MSDB 720 Lecture 1: Introduction to Statistical Modeling

A collection of vocabulary terms exploring the fundamentals of statistical modeling, specifically comparing the tasks of hypothesis testing, estimation, prediction, and classification as discussed in the MSBD 720 lecture by Aize Cao.

Data Analysis (Initial Steps)

The process of exploring data characteristics, screening for errors, and identifying distribution patterns to determine if transformations or non-parametric techniques are required.

Hypothesis Testing

A statistical task involving formal tests and model comparisons (e.g. AIC) using methods such as 2-sample t-tests, ANOVA, multiple linear regression, or the log-rank test.

Estimation

A model-based statistical task focused on providing point and interval estimates for a predictor's effect or outcome probability, usually emphasizing adjusted (partial) effects.

Prediction

The estimation of an outcome or outcome tendency for a subject, made without specific knowledge of cost or utility functions.

Classification

A decision or forced choice typically used for binary response variables that requires knowledge of the utility function or the cost of making an incorrect decision.

Linear Regression

A multivariate model for continuous outcomes where coefficients represent slopes, expressed as \text{blood pressure (mmHg)} = \text{̑} + \beta_{salt} \times \text{salt consumption} + \beta_{age} \times age + \beta_{smoker} \times \text{ever smoker}.

Logistic Regression

A multivariate model for binary outcomes where coefficients represent odds ratios, expressed as \ln(\text{odds of high blood pressure}) = \text{̑} + \beta_{salt} \times \text{salt consumption} + \beta_{age} \times age + \beta_{smoker} \times \text{ever smoker}.

Cox Regression

A multivariate model for time-to-event outcomes where coefficients represent hazard ratios, expressed as $\\ln(\\text{rate of death}) = \alpha + \beta_{salt} \times \text{salt consumption} + \beta_{age} \times age + \beta_{smoker} \times \text{ever smoker}$.

Hazard Ratio

A value that indicates how much the rate of the outcome increases for every 1-unit increase in each predictor.

Odds Ratio

A value that indicates how much the odds of the outcome increase for every 1-unit increase in each predictor.

Slopes

In linear regression, these values indicate how much the outcome variable increases for every 1-unit increase in each predictor.

AIC

A formal model comparison tool used across statistical tasks like hypothesis testing, estimation, and prediction.

Utility Function

A function based on subjects' preferences and decision costs that is required to move from a prediction to a classification-based decision.

Overfitting

A potential modeling failure where the model is overly adapted to the specific sample data, losing generalizability.

Covariable Adjustment

The process of adjusting for other risk factors to obtain the correct estimate of relative effects, particularly important in non-randomized studies or nonlinear models.