Section 3.7: Biostatistics, Clinical Trial Design & Literature Evaluation

Biostatistics, Clinical Trial Design & Literature Evaluation

Hypothesis Testing and Error Types

Biostatistics provides the quantitative framework for clinical decision-making. When evaluating new therapeutic interventions, researchers formulate hypotheses to test:

• Null Hypothesis ($H_0$): Assumes there is no statistically significant difference or association between the compared groups (e.g., Drug A has the same effect as placebo).
• Alternative Hypothesis ($H_1$): Assumes there is a statistically significant difference or association between the groups.

When conducting statistical tests, researchers face two types of errors:

• Type I Error ($\alpha$): Rejecting the null hypothesis when it is actually true (a false positive). The significance level ($\alpha$) is typically set at 0.05, representing a 5% maximum acceptable probability of making a Type I error.
• Type II Error ($\beta$): Failing to reject the null hypothesis when it is actually false (a false negative).
• Statistical Power ($1-\beta$): The probability of correctly rejecting the null hypothesis when a true difference exists. Factors that increase statistical power include larger sample sizes, larger treatment effect sizes, lower data variability, and a larger alpha level.

Confidence Intervals and P-Values

• P-Value: The probability of obtaining results as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true. A $p < 0.05$ indicates statistical significance.
• Confidence Interval (CI): Provides an estimate of the precision of the study effect. Typically set at 95%, a CI indicates that if the study were repeated 100 times, the true population parameter would fall within the interval 95 times.
  • Interpreting Ratios (RR, OR, HR): If the 95% CI includes the value 1 (e.g., $95% \text{ CI } = 0.85-1.25$), the results are not statistically significant.
  • Interpreting Differences (Mean Difference): If the 95% CI includes the value 0 (e.g., $95% \text{ CI } = -2.5 \text{ to } 5.0$), the results are not statistically significant.

Selection of Statistical Tests

The choice of statistical test depends on the distribution of the data (normally distributed vs. skewed) and the type of variable being measured:

1. Parametric Tests (Normally Distributed, Continuous Data)

• Student's t-test: Compares the means of two groups.
  • Independent (Unpaired) t-test: Compares two independent groups (e.g., Drug A vs. Placebo).
  • Paired t-test: Compares the same group at two time points (e.g., blood pressure before and after treatment).
• Analysis of Variance (ANOVA): Compares the means of three or more groups (e.g., Drug A low-dose vs. high-dose vs. placebo).

2. Non-Parametric Tests (Skewed Data or Nominal/Ordinal Variables)

• Chi-Square Test: Compares categorical outcomes between independent groups (e.g., cure rate [yes/no] between Drug A vs. Drug B).
• Fisher's Exact Test: Used instead of Chi-Square when sample sizes are small (expected cell counts < 5).
• Mann-Whitney U Test: Compares ordinal or non-normally distributed continuous data between two independent groups (non-parametric equivalent of independent t-test).
• Wilcoxon Signed-Rank Test: Non-parametric equivalent of the paired t-test.
• Kruskal-Wallis Test: Non-parametric equivalent of ANOVA.

Clinical Risk Metrics

To interpret literature, pharmacists must calculate clinical metrics of benefit and harm:

• Absolute Risk (AR): The probability of an event in a group.
• Absolute Risk Reduction (ARR): The absolute difference in event rates between control and treatment groups. $\text{ARR} = \text{Event Rate}_{\text{Control}} - \text{Event Rate}_{\text{Treatment}}$
• Relative Risk (RR): The ratio of risk in the treatment group to risk in the control group.
• Relative Risk Reduction (RRR): The proportional reduction in rates between groups. $\text{RRR} = \frac{\text{ARR}}{\text{Event Rate}_{\text{Control}}} = 1 - \text{RR}$
• Number Needed to Treat (NNT): The number of patients who must be treated for a specific period to prevent one additional adverse outcome. $\text{NNT} = \frac{1}{\text{ARR}} \text (expressed as a decimal)$ Note: NNT must always be rounded up to the nearest whole number (e.g., 8.2 rounds to 9) to avoid overestimating clinical benefit.
• Number Needed to Harm (NNH): The number of patients treated to cause one additional adverse event. $\text{NNH} = \frac{1}{\text{Absolute Risk Increase (ARI)}}$ Note: NNH must be rounded down to the nearest whole number to avoid underestimating risk.

Clinical Trial Designs and Guidelines

To critically appraise clinical trials, pharmacists must understand trial designs (such as superiority, non-inferiority, and equivalence trials) and standard reporting checklists:

• Non-Inferiority Trials: Aim to prove that a new drug is not unacceptably worse than an active control, within a pre-defined clinical margin. If the 95% CI of the difference crosses this margin, non-inferiority is not demonstrated.
• Checklists: The CONSORT statement is used to evaluate randomized trials, STROBE for observational designs, and PRISMA for systematic reviews and meta-analyses.

Clinical Trial Phases