11.2 Inferential statistics and hypothesis testing

Inferential statistics and hypothesis testing are crucial tools in epidemiology. They help researchers draw conclusions about populations from sample data and test theories about disease causes. These methods quantify uncertainty in estimates and assess the strength of associations between exposures and health outcomes.

In epidemiologic studies, inferential statistics are used to test hypotheses about exposure-outcome relationships. Researchers compare observed data to what's expected if no association exists, adjusting for confounding factors. This process helps determine if findings are likely due to chance or represent real effects in the population.

Inferential Statistics in Epidemiology

Using Inferential Statistics to Make Population Inferences

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• Inferential statistics enable epidemiologists to draw conclusions about a population based on a sample of data
• Probability theory is applied to assess the likelihood that the sample results are representative of the entire population
• Inferential statistics quantify the uncertainty associated with estimates of effect sizes and other epidemiologic measures
  • This uncertainty is typically quantified by calculating confidence intervals and p-values
  • Confidence intervals indicate the precision of the estimates
  • P-values indicate the statistical significance of the estimates

Applying Inferential Statistics in Epidemiologic Studies

• Inferential statistics are employed to test hypotheses about associations between exposures and outcomes in a population
  • The observed data is compared to what would be expected under the null hypothesis of no association
  • This comparison allows epidemiologists to determine if the observed association is likely due to chance or represents a true effect in the population
• Inferential statistics can be used to adjust for potential confounding variables in epidemiologic studies
  • Regression models and other statistical techniques are used to control for the influence of extraneous factors
• Inferential statistics can be used to assess effect modification in epidemiologic studies
  • This involves examining how the association between an exposure and outcome varies across different subgroups of the population (age groups, gender)

Hypothesis Testing in Epidemiology

Formulating Epidemiologic Hypotheses

• Epidemiologic hypotheses typically state the association between an exposure and an outcome
  • The null hypothesis assumes no association between the exposure and outcome in the population
  • The alternative hypothesis assumes an association exists between the exposure and outcome
• The choice of statistical method for testing a hypothesis depends on the type of data and study design
  • Chi-square tests and Fisher's exact tests are used for categorical data (disease status, exposure status)
  • T-tests and ANOVA are used for continuous data (blood pressure, age)

Testing Hypotheses in Different Study Designs

• In cohort studies, the incidence of the outcome in the exposed and unexposed groups can be compared
  • Relative risk or hazard ratios are used to estimate the magnitude of the association while accounting for the duration of follow-up
• In case-control studies, the odds of exposure in the cases and controls can be compared
  • Odds ratios are used to estimate the strength of the association between the exposure and outcome
  • Odds ratios do not provide information about the absolute risk or incidence of the outcome
• In cross-sectional studies, the prevalence of the outcome in the exposed and unexposed groups can be compared
  • Prevalence ratios or prevalence odds ratios are used to estimate the association at a single point in time
• Regression models can be used to test hypotheses while controlling for potential confounding variables
  • Linear regression is used for continuous outcomes (blood pressure)
  • Logistic regression is used for binary outcomes (disease status)
  • These models estimate the independent effect of the exposure on the outcome while holding other variables constant

Interpreting Statistical Results

Understanding P-values and Confidence Intervals

• P-values indicate the probability of observing an association as strong as or stronger than the one observed, assuming the null hypothesis is true
  • A small p-value (typically < 0.05) suggests the observed association is unlikely due to chance alone
• Confidence intervals provide a range of plausible values for the true effect size in the population
  • A 95% confidence interval indicates that if the study were repeated many times, 95% of the intervals would contain the true population value
  • The width of the confidence interval reflects the precision of the estimate
    • Narrower intervals indicate greater precision
    • Precision depends on the sample size, data variability, and confidence level
  • If the confidence interval for a measure of association (relative risk, odds ratio) includes the null value of 1, the association is not considered statistically significant at the specified confidence level

Assessing Effect Sizes and Measures of Association

• Effect sizes quantify the magnitude of the association between the exposure and outcome
  • Effect sizes are used to assess the practical importance of the association beyond its statistical significance
• Relative measures of effect indicate how many times higher or lower the risk or odds of the outcome are in the exposed group compared to the unexposed group
  • Examples include relative risks and odds ratios
• Absolute measures of effect indicate the excess risk or number of cases of the outcome attributable to the exposure in the population
  • Examples include risk differences and attributable risks

Significance vs Practical Importance

Assessing Statistical Significance

• Statistical significance refers to the likelihood that an observed association is due to chance rather than a true effect in the population
  • This is typically assessed using p-values and confidence intervals
  • Smaller p-values and narrower confidence intervals indicate greater statistical significance
• The assessment of statistical significance should consider the strengths and limitations of the study design and data
  • A study with a large sample size may have the power to detect statistically significant associations that are not practically important
  • A study with a small sample size may fail to detect important associations that are not statistically significant

Evaluating Practical Importance

• Practical importance refers to the magnitude and public health relevance of an observed association, regardless of its statistical significance
  • This is typically assessed using effect sizes and measures of population impact (attributable risks, population attributable fractions)
• The interpretation of epidemiologic findings should consider the consistency of the results with previous studies and the biological plausibility of the association
  • Findings consistent with established knowledge and having a clear biological mechanism are more likely to be causal and practically important
• The assessment of statistical significance and practical importance should inform the translation of epidemiologic findings into public health action
  • Findings that are both statistically significant and practically important may warrant interventions to reduce the exposure or mitigate its effects
  • Findings that are neither statistically significant nor practically important may not justify further action