10.1 Biostatistics and Critical Appraisal of Clinical Literature

10.1 Biostatistics and Critical Appraisal of Clinical Literature

Exam Focus: The PEBC Pharmacist Evaluating Examination requires candidates to critically appraise biomedical literature, interpret epidemiological data, and select appropriate statistical tests. Candidates must master calculations for Absolute Risk Reduction ($ARR$), Relative Risk Reduction ($RRR$), Number Needed to Treat ($NNT$), and Number Needed to Harm ($NNH$), evaluate confidence intervals, identify trial biases, and understand Intention-to-Treat ($ITT$) versus per-protocol methodologies.

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Data Types and Measurement Scales

Selecting the appropriate statistical test begins with correctly identifying the scale of measurement of the variables under study.

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Descriptive Statistics: Central Tendency and Dispersion

Descriptive statistics summarize and describe the characteristics of a specific dataset without drawing generalized conclusions about the broader population.

1. Measures of Central Tendency

• Mean (Arithmetic Average): The sum of all values divided by the total number of observations ($n$). Parametric measure; highly sensitive to extreme outliers and skewed data.
• Median: The middle observation when data are sorted in ascending order (the 50th percentile). Non-parametric measure; robust to extreme values and preferred for skewed or ordinal datasets.
• Mode: The most frequently occurring value in a dataset. Useful for nominal categorical data.

2. Measures of Dispersion (Spread)

• Standard Deviation ($SD$): Quantifies the degree of dispersion or spread of individual data points around the sample mean in a normally distributed dataset. In a standard normal distribution:
  • $\text{Mean} \pm 1,SD$ encompasses approximately 68.2% of observations.
  • $\text{Mean} \pm 2,SD$ encompasses approximately 95.4% of observations ($\pm 1.96,SD$ covers exactly 95.0%).
  • $\text{Mean} \pm 3,SD$ encompasses approximately 99.7% of observations.
• Interquartile Range ($IQR$): The distance between the 25th percentile ($Q_1$) and the 75th percentile ($Q_3$), representing the middle 50% of observations ($IQR = Q_3 - Q_1$). Reported alongside the median for skewed or ordinal distributions.
• Standard Error of the Mean ($SEM$): Measures the precision with which the sample mean estimates the true population mean, calculated as: $\text{SEM} = \frac{SD}{\sqrt{n}}$ $SEM$ is always smaller than the $SD$ and should never be used as a substitute for $SD$ to describe data variability.

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|                    DATA DISTRIBUTION PATTERNS                           |
+-------------------------------------------------------------------------+
|  1. NORMAL (GAUSSIAN) DISTRIBUTION: Symmetrical, Bell-Shaped           |
|     Mean = Median = Mode                                                |
|                                                                         |
|  2. POSITIVELY SKEWED (RIGHT-SKEWED): Tail stretches to the right       |
|     Mean > Median > Mode  (e.g., Length of hospital stay, drug costs)   |
|                                                                         |
|  3. NEGATIVELY SKEWED (LEFT-SKEWED): Tail stretches to the left        |
|     Mean < Median < Mode  (e.g., Age at natural death in Canada)        |
+-------------------------------------------------------------------------+

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Inferential Statistics, Hypothesis Testing, and Error Types

Inferential statistics use sample data to make generalized inferences about an underlying target population.

Formulating Hypotheses

• Null Hypothesis ($H_0$): States that there is no true difference, effect, or association between the study groups (any observed difference is due purely to random sampling variation).
• Alternative Hypothesis ($H_a$ or $H_1$): States that there is a true difference or effect between the treatment groups.

Type I and Type II Errors

• Alpha ($\alpha$): The probability of committing a Type I error (conventionally set a priori at $\alpha = 0.05$).
• Beta ($\beta$): The probability of committing a Type II error (conventionally set at $\beta = 0.10$ to $0.20$).
• Statistical Power ($1 - \beta$): The probability of correctly rejecting the null hypothesis when a true clinical difference exists (typically targeted at $\ge 80%$ to $90%$). Power increases with larger sample sizes ($n$), larger effect sizes, lower data variance, and higher alpha thresholds.

