What is Parametric Analysis in Epidemiology?
Parametric analysis in epidemiology refers to the use of statistical methods that assume a specific distribution for the data. These methods are used to make inferences about population parameters such as means, variances, and proportions. Common parametric models include linear regression, logistic regression, and survival analysis models like the Cox proportional hazards model.
Why Use Parametric Methods?
Parametric methods provide several advantages. They can be more efficient than non-parametric methods, as they use all available data to estimate parameters. They also allow for more complex modeling, including the ability to control for multiple confounders. Moreover, when the assumptions of parametric methods are met, they tend to provide more precise and accurate estimates.
Assumptions of Parametric Methods
One major assumption of parametric methods is that the data follows a specific distribution, such as the normal distribution. Other assumptions may include independence of observations, homogeneity of variance, and linearity in the case of linear regression. Violation of these assumptions can lead to biased estimates and incorrect inferences.
Common Parametric Models in Epidemiology
Linear Regression
Linear regression is used to model the relationship between a continuous dependent variable and one or more independent variables. It assumes that the residuals (errors) are normally distributed and have constant variance.
Logistic Regression
Logistic regression is used when the dependent variable is binary. It estimates the probability that a given event will occur as a function of the independent variables. This model assumes that the log-odds of the dependent variable is a linear combination of the independent variables.
Cox Proportional Hazards Model
The Cox proportional hazards model is used in survival analysis to explore the relationship between the survival time of subjects and one or more predictor variables. It assumes that the hazard ratios are constant over time, which is known as the proportional hazards assumption.
How to Check Assumptions?
Various diagnostic tools and tests are available to check the assumptions of parametric models. For instance, residual plots can be used to assess normality and homoscedasticity in linear regression. The Hosmer-Lemeshow test is often used to check the fit of logistic regression models. Similarly, Schoenfeld residuals can be used to test the proportional hazards assumption in Cox models.
Limitations of Parametric Methods
Despite their advantages, parametric methods have limitations. They can be sensitive to outliers and violations of model assumptions. In cases where the assumptions are not met, non-parametric methods may be more appropriate. Additionally, parametric methods may not perform well with small sample sizes or highly skewed data.
Conclusion
Parametric methods are powerful tools in epidemiology, offering efficiency and precision when their assumptions are met. However, it is crucial to carefully check these assumptions and consider alternative methods when necessary. Proper application of parametric methods can lead to valuable insights and improved public health outcomes. 
