Day 40: Survival Analysis in SPSS – Analyzing Time-to-Event Data

Day 40: Survival Analysis in SPSS – Analyzing Time-to-Event Data

Welcome to Day 40 of your 50-day SPSS learning journey! Today, we’ll explore Survival Analysis, a statistical method used to examine the time until an event occurs. This technique is widely used in medical research, business analytics, engineering, and social sciences.

What is Survival Analysis?

Survival Analysis examines the time-to-event data, where the event could be:
✔ Time until customer churn in a business.
✔ Time until patient recovery or death in healthcare.
✔ Time until machine failure in engineering.
✔ Time until employee turnover in HR analytics.

Unlike standard regression models, Survival Analysis handles censored data, meaning that some events might not have occurred yet (e.g., some customers haven’t left the company).

Key Concepts in Survival Analysis

  1. Survival Function (S(t)): Probability that an individual survives beyond time t.
  2. Hazard Function (h(t)): Instantaneous rate at which an event occurs at time t.
  3. Censoring: When an event has not yet happened at the time of analysis.
    • Right-Censored: The event hasn't occurred yet.
    • Left-Censored: The event occurred before observation began.
  4. Kaplan-Meier Estimator: A method to estimate survival probabilities over time.
  5. Cox Proportional Hazards Model: A regression method for survival data that includes predictor variables.

When to Use Survival Analysis?

Use Survival Analysis when:
✔ You have time-to-event data.
✔ Some observations are censored (event has not occurred yet).
✔ You want to compare survival times between different groups.

How to Perform Kaplan-Meier Survival Analysis in SPSS

Step 1: Open Your Dataset

For this example, use the following dataset:

ID Tenure (Months) Churned (1=Yes, 0=No) Subscription Type
1 12 1 Basic
2 18 0 Premium
3 8 1 Basic
4 24 0 Premium
5 15 1 Standard
6 30 0 Standard
  • Tenure: Time until churn (event).
  • Churned: Event indicator (1 = churn, 0 = still active).
  • Subscription Type: Grouping variable (Basic, Standard, Premium).

Step 2: Access the Kaplan-Meier Survival Tool

  1. Go to Analyze > Survival > Kaplan-Meier.
  2. Move Tenure (Months) to Time.
  3. Move Churned to Status, then set "1" as the event value.
  4. Move Subscription Type to the Factor box (optional, for group comparisons).

Step 3: Customize Output Options

  1. Click Options:
    • Select Survival tables and plots.
    • Select Log-rank test (for comparing groups).
  2. Click OK.

Interpreting the Kaplan-Meier Output

1. Survival Table

  • Shows probability of surviving over time.
  • Example: After 12 months, 80% of customers are still active.

2. Kaplan-Meier Survival Curve

  • A stepwise plot showing survival probabilities over time.
  • A steeper decline means higher event occurrence (e.g., more customers leaving).

3. Log-Rank Test

  • Compares survival distributions between groups.
  • p < 0.05 → Significant difference between subscription types.

Example Interpretation:

  • Premium customers have the highest retention rates.
  • Basic customers churn faster than Standard and Premium.

How to Perform Cox Proportional Hazards Regression in SPSS

Step 1: Access the Cox Regression Tool

  1. Go to Analyze > Survival > Cox Regression.
  2. Move Tenure (Months) to Time.
  3. Move Churned to Status, then set "1" as the event value.
  4. Move Subscription Type and other predictors (e.g., Age, Income) to Covariates.

Step 2: Customize Model Options

  1. Click Options:
    • Check Hazard Ratios (Exp(B)).
    • Check Goodness-of-fit tests.
  2. Click OK.

Interpreting the Cox Regression Output

1. Exp(B) (Hazard Ratios)

  • Exp(B) > 1 → Increases risk of event (higher churn).
  • Exp(B) < 1 → Reduces risk of event (lower churn).
Predictor B Exp(B) p-value
Subscription (Basic) 1.20 3.32 0.01
Subscription (Standard) 0.50 1.65 0.05
Subscription (Premium) -0.30 0.74 0.10

2. Model Fit Tests (Log-Likelihood, Chi-Square, AIC/BIC)

  • p < 0.05 indicates a significant effect.

Interpretation:

  • Basic plan customers churn 3.32x faster than Premium customers.
  • Standard plan customers churn 1.65x faster than Premium customers.
  • Premium customers have the lowest risk of churn.

Practice Example: Perform Survival Analysis

Use the following dataset:

ID Time (Months) Event (1=Yes, 0=No) Treatment Group
1 6 1 A
2 12 0 B
3 9 1 A
4 18 0 B
  1. Perform Kaplan-Meier Survival Analysis.
  2. Compare survival curves between Treatment A and Treatment B.
  3. Run Cox Regression to test if Treatment Group predicts survival time.

Common Mistakes to Avoid

  1. Ignoring Censoring: Make sure censored cases are correctly identified.
  2. Using Kaplan-Meier for Continuous Predictors: Use Cox Regression instead.
  3. Misinterpreting Hazard Ratios: Exp(B) values above 1 indicate higher risk, below 1 indicate lower risk.

Key Takeaways

✔ Kaplan-Meier Analysis estimates survival probabilities over time.
✔ Cox Regression models the effect of predictors on survival time.
✔ Hazard Ratios (Exp(B)) indicate risk levels.

What’s Next?

In Day 41, we’ll explore Time Series Forecasting in SPSS, where you’ll learn how to predict future trends using historical data. Stay tuned! 🚀


Labels: