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 Interpreting results: Number at risk

## Number of subjects at risk at various times

The idea behind the number at risk table is that - in order to calculate survival probability using the Kaplan-Meier product limit method - we need to know how many individuals were still accounted for in the study that had not yet experienced the event of interest. Therefore, the number at risk at any specific time point will be equal to the total number of subjects remaining in the study including any individuals that experience the event of interest or individuals that are censored at this time point. If your unit of time is “days”, you can consider the number at risk to be those individuals who have not yet experienced the event of interest or been censored at the beginning of the day (before any event or censoring could occur).

Keep in mind that the number at risk doesn’t change unless an individual experiences the event of interest or is censored. Thus, we only need to report a new number at risk at time points where one of these situations occurs.

Consider an example using the sample survival data available in Prism. On the Welcome Dialog, select the Survival data table type, then select “Start with sample data to follow a tutorial”. Choose the tutorial data set “Comparing two groups”, and click Create. The data are given here in the following table.

Days elapsed

Control

Treated

46

1

46

0

64

0

78

1

78

1

124

1

130

0

150

0

150

0

9

1

26

1

43

0

46

1

64

1

75

1

100

1

130

0

150

0

If you switch to the Survival results sheet, and select the Number at risk tab, the table will contain the following values:

Days elapsed

Control

Treated

0

8

9

9

9

26

8

43

7

46

8

6

64

6

5

75

4

78

5

100

3

124

4

130

3

2

15

2

1

Consider the values in the “Control” column. The experiment begins with 8 subjects in the control group. The first time point involving a subject in the Control group occurs on day 46 (see the first table on this page). Immediately before this time point, there are still 8 subjects considered to be “at risk”, and so the value shown in this table is 8. At this time point, one subject experienced the event of interest and another was censored in this group, resulting in a total of two patients being removed from the “at risk” group. The next time point involving a subject in the Control group occurs at 64 days. Because this group started with 8 subjects and two were removed from the “at risk” group after 46 days, the new “at risk” total for the control group at day 64 is 6. At this time point one subject was censored, and the next time point involving the control group happens at day 78. Using the same logic, one subject was removed from the “at risk” group after day 64, so the new total in the “at risk” group for day 78 is 5. This technique can be used to determine the number of subjects at risk in each group at each relevant time point.

Note that Prism does not graph this table automatically. However, if you would like to create a graph of the number of subjects at risk over time, you can perform these following steps:

1.Navigate to the results tab for the number of subjects at risk

2.Click the “Create new graph” button in the Sheet section of the toolbar

3.In the dialog that appears, select the number at risk table from the dropdown menu in the “Data sets to plot” section. Also select “XY” from the dropdown menu in the “Kind of graph” section

4.Select your preferred graph type (try Points only or Points & connecting line) and click “Create”

5.Change the Y axis title from its default to “Number of subjects at risk”