Biostatistics Notes

Role of Biostatistics in Pharmacy

• Statistics involves the collection, analysis, and interpretation of data.
• It's a crucial tool in pharmacological research for:
  • Summarizing experimental data using descriptive statistics.
  • Conducting hypothesis testing.
• It helps determine if one drug's pharmacological effect is superior to another, impacting drug development.
• Statistics aids in formulating experimental designs and drawing appropriate inferences from data, reducing the risk of misleading claims and increasing confidence in translating proof-of-concept studies to clinical applications.

Key Statistical Terms

• Population: All objects of a similar type in the universe, represented by "N".
• Sample: A fraction of the population that represents the population of interest, represented by "n". Samples are used to make generalizations about the population.
• **Sampling Types:
  • Simple Random Sampling: Individuals are chosen randomly.
  • Stratified Random Sampling: Population is divided into mutually exclusive groups (strata) based on a specific factor (e.g., race, gender).
  • Cluster Sampling: The population is divided into clusters, and random samples are taken from each cluster.
  • Convenience Sampling: Participants are selected based on the researcher's convenience.

Measurement Scales

• Nominal/Categorical Scale: Classifies observations into named categories (e.g., HIV status: positive/negative).
• Ordinal Scale: Categories with a rank order (e.g., cancer stage: I, II, III, IV).
• Interval Scale: True numerical values on a number line (e.g., temperature in Celsius).
• Ratio Scale: Has all properties of an interval scale, with the ability to calculate ratios due to an absolute zero point (e.g., height, weight).

Variables and Data

• Variable: A characteristic being observed or measured.
• Data: Measured values assigned to a variable.
  • Example: Age of a person (age is the variable, 32 is the data).
  • Example: HIV status of a person (HIV status is the variable, +/- is the data).
• Types of Variables:
  • Dependent Variable (DV): The outcome variable.
  • Independent Variable (IV): The variable being manipulated.
    • Example: Effect of physical activity on serum cholesterol.
  • Confounding Variable: Affects the DV beyond the effect of the IV, but is not of specific research interest.
    • Example: Diet is a confounding variable when studying the effect of physical activity on serum cholesterol.

Continuous and Discrete Variables

• Continuous Variables: Data measured on interval or ratio scales (e.g., age, weight).
• Discrete Variables: Data with distinct, separate values, typically integers or whole numbers (e.g., number of students in a class).

Accuracy and Precision

• Accuracy: How closely a computed/measured value agrees with the true value.
• Precision: How closely individual computed/measured values agree with each other.
• Inaccuracy: Bias.
• Imprecision: Uncertainty.

Statistical Significance

• Statistical significance indicates whether a result is likely due to chance or a factor of interest.
• It provides evidence regarding the plausibility of the null hypothesis.
• The null hypothesis states that there is nothing more than random chance at work in the data.

Hypothesis Testing

• Hypothesis testing is also called significance testing.
• It tests claims about parameters.
• Steps:
  1. State the problem.
  2. Null and alternative hypotheses.
  3. Test statistic.
  4. P-value and interpretation.
  5. Significance level (optional).

P-Value

• The P-value is the probability of finding the observed, or more extreme, results when the null hypothesis is true.
• The null hypothesis is usually a hypothesis of "no difference."
• Statistical significance is often defined as P < 0.05, and highly significant as P < 0.001.

Type I and Type II Errors

• $α$ = probability of a Type I error.
• $β$ = Probability of a Type II error.
• Type I Error: Erroneous rejection of a true null hypothesis (false positive).
• Type II Error: Erroneous retention of a false null hypothesis (false negative).

• Alpha (α) represents the upper bound of the Type I error rate, not the exact rate.
• Beta (β) is the probability of making a Type II error.
• Power is (1 - β), the probability of observing an effect in the sample if one exists in the population.
• Many studies set alpha at 0.05 and beta at 0.20 (a power of 0.80).

Statistical vs. Clinical Significance

• Statistically significant differences may not always translate into clinically significant differences, and vice versa.
• Example 1: A drug reduces blood pressure from 180/100 to 145/90. This is statistically significant but may not be clinically significant.
• Example 2: A compound in grape juice inhibits cytochrome P450 enzymes, increasing bioavailability of certain medications by 5%. This may not be clinically significant if narrow therapeutic index medications are excluded.

Types of Statistics

• Descriptive Statistics: Present, organize, and summarize data numerically, graphically, or in tables. Includes measures of central tendency and dispersion.
• Inferential Statistics: Indicate whether a difference exists between groups or an association between variables. Used to determine if the difference or association is real or due to random chance (e.g., t-test, ANOVA).

Measures of Central Tendency and Dispersion

• Measures of Central Tendency:
  • Mean
  • Median
  • Mode
• Measures of Dispersion (Variability):
  • Range
  • Percentiles
  • Interquartile range
  • Variance
  • Standard deviation
  • Standard error of the mean

Mean

• The average numerical value for data within a variable.
• Calculated by summing all data for a variable and dividing by the total number of data points ($n$).
• Sensitive to extreme values, which can be misleading.

Median

• The value that divides a distribution into two equal parts.
• The middle value when observations are arranged in order of magnitude.
• If the number of observations is odd, it's the middle value.
• If the number of observations is even, it's the average of the two middle values.

Mode

• The most frequently occurring value in a data set.
• A data set can have no mode, one mode, or multiple modes.
• Can be used for qualitative and quantitative data.

