isolation. The magnitude of heterogeneity, study characteristics, confidence intervals, and clinical context all matter.

A fixed-effect model generally assumes one common underlying effect, with differences between observed estimates attributed to sampling error.

A random-effects model allows the underlying effects to vary across studies and models between-study heterogeneity.

The choice should reflect the scientific question rather than being based solely on whether a heterogeneity statistic is statistically significant.

Publication bias occurs when the availability or publication of study results depends on characteristics of the findings, such as statistical significance or direction of effect.

This can cause published evidence to differ systematically from the total body of evidence that was conducted.

A funnel plot displays study effect estimates against a measure of their precision or size.

In ideal circumstances, smaller studies tend to have greater variability and larger studies tend to have more precise estimates.

Asymmetry can suggest small-study effects or publication bias, but funnel-plot asymmetry does not prove publication bias.

A Statistical Analysis Plan describes the planned statistical analyses for a clinical study in sufficient detail to support consistent and reproducible analysis.

It typically covers analysis populations, endpoints, estimands where applicable, derivations, statistical methods, handling of missing data, multiplicity, sensitivity analyses, subgroup analyses, and presentation of results.

Finalizing the SAP before unblinding helps reduce the risk that analytical choices are influenced by knowledge of treatment results.

It supports the credibility, reproducibility, and prespecification of the confirmatory analysis.

TLF stands for Tables, Listings, and Figures.

These outputs communicate clinical-trial results and can include demographic summaries, adverse-event tables, efficacy analyses, laboratory summaries, patient listings, Kaplan-Meier plots, forest plots, and other graphical displays.

CDISC is the Clinical Data Interchange Standards Consortium.

CDISC standards support consistent organization and exchange of clinical research data.

Examples include SDTM for standardized tabulation data and ADaM for analysis datasets.

Traceability means that an analysis result can be followed back through the analysis dataset and derivations to the underlying source data.

Good traceability helps reviewers understand how a number in a clinical study report was generated.

Baseline is the prespecified measurement used as the reference for post-baseline change.

The exact definition varies by protocol and endpoint. It might be the last nonmissing assessment before first treatment, for example, but the actual rule must follow the study's protocol and SAP.

For example, if baseline is 100 and the Week 12 value is 80:

Percentage change is:

which gives −20%.

An adverse event is an unfavorable medical occurrence in a participant who receives a pharmaceutical product or other intervention, and it does not necessarily have to have a causal relationship with the treatment.

Causality, seriousness, severity, and other classifications are distinct concepts and should not be conflated.

Severe generally describes the intensity or magnitude of a symptom or event.

Serious is a regulatory classification based on specified outcomes or criteria.

An event can be severe without being serious, and an event can be serious without being severe in intensity.

In oncology, objective response rate is commonly defined as the proportion of participants achieving a prespecified response category such as complete response or partial response according to the applicable response criteria.

The exact definition, analysis population, assessment rules, and handling of missing assessments should be prespecified.

Duration of response is generally measured from the time a response is first documented according to prespecified criteria until progression or another defined event.

Because death and censoring rules can affect the analysis, the exact definition should follow the protocol and SAP.

I would not determine clinical effectiveness from the p-value alone.

If 0.05 was the prespecified significance level and the test was part of the prespecified confirmatory strategy, the result may meet the statistical criterion for that hypothesis.

I would also examine the treatment-effect estimate, confidence interval, endpoint definition, multiplicity, estimand, analysis population, missing-data handling, and clinical relevance.

For a conventional two-sided 5% hypothesis test of a null difference of zero, this is consistent with not rejecting the null hypothesis.

However, the width of the interval is also important. A very wide confidence interval could be compatible with both clinically meaningful benefit and clinically meaningful harm.

I would examine the confidence interval and precision of the estimate.

The result could reflect limited sample size, high variability, few events, or other sources of uncertainty.

I would avoid describing the treatment as definitively ineffective simply because the p-value exceeds 0.05.

I would first understand the clinical concern rather than immediately defending the statistical method.

I would explain the statistical reasoning in clinically meaningful language, review the protocol and SAP, and determine whether the disagreement reflects a scientific issue, an interpretation issue, or an implementation issue.

If appropriate, I would explore sensitivity analyses or alternative approaches while maintaining the prespecified primary analysis.

I would assess the scope and impact of the error, document the issue, correct the programming, rerun the affected analyses, and ensure appropriate independent review or validation.

I would also determine whether downstream outputs were affected and whether any previously reviewed materials need to be regenerated.

The priority is transparent documentation and controlled correction rather than simply fixing the code silently.

I would first determine whether the value is a data-entry, derivation, or measurement error.

If it is valid, I would not remove it simply because it makes the analysis less favorable.

I would assess its influence, consider appropriate model diagnostics, and perform prespecified or justified sensitivity analyses where appropriate.

I would distinguish between a legitimate data or programming correction and a post hoc analytical change motivated by the observed results.

For a confirmatory analysis, I would maintain the prespecified primary analysis and clearly document any exploratory or sensitivity analyses.

If an analysis change is genuinely necessary, it should be governed by the appropriate statistical and clinical review process and documented before results are interpreted as confirmatory.

I would not automatically choose a nonparametric test solely because the sample is small.

I would examine the endpoint, distribution, study design, estimand, precision, and relevant assumptions.

Exact methods, permutation methods, robust methods, or appropriate model-based approaches may be useful depending on the problem.

Crossing curves can suggest that the relative treatment effect changes over time and may raise concerns about the proportional-hazards assumption.

I would investigate the survival distributions and consider whether a single hazard ratio adequately summarizes the treatment effect.

