Kaplan-Meier survival curves

Command

Statistics Survival analysis Kaplan-Meier survival curves

Description

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 Also the outcome is unknown of those participants who have withdrawn from the study.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:

• in one column, a code can be entered to assign the case to a particular group (study group - control group).
• in a second column, the survival time has to recorded
• in a third column, it must be recorded whether or not the case has reached the endpoint (by entering the code 1) or whether the time is censored, i.e. the outcome is unknown (by entering the code 0);

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 The outcome of this case is unknown (withdrawn from study, or end of study) (data from Freireich et al., Blood 1963; 21:699-716).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.

Required input

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:

• Survival time

  The name of the variable containing the time to reach the event of interest, or the time of follow-up.

• Endpoint

  The name of a variable containing codes 1 for the cases that have reached the endpoint, or code 0 for the cases that have not reached the endpoint, either because they withdrew from the study, or the end of the study was reached.

• Factor

  For Factor select a qualitative or discrete variable (grouping variable - GROUP in the example). This qualitative factor may either be character or numeric codes. These codes are used to break-up the data into several subgroups. If you want to study the effect of a continues variable on survival time, you can convert this continuous variable into a discrete variable using the Create groups tools.

  MedCalc will allow comparison of survival curves for up to 6 subgroups.

  If no Factor variable is selected, then MedCalc will display only one survival curve (all data are considered to belong to one group).

• Select

  A selection criterion to include only a selected subgroup of cases in the graph.

• Options

  Linear trend for factor levels: Allows testing for a linear trend across levels of the factor. It is appropriate if factor levels have a natural ordering (for example, factor codes represent doses applied to different groups). Kaplan-Meier assumes that the factor levels are equally spaced.

  Graph:

  • Survival probability (%): plot Survival probability (%) against time (descending curves)
    
  • 100 - Survival probability (%): plot 100 - Survival probability (%) against time (ascending curves)
    

  Include 95% CI in graph: Allows to plot the 95% confidence interval for the survival curves.

  Mark censored data in graph: Mark censored data in the graph with a small vertical line.

  Number at risk table below graph: Shows a table below the graph with the number of subjects at risk.

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.

Graph

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:

Results

Sample size, median survival time and survival proportion

In this example, the sample size was 21 cases in both groups. The median survival time was 23 units in group 1, and 8 units group 2. The median survival time is the time at which half the subjects have reached the event of interest. If the survival curve does not fall to 0.5 (50%) then the median time cannot be computed.

Next the survival proportions (with standard error) are listed for all groups for each observed timepoint.

When you scroll down (press the Page Down key), 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 ratio

If you compare two survival curves then MedCalc also calculates the hazard ratio with its 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 significant different from the value 1 (corresponding to equal hazards) since the confidence interval 1.9812 to 8.8132 does not include the value 1.

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.

Literature

• Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.

See also

• Cox proportional-hazards regression
• Format graph
• Graph legend
• Add graphical objects
• Reference lines