Basics of Statistics for Clinical Studies

Congratulations on completing the essentials of case reports, review articles, and meta-analyses! Now, it’s time to step into the expansive world of database research, where large datasets offer unique opportunities to uncover patterns, trends, and associations that traditional studies cannot address. Whether you’re analyzing nationwide registries, electronic health records, or multi-center databases, this field empowers you to tackle complex questions and generate meaningful insights. By harnessing the power of big data, you can contribute to evidence-based medicine in ways that transform healthcare and advance patient care.

But before we dive into the specifics of database studies, let’s take a step back and review some basic statistics essential for understanding and interpreting clinical studies. A strong grasp of these concepts will provide the foundation you need to navigate the complexities of database research with confidence.

Descriptive Statistics: Summarizing Data
1. Percentages
  1. What they do: Show proportions in an easy-to-understand way.
  1. Example: In a group of 100 patients, 25% have hypertension.
  1. Why they matter: Percentages make it easy to compare groups and understand proportions at a glance.
1. Mean vs. Median
  1. Mean (Average): Add all numbers together, then divide by the total count.
    1. Example: For ages 20, 22, 23, 25, and 90, the mean age is 36.
    1. Use standard deviation along with mean to state how the values are spread out.
  1. Median: The middle value in an ordered dataset.
    1. Example: The median of the same ages is 23.
    1. Use interquartile ranges along with median to state how the values are spread out.
  1. When to use which: Use the median if you have extreme values (outliers) that could skew the mean.
Standard Deviation (SD): Measuring Variability
1. What it tells us: SD shows how spread-out values are around the mean.
1. Example: For a group with a mean height of 170 cm and SD of 5 cm, most people fall between 165 and 175 cm.
1. Why it matters: Smaller SDs mean data points are close to the mean, while larger SDs indicate a wider spread.
Confidence Intervals (CI): Measuring Precision
1. What it means: A CI provides a range within which the true value likely falls, with a specified level of confidence.
1. Example: If blood pressure reduction has a 95% CI of 15–25 mmHg, we are 95% confident the true reduction lies within this range.
1. Why it matters: Confidence intervals give an idea of the reliability of a result.
P-Values: Testing for Significance
1. What it does: Indicates the likelihood that a result happened by chance.
1. Example: A p-value of 0.03 means there’s a 3% chance the result is due to random variation.
1. Threshold: A p-value < 0.05 is generally considered statistically significant.
Comparing Groups: Parametric and Non-Parametric Tests
1. t-Test
  1. Purpose: Compares the means of two groups.
  1. Example: If a treatment group improves more than a placebo group with a p-value of 0.01, it suggests the treatment had an effect.
1. Mann-Whitney Test
  1. Purpose: Used for non-normally distributed data such as median, comparing ranks rather than values.
Risk Ratios and Odds Ratios: Understanding Probability
1. Risk Ratio (RR)
  1. Purpose: Compares the probability of an event between two groups.
  1. Example: If 12% of football players get injured compared to 4% of non-players, the RR is 3, meaning players are three times more likely to get injured.
  1. Interpretation:
    1. RR > 1: Increased risk.
    1. RR < 1: Reduced risk (protective effect).
    1. RR = 1: No difference in risk between groups.
1. Odds Ratio (OR)
  1. Purpose: Compares the odds of an event occurring between two groups, often used in case-control studies.
  1. Example: A study compares the odds of knee injuries in skiers vs. non-skiers.
    1. In the injury group: 40 skied, 60 didn’t → Odds = 40 / 60 = 0.67
    1. In the no-injury group: 20 skied, 80 didn’t → Odds = 20 / 80 = 0.25
    1. OR = 0.67 / 0.25 = 2.68
  1. Interpretation: Skiers have 2.68 times higher odds of knee injury than non-skiers.
    1. OR > 1: Increased odds of the outcome.
    1. OR < 1: Decreased odds (protective effect).
    1. OR = 1: No difference in odds between groups.
Correlation and Regression: Exploring Relationships
1. Correlation
  1. Purpose: Measures the strength and direction of a relationship between two variables.
