Kaplan-Meier survival curves
Performs survival analysis and generates a Kaplan-Meier plot.
In clinical trials the investigator is often interested in the time until participants in a study present a specific event or endpoint. This event usually is a clinical outcome such as death, disappearance of a tumor, etc.
The participants will be followed beginning at a certain starting-point, and the time will be recorded needed for the event of interest to occur.
Usually, the end of the study is reached before all participants have presented this event, and the outcome of the remaining patients is unknown. Also the outcome is unknown of those participants who have withdrawn from the study. For all these cases the time of follow-up is recorded (censored data).
In MedCalc, these data can be analyzed by means of a life-table, or Kaplan-Meier curve, which is the most common method to describe survival characteristics.
How to enter data
To be able to analyze the data, you need to enter the data in the spreadsheet as follows:
The order of these columns is of course not important. Also, the rows do not have to be sorted in any way.
The case in row 1 belonged to group 1, and reached the endpoint after 10 units of time. The case in row 3 also belonged to group 1 and was followed for 9 units of time. The outcome of this case is unknown (withdrawn from study, or end of study) (data from Freireich et al., Blood 1963; 21:699-716).
From these data, MedCalc can easily calculate and construct the Kaplan-Meier curve.
After you have selected the Kaplan-Meier survival curve option in the Graphs menu, the following dialog box is displayed:
In this dialog box the following data need to be entered:
When all data have been entered click the OK button, and the program will open 2 windows: one with the survival graphs, and one with the mathematical results.
The survival curves are drawn as a step function, as shown in the following example:
With the option "Include 95% CI in graph" selected, the graph looks like this:
When the option "Number at risk table below graph" is selected, the result is:
This table shows the number of cases that reached the endpoint (Number of events), the number of cases that did not reach the endpoint (Number censored), and the total number of cases.
Mean and median survival
The mean and median survival time are reported with their 95% confidence interval (CI).
The mean survival time is estimated as the area under the survival curve in the interval 0 to tmax (Klein & Moeschberger, 2003).
The median survival is the smallest time at which the survival probability drops to 0.5 (50%) or below. If the survival curve does not drop to 0.5 or below then the median time cannot be computed. The median survival time and its 95% CI is calculated according to Brookmeyer & Crowley, 1982.
At each observed timepoint, the survival proportions (with standard error) are listed for all groups, as well as the overall survival proportion.
Comparison of survival curves (Logrank test)
When you scroll down, you see the result of the logrank test for the comparison between the two survival curves:
In this example, 9 cases in group 1 and 21 cases in group 2 presented the outcome of interest. The Chi-squared statistic was 16.79 with associated P-value of less than 0.0001. The conclusion therefore is that, statistically, the two survival curves differ significantly, or that the grouping variable has a significant influence on survival time.
Hazard ratios with 95% Confidence Interval
When you have specified a factor then MedCalc also calculates the hazard ratios with 95% confidence interval (CI). Hazard is a measure of how rapidly the event of interest occurs. The hazard ratio compares the hazards in two groups.
In the example the hazard ratio is 4.1786 so that the estimated relative risk of the event of interest occurring in group 2 is 4.1786 higher than in group 1. This hazard ratio is significantly different from the value 1 (corresponding to equal hazards) since the confidence interval 1.9812 to 8.8132 does not include the value 1.
The hazard ratios are calculated according to Klein & Moeschberger, 2003.
Note that the computation of the hazard ratio assumes that the ratio is consistent over time, so therefore if the survival curves cross, the hazard ratio statistic should be ignored.
Logrank test for trend
If more than two survival curves are compared, and there is a natural ordering of the groups, then MedCalc can also perform the logrank test for trend. This tests the probability that there is a trend in survival scores across the groups.