Depending on the estimand and analysis plan, alternatives could include restricted mean survival time or time-varying effects.

I would clarify what level of analysis is needed and distinguish a preliminary exploratory result from a validated production output.

For an urgent exploratory request, I can provide a clearly labeled preliminary analysis while explaining what remains to be validated.

For a regulatory or final deliverable, I would not bypass required quality controls simply to meet an arbitrary deadline.

Both can manipulate clinical-trial data.

The DATA step is particularly useful for row-wise processing, conditional logic, retained values, BY-group processing, and many derivation workflows.

PROC SQL is especially convenient for joins, aggregations, subqueries, and relational operations.

The best choice depends on readability, performance, validation requirements, and the task.

BY-group processing allows SAS to process observations according to groups defined by one or more variables.

Automatic variables such as FIRST.variable and LAST.variable can identify the beginning and end of each group.

proc sort data=adsl;
  by usubjid;
run;

data first_record;
  set adsl;
  by usubjid;

  if first.usubjid;
run;

Normally, variables created in a DATA step are reset to missing at the beginning of each iteration unless they are read from an input dataset.

The RETAIN statement prevents a variable from being reset, allowing its value to persist across observations.

data example;
  set source;
  retain previous_value;

  change = value - previous_value;

  previous_value = value;
run;

• Are the datasets sorted by the BY variables?
• Are the key variables correctly defined?
• Are there duplicate keys?
• Is the intended join one-to-one, one-to-many, or many-to-many?
• Could the merge unintentionally duplicate observations?

proc freq data=adae;
  tables trt01p*aept01 / missing;
run;

PROC FREQ can be used for frequency tables, cross-tabulations, categorical summaries, and useful data-quality checks.

• Extensive statistical methodology
• Strong visualization capabilities
• Large package ecosystem
• Reproducible scripting
• Data manipulation capabilities
• Flexible reporting workflows

However, regulated clinical-trial programming also requires appropriate validation, documentation, version control, and process controls.

library(dplyr)

summary_data <- data %>%
  group_by(TRT01P) %>%
  summarise(
    n = n(),
    mean = mean(AVAL, na.rm = TRUE),
    sd = sd(AVAL, na.rm = TRUE)
  )

library(survival)
library(survminer)

fit <- survfit(
  Surv(TIME, EVENT) ~ TRT01P,
  data = adtte
)

ggsurvplot(
  fit,
  data = adtte,
  risk.table = TRUE
)

Validation means obtaining documented evidence that the program and resulting outputs are fit for their intended purpose.

Depending on the environment, this can involve independent programming, code review, test datasets, automated checks, output comparison, controlled software versions, and documented issue resolution.

• Correct statistical logic
• Clear derivations
• Reproducibility
• Appropriate documentation
• Controlled inputs and outputs
• Quality-control procedures
• Traceability
• Consistent naming conventions
• Appropriate handling of edge cases
• Independent review where required

An analysis dataset contains appropriately derived variables and records needed to perform a specific statistical analysis.

It should support the planned analyses while maintaining traceability to standardized or source data.

Suppose BASE is 100 and AVAL is 80.

The derived PCHG variable can then be used in tables, figures, and statistical analyses according to the SAP.

I would verify the population, treatment groups, denominators, derived variables, statistical calculations, formatting, labels, footnotes, and consistency with the SAP.

I would also compare selected values against independent calculations or programs and investigate unexpected differences.

Bayesian inference combines prior information with observed data through a probabilistic model to obtain a posterior distribution.

Frequentist inference generally treats parameters as fixed quantities and bases inference on the sampling distribution of statistics or estimators.

A prior distribution represents information or assumptions about an unknown parameter before incorporating the current study data.

The prior should be justified according to the scientific context, and sensitivity to reasonable alternative priors may be important.

The posterior distribution represents updated uncertainty about the parameter after combining the prior information with the observed data.

It forms the basis for Bayesian estimates, credible intervals, posterior probabilities, and Bayesian decision-making.

A Bayesian credible interval is an interval containing a specified posterior probability of the parameter, conditional on the model, prior, and observed data.

This differs conceptually from a frequentist confidence interval, whose coverage interpretation is based on repeated sampling.

Repeatedly examining accumulating data can increase the chance of rejecting a true null hypothesis if ordinary fixed-sample significance thresholds are used.

Therefore, confirmatory trials may use prespecified group-sequential designs, alpha-spending methods, or other approaches to control the relevant error rate.

An adaptive design allows prespecified modifications to aspects of a clinical trial based on accumulating data while maintaining the trial's statistical integrity.

Examples can include sample-size re-estimation, dropping an ineffective arm, or changing allocation according to prespecified rules.

A non-inferiority trial is designed to determine whether a new treatment is not unacceptably worse than a comparator by more than a prespecified non-inferiority margin.

The margin must be clinically justified and the analysis requires careful consideration of both statistical and clinical assumptions.

An equivalence trial seeks to demonstrate that the treatment difference lies within a prespecified interval around zero.

A non-inferiority trial generally focuses on excluding an unacceptable disadvantage in one direction.

Suppose an event rate decreases from 10% to 5%.

The relative risk is:

The relative risk reduction is therefore 50%, while the absolute risk reduction is 5 percentage points.

Both provide useful but different perspectives.

When an appropriate absolute risk reduction is available:

If the absolute risk reduction is 0.05:

Interpretation depends on the outcome definition and follow-up period.

Connect your interest in quantitative reasoning with the real-world impact of statistical analysis.

For a clinical-trial position, emphasize the role of biostatistics in designing efficient studies, quantifying uncertainty, evaluating treatment effects, and supporting evidence-based medical decisions.