The p-value versus Clinical Significance

• p-value: The probability of obtaining a result as extreme as, or more extreme than, the observed trial result, assuming the null hypothesis is true. A $p < 0.05$ indicates statistical significance, meaning random chance is an unlikely explanation for the observed difference.
• Clinical Significance: Refers to the practical, real-world clinical importance of the treatment effect. A statistically significant reduction in systolic blood pressure of $0.8\text{ mmHg}$ ($p = 0.002$) across 50,000 trial participants may lack clinical importance if the Minimal Clinically Important Difference (MCID) is $5.0\text{ mmHg}$.

95% Confidence Intervals (95% CI)

A 95% Confidence Interval provides a range of values within which the true population parameter is expected to fall with 95% certainty. The width of the interval indicates precision: narrower intervals reflect larger sample sizes and greater precision.

• For Difference Metrics (Mean Difference, $ARR$, Absolute Risk Increase): If the 95% CI crosses or includes 0.0, the result is not statistically significant ($p \ge 0.05$).
• For Ratio Metrics (Relative Risk, Odds Ratio, Hazard Ratio): If the 95% CI crosses or includes 1.0, the result is not statistically significant ($p \ge 0.05$).

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Statistical Test Selection Matrix

Choosing the correct inferential statistical test depends on the type of data, distribution normality, number of groups, and whether samples are independent or paired.

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Clinical Trial Risk and Effect Size Calculations

Evaluating the magnitude of benefit or harm requires transforming raw trial counts into standardized epidemiological metrics using a standard $2 \times 2$ contingency table.

+-------------------------------------------------------------------------+
|                         2 x 2 CONTINGENCY TABLE                         |
+-------------------------------------------------------------------------+
|                     | Disease / Event Present | Disease / Event Absent  |
| ------------------- | :---------------------: | :---------------------: |
| Treatment Group     |            a            |            b            |
| Control Group       |            c            |            d            |
+-------------------------------------------------------------------------+

1. Event Rates

• Experimental Event Rate ($EER$): $EER = \frac{a}{a + b}$
• Control Event Rate ($CER$): $CER = \frac{c}{c + d}$

2. Relative Risk ($RR$) and Relative Risk Reduction ($RRR$)

• Relative Risk / Risk Ratio ($RR$): The ratio of the risk of an event occurring in the experimental group compared to the control group: $RR = \frac{EER}{CER}$
  • $RR = 1.0$: No difference in risk between groups.
  • $RR < 1.0$: Experimental intervention reduces risk (protective effect).
  • $RR > 1.0$: Experimental intervention increases risk (harmful effect).
• Relative Risk Reduction ($RRR$): The proportional reduction in event rates attributable to the intervention relative to baseline risk: $RRR = \frac{CER - EER}{CER} = 1 - RR$

3. Absolute Risk Reduction ($ARR$) and Number Needed to Treat ($NNT$)

• Absolute Risk Reduction ($ARR$): The absolute arithmetic difference in event rates between control and treatment groups: $ARR = CER - EER$
• Number Needed to Treat ($NNT$): The number of patients who must be treated with the intervention for a specified duration to prevent one additional adverse clinical event: $NNT = \frac{1}{ARR} = \frac{1}{CER - EER}$
  • Rounding Rule for NNT: Always round UP to the next whole integer (e.g., $NNT = 14.2 \rightarrow 15$).

4. Absolute Risk Increase ($ARI$) and Number Needed to Harm ($NNH$)

• Absolute Risk Increase ($ARI$): When an intervention increases the rate of an adverse event ($EER > CER$): $ARI = EER - CER$
• Number Needed to Harm ($NNH$): The number of patients exposed to the drug to cause one additional adverse event: $NNH = \frac{1}{ARI} = \frac{1}{EER - CER}$
  • Rounding Rule for NNH: Always round DOWN to the nearest whole integer for conservative risk assessment (e.g., $NNH = 22.8 \rightarrow 22$).

5. Odds Ratio ($OR$) and Hazard Ratio ($HR$)

• Odds Ratio ($OR$): Used primarily in retrospective case-control studies where baseline incidence rates cannot be calculated: $OR = \frac{\text{Odds of exposure in cases}}{\text{Odds of exposure in controls}} = \frac{a / c}{b / d} = \frac{a \times d}{b \times c}$
• Hazard Ratio ($HR$): Derived from Cox proportional hazards survival regression models; represents the relative likelihood of an event occurring at any specific point in time across longitudinal follow-up.

