Biostatistics

15.

Survival Analysis

15.1.

Time-to-Event Data Concepts

15.1.1.

Event Definition

15.1.1.1.

Death, Disease Recurrence, Recovery

15.1.1.2.

Competing Events

15.1.2.

Time Scale Selection

15.1.2.1.

Calendar Time vs Follow-up Time

15.1.2.2.

Age as Time Scale

15.1.3.

Study Design Considerations

15.1.3.1.

Entry and Exit Criteria

15.1.3.2.

Follow-up Procedures

15.2.

Censoring Mechanisms

15.2.1.

Right Censoring

15.2.1.1.

Administrative Censoring

15.2.1.2.

Loss to Follow-up

15.2.1.3.

Competing Risks

15.2.2.

15.2.2.1.

Definition and Examples

15.2.2.2.

Analysis Challenges

15.2.3.

Interval Censoring

15.2.3.1.

Definition and Examples

15.2.3.2.

Analysis Methods

15.2.4.

Informative vs Non-Informative Censoring

15.2.4.1.

Assumptions and Implications

15.2.4.2.

Sensitivity Analysis

15.3.

Survival Function Concepts

15.3.1.

Survival Function

15.3.1.1.

Definition and Properties

15.3.1.2.

15.3.2.

Hazard Function

15.3.2.1.

Instantaneous Risk

15.3.2.2.

Relationship to Survival Function

15.3.3.

Cumulative Hazard Function

15.3.3.1.

Definition and Applications

15.3.3.2.

Nelson-Aalen Estimator

15.4.

Non-Parametric Methods

15.4.1.

Kaplan-Meier Estimator

15.4.1.1.

Construction and Calculation

15.4.1.2.

15.4.1.3.

Confidence Intervals

15.4.1.4.

Median Survival Time

15.4.2.

Comparing Survival Curves

15.4.2.1.

15.4.2.1.1.

Test Statistic and Distribution

15.4.2.1.2.

Assumptions and Limitations

15.4.2.2.

15.4.2.2.1.

Weighted Comparison

15.4.2.2.2.

15.4.2.3.

Stratified Tests

15.4.2.3.1.

Controlling for Confounders

15.5.

Semi-Parametric Methods

15.5.1.

Cox Proportional Hazards Model

15.5.1.1.

Model Specification

15.5.1.2.

Partial Likelihood

15.5.1.3.

Hazard Ratio Interpretation

15.5.2.

Model Assumptions

15.5.2.1.

Proportional Hazards Assumption

15.5.2.1.1.

Testing Methods

15.5.2.1.2.

Schoenfeld Residuals

15.5.2.1.3.

Time-Dependent Effects

15.5.3.

15.5.3.1.

Variable Selection

15.5.3.2.

Interaction Terms

15.5.3.3.

15.5.4.

Model Diagnostics

15.5.4.1.

Residual Analysis

15.5.4.2.

Influence Diagnostics

15.5.4.3.

Goodness-of-Fit Assessment

15.6.

Parametric Survival Models

15.6.1.

Exponential Model

15.6.1.1.

Constant Hazard Assumption

15.6.1.2.

Parameter Estimation

15.6.2.

15.6.2.1.

Shape and Scale Parameters

15.6.2.2.

Hazard Function Forms

15.6.3.

Log-Normal and Log-Logistic Models

15.6.3.1.

Applications and Properties

15.6.4.

Model Selection

15.6.4.1.

Likelihood-Based Criteria

15.6.4.2.

Graphical Methods

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