  1. Example: Height and weight may have a strong positive correlation, meaning taller people often weigh more.
1. Regression
  1. Purpose: Predicts the value of one variable based on another.
  1. Example: Fasting blood glucose might be used to predict HbA1c levels in diabetic patients.
Survival Analysis: Understanding Time-to-Event Data
1. Kaplan-Meier Curves
  1. Purpose: Show how long it takes for an event (like death or recovery) to occur in a group.
  1. Example: Comparing survival rates between two treatment groups reveals which group fares better over time.
Sensitivity and Specificity: Evaluating Diagnostic Tests
1. Sensitivity
  1. Purpose: Measures how well a test identifies those with a condition (true positives).
  1. Example: A test with 90% sensitivity correctly identifies 90 out of 100 people with the disease.
1. Specificity
  1. Purpose: Measures how well a test identifies those without the condition (true negatives).
1. Predictive Values
  1. Positive Predictive Value (PPV): Likelihood that a positive result is accurate.
  1. Negative Predictive Value (NPV): Likelihood that a negative result is accurate.
Deep Dive into Regression Analysis: Univariate and Multivariate
1. What is Regression? Regression is a powerful statistical tool used to understand the relationship between one or more independent variables and a dependent variable. In healthcare, it can help predict outcomes like blood pressure levels based on factors such as age or weight.
1. Simple Linear Regression (Univariate Analysis)
  1. Purpose: Examines the relationship between one independent variable and one dependent variable.
  1. Example: Predicting fasting blood sugar levels based on the patient’s weight.
  1. Independent variable: Weight (x-axis)
  1. Dependent variable: Blood sugar (y-axis)
  1. When to Use Simple Linear Regression: When the relationship between the independent and dependent variable is linear, and when the dependent variable is continuous (e.g., blood sugar level, weight).
1. Multiple Linear Regression (Multivariate Analysis)
  1. Purpose: Uses multiple independent variables to predict a dependent variable, accounting for confounders.
  1. Example: Predicting blood pressure using age, weight, and smoking status.
  1. Independent variables: Age, weight, smoking status
  1. Dependent variable: Blood pressure
  1. Why Use Multiple Regression: To understand the combined effect of multiple factors on an outcome and to control for confounding variables (e.g., controlling for age when studying the effect of smoking on blood pressure).
1. Key Assumptions of Regression Models: For regression to give valid results, certain assumptions must be met:
  1. Linearity: The relationship between the independent and dependent variables should be linear.
  1. Independence: Observations should be independent of each other.
  1. Homoscedasticity: The variance of errors should be consistent across all values of the independent variables.
  1. Normality: Residuals (differences between predicted and actual values) should follow a normal distribution.
1. Interpreting Regression Results
  1. Coefficient (Slope): Tells how much the dependent variable changes with a one-unit change in the independent variable.
    1. Example: A slope of 2 for weight means that for each additional kilogram, blood sugar increases by 2 units.
  1. R² (Coefficient of Determination): Measures how well the independent variables explain the variability in the dependent variable.
    1. Example: R² = 0.8 means 80% of the variability in the dependent variable is explained by the independent variables.
  1. P-value: Indicates whether the relationship between the independent and dependent variable is statistically significant (usually, p < 0.05).
1. Multivariate Analysis: Beyond Linear Regression
  1. Logistic Regression: Used when the dependent variable is binary (e.g., disease present or absent). Predicts the probability of an event occurring.
  1. Cox Proportional Hazards Model: A type of regression used for survival analysis. Models the effect of several variables on the time until an event occurs (e.g., death, discharge from hospital).
1. When to Use Univariate vs. Multivariate Analysis?
  1. Univariate Analysis: Used when you want to study the effect of one variable at a time. Example: Evaluating the relationship between BMI and blood pressure.
  1. Multivariate Analysis: Used when multiple variables are likely to influence the outcome. Example: Assessing how age, BMI, and smoking together impact blood pressure.
1. Practical Tips for Running Regression Models
  1. Software tools: Use R, Python, SPSS, or Excel to run regression models efficiently.
  1. Check multicollinearity: In multiple regression, ensure independent variables are not highly correlated (use VIF—Variance Inflation Factor).
  1. Model diagnostics: Use residual plots to ensure assumptions of linearity and homoscedasticity are met.
Deep Dive into Relative Risk, Odds Ratio, Number Needed to Treat, and Number Needed to Harm
1. Relative Risk (RR)
  1. What is Relative Risk? Relative Risk (RR) is the ratio of the probability of an event occurring in the treatment (or exposed) group compared to the control (or unexposed) group. It is mainly used in cohort studies.
  1. Formula: RR = Risk in treatment group / Risk in control group.
  1. Example: A study on football players vs. non-football players assesses the risk of leg fractures:
    1. 12 out of 1000 football players suffer a fracture → Risk = 12 / 1000 = 0.012
    1. 4 out of 1000 non-players suffer a fracture → Risk = 4 / 1000 = 0.004
    1. RR = 0.012 / 0.004 = 3
  1. Interpretation: Football players are three times more likely to suffer a leg fracture than non-players.
    1. RR > 1: Increased risk.
    1. RR < 1: Reduced risk (protective effect).
    1. RR = 1: No difference in risk between groups.
1. Odds Ratio (OR)
  1. What is Odds Ratio? Odds Ratio (OR) compares the odds of an event occurring in one group to the odds of the same event occurring in another group. It’s often used in case-control studies.
  1. Formula: OR = Odds of event in cases / Odds of event in controls.
  1. Example: A study compares the odds of knee injuries in skiers vs. non-skiers:
    1. In the injury group: 40 skied, 60 didn’t → Odds = 40 / 60 = 0.67
    1. In the no-injury group: 20 skied, 80 didn’t → Odds = 20 / 80 = 0.25
    1. OR = 0.67 / 0.25 = 2.68
  1. Interpretation: Skiers have 2.68 times higher odds of knee injury than non-skiers.
    1. OR > 1: Increased odds of the outcome.
    1. OR < 1: Decreased odds (protective effect).
    1. OR = 1: No difference in odds between groups.
1. Number Needed to Treat (NNT)
  1. What is NNT? NNT represents the number of patients who need to receive a treatment for one additional patient to benefit. It tells us how effective a treatment is.
  1. Formula: NNT = 1 / Absolute Risk Reduction (ARR).
  1. Example: A study tests an antifungal drug:
    1. 80% of treated patients recover vs. 60% of placebo patients.
    1. ARR = 80% – 60% = 20% = 0.2
    1. NNT = 1 / 0.2 = 5
  1. Interpretation: We need to treat 5 patients for one to benefit from the antifungal treatment.
1. Number Needed to Harm (NNH)
  1. What is NNH? NNH tells us how many patients need to be exposed to a treatment before one additional patient experiences a harmful side effect. It is the opposite of NNT.
  1. Formula: NNH = 1 / Absolute Risk Increase (ARI).
  1. Example: A study shows that 6% of patients on a new drug develop ulcers, compared to 1% of patients on placebo.
    1. ARI = 6% – 1% = 5% = 0.05
    1. NNH = 1 / 0.05 = 20
  1. Interpretation: For every 20 patients treated with the drug, one patient will develop an ulcer.
1. Comparing NNT and NNH: Finding a Balance
  1. When evaluating a treatment, it’s important to compare the NNT and NNH.
    1. A good treatment: Low NNT (high benefit) and high NNH (low harm).
    1. Example: If a drug has an NNT of 10 (effective) but an NNH of 5 (risky), the risk might outweigh the benefit.

Conclusion

This chapter simplifies key statistical concepts for interpreting research results and making data-driven decisions. From basic descriptive statistics to deeper analyses like regression and risk ratios, mastering these tools equips you to assess studies critically, predict outcomes, and apply evidence effectively.

References

BMJ Statistical Guidelines
Available at: https://www.bmj.com/about-bmj/resources-authors/statistics-notes
1. National Institute of Health (NIH) – National Library of Medicine: “Statistical Concepts Series” Available at: https://pubmed.ncbi.nlm.nih.gov/
1. Rosner, Bernard (Bernard A.). Fundamentals of Biostatistics. Boston: Brooks/Cole, Cengage Learning, 2011.

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