Calculated Survival

Survival Analysis:

\[ S(t) = \prod_{i: t_i \leq t} \left(1 - \frac{d_i}{n_i}\right) \]

Time-to-Event Data:

Enter comma-separated values (e.g., 12,24,36,48)

Event Data (1=event, 0=censored):

Enter comma-separated values matching time data

Time Point for Survival Estimate:

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Estimated Survival Probability:

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1. What is Survival Analysis?

Survival analysis is a branch of statistics for analyzing the expected duration of time until one or more events happen. It's widely used in medical research, engineering, economics and other fields to analyze time-to-event data.

2. How Does the Calculator Work?

The calculator uses the Kaplan-Meier estimator:

\[ S(t) = \prod_{i: t_i \leq t} \left(1 - \frac{d_i}{n_i}\right) \]

Where:

\( S(t) \) — Survival probability at time t
\( t_i \) — Time when at least one event occurred
\( d_i \) — Number of events at time \( t_i \)
\( n_i \) — Number of individuals at risk just before \( t_i \)

Explanation: The estimator calculates the probability of surviving past certain time points by considering the number of subjects at risk and events at each time point.

3. Importance of Survival Analysis

Details: Survival analysis is crucial for understanding time-to-event outcomes in clinical trials, reliability engineering, customer churn analysis, and many other applications where time until an event is important.

4. Using the Calculator

Tips: Enter time-to-event data and corresponding event indicators (1 for event, 0 for censored). Specify the time point for which you want the survival probability estimate.

5. Frequently Asked Questions (FAQ)

Q1: What is censored data?
A: Censored data occurs when we don't observe the event for some subjects during the study period (e.g., patient drops out or study ends before event occurs).

Q2: What's the difference between Kaplan-Meier and Cox regression?
A: Kaplan-Meier is non-parametric and estimates survival function, while Cox regression is semi-parametric and models the effect of covariates on survival.

Q3: When should I use survival analysis?
A: Use it when you have time-to-event data and especially when there's censoring in your data (common in medical studies and reliability testing).

Q4: What are the assumptions of Kaplan-Meier?
A: Key assumptions include: independent censoring, events are recorded at exact times, and censoring is non-informative.

Q5: How do I interpret the survival probability?
A: A survival probability of 0.75 at 12 months means 75% of subjects survived beyond 12 months in your study population.