+-------------------------------------------------------------------------+
|                   WORKED CLINICAL CALCULATION EXAMPLE                   |
+-------------------------------------------------------------------------+
|  Trial: SGLT2 inhibitor vs Placebo for HF hospitalizations over 2 years  |
|  - Placebo (Control): 120 events out of 1000 patients (CER = 12% = 0.12)|
|  - SGLT2i (Treatment): 72 events out of 1000 patients (EER = 7.2%= 0.072)|
|                                                                         |
|  CALCULATIONS:                                                          |
|  - RR  = 0.072 / 0.12 = 0.60                                            |
|  - RRR = (0.12 - 0.072) / 0.12 = 0.048 / 0.12 = 0.40 (40% reduction)    |
|  - ARR = 0.12 - 0.072 = 0.048 (4.8% absolute reduction)                 |
|  - NNT = 1 / 0.048 = 20.83 --> Round UP to 21                           |
|  Conclusion: Treating 21 heart failure patients with the SGLT2i for 2   |
|  years prevents 1 hospital admission.                                   |
+-------------------------------------------------------------------------+

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Critical Appraisal of Clinical Trial Methodologies

Hierarchy of Evidence

1. Systematic reviews and Meta-analyses of randomized controlled trials (RCTs)
2. High-quality double-blind Randomized Controlled Trials (RCTs)
3. Prospective Cohort Studies
4. Retrospective Case-Control Studies
5. Cross-Sectional Surveys
6. Case Series and Case Reports
7. Expert Opinion and in vitro bench research

Randomization and Blinding

• Randomization: Balances known and unknown baseline prognostic factors between groups (simple, block, or stratified randomization).
• Allocation Concealment: Prevents investigators from predicting or influencing group assignments prior to enrollment (e.g., central computerized assignment, sealed opaque envelopes).
• Blinding (Masking): Prevents performance and ascertainment bias:
  • Single-blind: Patient is unaware of assignment.
  • Double-blind: Patient and treating clinicians/outcome assessors are unaware.
  • Triple-blind: Patient, clinicians, outcome assessors, and data analysts/biostatisticians are all blinded.

Intention-to-Treat ($ITT$) versus Per-Protocol ($PP$)

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|                   ANALYSIS POPULATION METHODOLOGIES                     |
+-------------------------------------------------------------------------+
|  1. INTENTION-TO-TREAT (ITT):                                           |
|  - Analyzes all randomized subjects in their assigned treatment groups,  |
|    regardless of protocol deviations, non-adherence, or early dropout.  |
|  - Preserves baseline randomization balance and prevents attrition bias. |
|  - Reflects real-world clinical effectiveness (conservative estimate).  |
|                                                                         |
|  2. PER-PROTOCOL (PP) / AS-TREATED:                                     |
|  - Analyzes only subjects who completed the prescribed trial protocol   |
|    with strict compliance and no major deviations.                      |
|  - Measures maximal pharmacological efficacy under ideal conditions.    |
|  - Prone to attrition bias; breaks baseline prognostic randomization.  |
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Trial Design Frameworks

• Superiority Trials: Designed to prove that a new intervention is clinically superior to a placebo or active control.
• Non-Inferiority Trials: Designed to establish that a new treatment is not clinically worse than an active standard-of-care comparator by more than a predefined margin (the non-inferiority margin, $\Delta$). Commonly utilized when a new drug offers secondary benefits (e.g., oral dosing vs IV, reduced toxicity, improved tolerability, lower cost).

Common Methodological Biases

• Selection Bias: Systematic differences between baseline characteristics of participants enrolled versus those not enrolled.
• Recall Bias: Differential recall of past exposures between diseased cases and healthy controls in retrospective studies.
• Publication Bias: Tendency for journals to publish positive trials over negative/neutral studies; evaluated visually using funnel plots (asymmetry indicates publication bias) and Egger tests.
• Confounding by Indication: Occurs in observational studies when the clinical indication for prescribing a drug is itself independently associated with the adverse outcome.