In most cases, survival analysis combines a binary outcome as to whether or not an event occurred, coupled with the time at which the event occurred measured from the start of an intervention (say, the start of a randomized treatment). Of course, not all patients experience an event, such as death or disease progression, so the analysis incorporates these additional patients into the analysis by including them at the end of their follow-up as censored observations. This analysis allows us to compute summary statistics, such as the median survival time, for a group of patients, many of whom may not experience the event of interest over the duration of the clinical trial. Most of us are familiar with the often-used Kaplan-Meier (KM) plot that summarizes a time-to-event (TTE) endpoint for ease of communication (Figure 1).
Here, the Y-axis summarizes the probability of survival while the X-axis summarizes time, often reported as days measured from the start of randomized treatment. The probability of surviving to a given time is displayed by KM curves, one for each treatment, until the last patient in the arm experiences either an event (where a step occurs) or is censored, meaning that the patient reached the end of their follow-up without an event occurring. This particular KM plot has two annotations. The first is the total number of events experienced on each treatment arm over the entire duration of the study. The second is a risk table, communicating the number of patients who are still at risk (yet to have an event or be censored) at a given point in time. Censored observations are represented by vertical pipe symbols. This version of the KM plot has become the standard way to summarize TTE endpoints for many medical journals (search for survival plot on the page) and for submissions to the U.S. Food and Drug Administration.
The KM plot is useful for summarizing TTE data, but can we take advantage of the time element to ask what-if questions of our analysis and to assess the robustness of our results with accumulating data? With the Dynamic Survival report for JMP Clinical 19, now we can.
The Dynamic Survival report provides a more informative and interactive experience for summarizing time-to-event endpoints from the CDISC ADaM ADTTE domain. The report displays a KM plot (as either a survival [decreasing] or failure [increasing] plot – switching is available with the click of a button), annotations for the total number of events (as well as the proportion of total events for Relative analyses), and a number-at-risk table to display the number of patients who have yet to have an event or be censored according to a user-supplied time interval. A further enhancement of the KM plot is that various statistics can be summarized using a second Y-axis, including the log-rank and Wilcoxon tests, or hazard ratios between treatment arms from a corresponding proportional hazards model. The dialog for Dynamic Survival is presented in Figure 2.
Dynamic Survival uses the JMP Survival and Fit Proportional Hazards platforms to analyze a single endpoint from the ADTTE domain. Essentially, the Survival and Fit Proportional Hazards platforms analyze the TTE endpoint separately for distinct time categories that are produced according to the type of analysis requested by the user: Absolute or Relative (default).
For example, suppose we observe TTE data plotted by patient and date (Figure 3). Each patient’s time is measured from a start date to an end date where the patient experiences an event or is censored for not having experienced an event prior to the end of their follow-up.
Suppose there was interest in conducting an interim analysis at a date indicated by the dashed horizonal reference line (Figure 4). For this analysis, patients whose follow-up extends beyond this reference date would be censored at this date (Figure 5). This interim analysis conducted using the data from Figure 5 would include six patients, only one of whom had an event prior to the reference date.
While it is typical to preplan for a small number of interim analyses to assess the outcome for a TTE endpoint, there may be interest in understanding how robust the results are to the timing of the interim analysis. What if the analysis had been conducted two weeks earlier? Four weeks? How would the results change? An Absolute analysis from the Dynamic Survival report allows us to answer this question easily. Based on the Interval for Time Categories in the dialog (Figure 2), the analyst can recompute the TTE analysis in seven- to 90-day intervals counting backward from the observed maximum event/censor date. The Time Category values in the Section Filter include dates according to this interval as long as the date is greater than the minimum event/censor date. Because the analysis is based on absolute time, patients may be excluded from Time Categories as illustrated in Figure 5.
Figure 6 is an Absolute analysis of the Nicardipine Time to Death endpoint from ADTTE. At the top of the figure, the total Number of Events experienced for each arm is summarized; the bottom of the figure presents a table for the Number of Patients at Risk in 20-day increments (Number at Risk Interval, Figure 2).
The Section Filter enables the user to select a Time Category date according to the maximum event/censor date and Interval for Time Categories (10 days were used, as in Figure 2). If it is of interest, the user can select “Time Category” in the filter and use the animation controls to play an animation of how the TTE analysis will change over time. The Right Axis Statistic will plot either of the p-values (from the Survival platform) or hazard ratios (from the Fit Proportional Hazards platform) by adding a second Y-axis. The button Failure Plot changes the survival plot to a failure plot, where the Y-axis starts at 0 and increases upward as events occur; Add Intervals will add 95% confidence bands around the KM curves; Add Simultaneous Intervals will add 95% simultaneous confidence bands around the KM curves. For example, Figure 7 shows both confidence bands and the NIC.15 vs Placebo hazard ratio across time for data based on the Time Category 1988-12-11, which summarizes data through roughly half of the total observed follow-up. Notice how the sample size is reduced to roughly half of the starting sample size, 254 and 261 on NIC.15 and Placebo, respectively. In this summarized data, 49 and 44 events are experienced on the NIC.15 and Placebo arms. And we can assess the robustness of the hazard ratio to accumulating data across time.
A few notes about Absolute analyses:
- Analyzing survival data on an Absolute scale can be used to assess sensitivity of a TTE analysis to the timing of an interim analysis.
- In addition to changing the follow-up time to an event/censor outcome, the sample size can change as patients are excluded from analysis if the Time Category date precedes the start date.
- Statistics are summarized according to the maximum time observed according to the dates included in the Time Categories. It is natural to see statistics summarized at fewer times than there are dates in Time Categories.
In contrast to the Absolute analysis described in Figure 3, the Relative analysis (Figure
In a manner similar to the Absolute analysis, suppose there was interest in conducting an analysis at a Relative time indicated by the dashed horizonal reference line (Figure 9). For this analysis, patients whose follow-up extends beyond this reference time would be censored at this time (Figure 10). Unlike the Absolute analysis, this analysis would include every patient, since every patient is included in the analysis since time 0.
Figure 11 shows a Relative analysis for Nicardipine for Time Category 100 (which can be thought of as 100 days of follow-up from Time 0, usually when the patient starts dosing). Both confidence intervals have been added to the figure, as well as a line for the hazard ratio for Nicardipine vs. Placebo. By day 100, there are seven patients still at risk for each treatment arm, and the initial sample sizes coincide with the total sample sizes of treated patients in each arm. Notice that the Number of Events includes the proportion of Total Events experienced for each arm. By day 100, all 80 events have been experienced on the NIC.15 arm, and 78 of 81 events (96.3%) have been experienced on Placebo, indicating that there are three events left to occur by the end of the analysis. A Relative analysis makes it possible to view an animation and watch as the proportion of events grows over time. Admittedly, the animation can be seen as a bit frivolous, but it certainly can create some drama in the communication of positive study results to the team.
A few notes about Relative analyses:
- Analyzing survival data on a Relative scale can be used to assess the sensitivity of statistics to accumulating data (such as statistical tests and proportional hazards). For example, plots can be used to assess whether KM plots have constant proportional hazards across time.
- It allows for proper animation of the changing survival/failure curves and for viewing of the proportion of total events over time.
- Sample size does not change across the Time Categories since all patients are naturally included beginning at Time 0.
- Because the Relative analysis is based on the time since the start date (usually in days), the statistics are computed at each and every observed event/censor time.
We leave you with an animation of time to death for Nicardipine patients.
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.