Range

• The difference between the maximum and minimum values in a data set.
• The simplest measure of dispersion.

Percentiles

• Divide the distribution into 100 equal parts, each representing 1% of the data set.
• The median is the 50th percentile.
• $Percentile = (number \ of \ values \ below \ score) ÷ (total \ number \ of \ scores) \times 100$

Interquartile Range (IQR)

• The difference between the 25th (Q1) and 75th (Q3) percentiles.
• $Outliers < Q1 - 1.5(Q3 - Q1) \ or > Q3 + 1.5(Q3 - Q1)$

Variance

• A measure of dispersion that accounts for the spread of all data points in a data set.

Standard Deviation

• A measure of the average distance of individual data points from the mean.
• Applies to normally distributed quantitative data.
• Directly proportional to variability; larger variability means larger standard deviation ($SD$).

Standard Error of the Mean (SEM)

• Measures the accuracy of a sample mean by measuring the sample-to-sample variability of the sample means.
• Describes how precise the sample mean is as an estimate of the true population mean.
• $SEM = standard \ deviation / \sqrt{sample \ size}$

Measures of Shape

• The distribution of the dependent variable is important for choosing the appropriate statistical test.
• Most parametric statistical tests require a normal distribution.

Graphical Representations

• Useful for visually inspecting the distribution of variables, especially with large sample sizes.
• Common types: Histograms, boxplots, and scatterplots.
• Histograms show the range and frequency of data.

Boxplot

• Displays the distribution of data based on a 5-point summary: minimum, Q1, median, Q3, maximum.
• IQR = Q3 – Q1.
• Fences are calculated to identify outliers: $FU = Q3 + 1.5(IQR)$, $FL = Q1 – 1.5(IQR)$

Commonly Used Inferential Statistics

• Student's t-test: Compares the means of two groups to determine statistical significance.
• Analysis of Variance (ANOVA): Compares the means of two or more groups for statistical significance.
• Correlation: Examines the association between two or more variables.
• Regression: Examines how one or more independent variables predict a dependent variable.

Pharmacoepidemiology

• The study of the use and effects of drugs in large numbers of people.
• Applies epidemiology principles to study the effects of medications in human populations.

Pharmacoepidemiology Research Questions

• Patterns of Use:
  • What are the patterns of drug utilization?
  • How are drugs used in specific patient populations?
  • How long do people take a drug?
• Safety:
  • What is the frequency of drug-induced outcomes?
  • Are there drug–drug interactions?
  • Are there drug–disease interactions?
• Effectiveness:
  • What are the clinical benefits of a drug?
  • Is a drug effective when used in the “real world”?
  • Is drug A more effective than drug B?
• Economic Evaluations:
  • What are the economic consequences of therapy?

Study Designs Used in Pharmacoepidemiology

• Identification/Exploration of Associations: Case studies, case series, prevalence studies, cross-sectional studies.
• Determination of Causal Relationships: Randomized controlled trials, quasi-experiments.

Sensitivity, Specificity, and Predictive Values

• Measure the ability of a test to correctly identify those experiencing an event and those who did not.
• True-positives (TP): Have the disease and test positive.
• False-positives (FP): Do not have the disease but test positive.
• True-negatives (TN): Do not have the disease and test negative.
• False-negatives (FN): Have the disease but test negative.

Formulas

• $Sensitivity = [a/(a+c)] \times 100$
• $Specificity = [d/(b+d)] \times 100$
• $Positive \ Predictive \ Value (PPV) = [a/(a+b)] \times 100$
• $Negative \ Predictive \ Value (NPV) = [d/(c+d)] \times 100$

Risk Ratio (RR)

• The ratio of the risk of developing an event in exposed individuals to that in unexposed individuals.
• $RR = Risk \ in \ Exposed / Risk \ in \ Unexposed$
• RR of 1 indicates equal risk in both groups.
• RR > 1 means exposure is associated with the event.
• RR < 1 suggests that the exposure has protective effects.

Odds Ratio (OR)

• The ratio of the probability of an event to that of the nonevent.
• $OR = (events \ in \ cases / nonevents \ in \ cases) / (events \ in \ control / nonevents \ in \ control)$
• OR of 1 is a baseline for comparison.
• OR > 1 indicates higher odds for the event in the exposed group.
• OR < 1 suggests an event is less likely in the exposed group.

Measuring Therapeutic Effects

• Relative Risk Reduction (RRR)
• Absolute Risk Reduction (ARR)
• Number Needed to Treat (NNT)
• Number Needed to Harm (NNH)

Relative Risk Reduction (RRR)

• Measures the extent to which an exposure (therapy) reduces a risk.
• $RRR = (Risk \ in \ Untreated - Risk \ in \ Treated) / Risk \ in \ Untreated$

Absolute Risk Reduction (ARR)

• The absolute difference in event rates between the exposed and unexposed groups.
• $ARR = |Event \ Rate \ in \ Treated - Event \ Rate \ in \ Untreated|$

Number Needed to Treat (NNT)

• The number of individuals who need to be treated for one to benefit.
• $NNT = 1 / ARR$

Number Needed to Harm (NNH)

• The number of persons who need to be treated for one to experience an adverse event.
• $NNH = 1 / (Incidence \ Rate \ in \ Treatment - Incidence \ Rate \ in \ Control)$