## Information

The Kaplan–Meier method is a non parametric method used for the survival analysis. The survival probability calculator generates the Kaplan-Meier curve with confidence interval and calculates the Log-Rank test for more than of two groups.

**Event of interest** (D_{t}): Maintenance failure, recovery, disease occurrence, death, etc.

**Censored event** (C_{t}): the event of interest didn't happen since the subject left the experiment before the ending time, or due to the termination of the experiment.

**n**_{t}: number of participants that didn't have an event yet (event of interest or censored event).

**Proportion surviving interval (P**_{t}): the proportion of survival participants between period t-1 and period t.

**Survival rate (S**_{t} / Cumulative Survival/ Survival function): the proportion of survival participants from period 0 to period t.

**Sum** = ΣD_{t}/n_{t}(n_{t} - D_{t})

**S.E**_{t}: the standard deviation of the survival rate. S.E = S_{t}√(Sum)

**Lower**_{t}: Lower bound of S_{t} confidence interval .

**Upper**_{t}: Upper bound of S_{t} confidence interval.

### Chart type

**Line** –Survival rate (St) per time.

**Confidence interval** – added the Confidence interval areas to the line, with confidence level of (1 - α).

**S.E area** – present S_{t} ± 1*S.E, the S.E is the area below and above the line.

**S.E error bars** – present S_{t} ± 1*S.E, the S.E is presented as error bar.

### Log rank test calculator

Target: test the null assumption that the "time to event" distribution is identical for all the groups.

The test uses the chi-square distribution.

The log-rank test model assumes the events per subject distributes evenly between the groups. The expected number of events is calculated per each time value.

Example with two groups A and B.

Expected value = n

_{A}(d

_{A} + d

_{B})/(n

_{A} + n

_{B})

The page was created per Anna P request.