Statistical Analysis in Drug Trials

## Hypothesis Testing Framework

Clinical trials test a null hypothesis: the experimental drug has no effect compared to the control. The statistical analysis determines whether observed differences are large enough to reject this null hypothesis with acceptable confidence. The two critical errors are Type I (false positive, concluding a drug works when it does not) and Type II (false negative, concluding it does not work when it does).

## Key Statistical Concepts

### P-Values

The p-value represents the probability of observing a result as extreme as the actual result if the null hypothesis were true. The conventional threshold is p < 0.05 (5% false-positive risk). For pivotal trials, regulatory agencies may require more stringent thresholds (p < 0.01 or lower).

### Confidence Intervals

A 95% confidence interval provides the range within which the true treatment effect lies with 95% probability. Confidence intervals are more informative than p-values because they communicate both the magnitude and precision of the estimated effect. Regulatory decisions increasingly rely on confidence intervals rather than p-values alone.

### Statistical Power

Power is the probability of detecting a true treatment effect if one exists (1 - Type II error rate). Pivotal trials are typically designed with 80-90% power. Underpowered trials risk missing real effects, wasting resources and exposing patients to investigational treatment without generating useful data.

## Sample Size Calculation

Sample size depends on four factors: the expected treatment effect size, the variability of the outcome measure, the desired significance level (alpha), and the desired power (1-beta). Smaller expected effects and higher variability require larger samples. This calculation must be completed before the trial begins and documented in the protocol.

## Analysis Populations

### Intention-to-Treat (ITT)

All randomized participants are analyzed in their assigned group regardless of adherence or completion. ITT preserves randomization benefits and provides a conservative estimate of treatment effect.

### Per-Protocol (PP)

Only participants who completed the trial without major protocol deviations are included. PP analysis estimates the treatment effect under ideal conditions but is susceptible to selection bias.

### Safety Population

All participants who received at least one dose of study medication, analyzed according to actual treatment received. This is the standard population for adverse event analysis.

## Key Takeaways

- Clinical trials test whether drug effects exceed what random variation would produce
- P-values below 0.05 are standard, but confidence intervals are more informative
- Trials require 80-90% power to reliably detect true treatment effects
- Intention-to-treat analysis is the primary method; per-protocol is supportive
- Sample size must be justified before the trial begins, not adjusted afterward