Prism offers two choices:

1.The symmetrical method was the only method offered in Prism 4 and earlier, and is now offered only for compatibility. It uses the method of Greenwood, and we do not recommend it.

2.The asymmetrical method is more accurate and recommended. It is explained on page 42 and 43 of Machin (1). That book does not give a name or reference for the method, but the idea is that it first performs a transform (square root and logarithm) that makes the uncertainty of survival close to Gaussian. It then computes the standard error and a symmetrical 95% CI on this transformed scale. Finally, it back-transforms the confidence limits back to the original scale

Survival analysis computes median survival with its confidence interval. The reason for this is that the median survival time is completely defined once the survival curve descends past 50%, even if many subjects have yet to experience the event of interest. And the median survival is defined even if data from some subjects were censored.

In contrast, the mean survival time is simply not defined until every subject experiences the event of interest. Only when you know the survival time for each subject (i.e. no subjects were censored) can this value be calculated. These conditions occur in only a small number of studies, so Prism does not compute the mean survival time.

But there is an easy workaround. If you know the survival times for each subject, simply enter them into a column table and perform the Descriptive statistics analysis to calculate the mean and confidence interval of this set of values.

Prism can create Kaplan-Meier survival curves - and compare these curves using the logrank test (or the Gehan-Breslow-Wilcoxon test) - only from raw data in a survival data table.

If you already know the probability of survival at each time point and would just like to make a graph, then you should not enter data into a survival data table. Instead, create an XY data table. Enter each of the time points as X values (numbers, not dates), and the corresponding survival probabilities for these time points as Y values (with no subcolumns). If you would also have information on the standard error for the survival probability at each time, you can format the XY data table to allow you to enter this information in subcolumns of the Y column using the format “Enter and plot error values already calculated elsewhere” with the option “Mean with SEM”.

Once the data are entered appropriately, you can polish the resulting graph. If you would like for the graph to include the staircase-style curve (traditional for survival curves), open the Format Graph dialog, and in the “Show connecting line/curve” section, select the Survival curve in the style dropdown menu.

If you enter survival percentages on an XY table, it will not be possible to perform survival calculations. You won’t be able to compute error bars or confidence bands, and won’t be able to compare survival curves using the tests that Prism offers.

If there are no censored observations

If you follow each subject until the event of interest occurs (the event is often death, but survival curves can track time until any one-time event), then the curve will eventually reach 0. At the time (X value) when the last subject experiences the event of interest, the probability of survival will be zero.

If all subjects are followed for exactly the same amount of time

If all subjects are followed for the same amount of time, the situation is easy. If one third of the subjects have yet to experience the event of interest by the end of the study, then the probability of survival is 33%.

If some subjects are censored along the way

If the observations for any subjects are censored, then the bottom point on the survival curve will not equal the fraction of subjects that make it to the end of the study without experiencing the event of interest.

Prior to censoring, a subject contributes to the fractional survival value. Afterward, she or he doesn't affect the calculations. At any given time, the survival probability value is the proportion of subjects followed that long who have survived.

Subjects whose observations are censored - either because they left the study, or because the study ended - can't contribute any information beyond the time of censoring. You don't know whether or not they would have experienced the event of interest after the time of censoring (or do know, but can't use the information because the experimental protocol was no longer being followed). So if any subjects are censored before the last time shown on the survival curve's X axis, the final survival probability shown on the survival graph will not correspond to the actual fraction of the subjects who did not experience the event of interest. That simple survival percentage that you can easily compute by hand is not meaningful, because not all the subjects were not followed for the same amount of time.

When will the survival curve drop to zero?

If the survival curve goes all the way down to 0% survival, that does not mean that every subject in the study experienced the event of interest. Some subjects may have been censored at earlier time points (either because they left the study, or because the study ended before they experienced the event of interest). The survival probability will drop to zero when the observation at the last time point is a subject that experiences the event of interest, and not one that is censored. If your data are sorted by X value (which Prism can do using Edit..Sort), the curve will descend to 0% survival if the last Y value is 1 (event of interest), and will end above 0% if the last Y value is 0 (censored).

In the example below, the event of interest is death. Four of the ten subjects die. But the survival curve descends to zero, not to 60%. Why? Because six subjects were censored between 1 and 27 months. We have no idea what would have happened had they stayed in the study until month 28. Since we don't know if they would have lived or died, their data simply doesn't count after the time of censoring (but definitely counts before that). At time 27, only one subject is still being followed, and she or he died at month 28, dropping the probability of survival down to zero.

Median survival is the time it takes to reach 50% survival. If more than 50% of the subjects are alive at the end of the study, then the median survival time is simply not defined.

The P value comes from the logrank test, which compares the entire curve, and works fine even if the survival probability is always greater than 50%. Two curves can be very different, even if they never decrease below 50% survival probability.

When Prism computes survival curves, it can also compute the 95% confidence interval at each time point (using two alternative methods). The methods are approximations, but can be interpreted like any confidence interval. You know the observed survival probability at a certain time in your study, and can be 95% confident (given a set of assumptions) that the confidence interval contains the true population value (which you could only know for sure if you had observations for every member of the studied population - if working with humans, this would mean every single person in existence).

When these confidence intervals are plotted as error bars (left graph below) there is no problem. Prism can also connect the ends of these error bars and create a shaded region (right graph below). This survival curve plots the survival of a sample of only seven individuals, so the confidence intervals are very wide.

The shaded region looks like hte confidence bands computed by linear and nonlinear regression, so it is tempting to interpret these regions as confidence bands. However, it is not correct to say that you can be 95% certain that these bands contain the entire survival curve. It is only correct to say that - at any time point - you can be 95% confident that the interval contains the true survival probability. The true survival curve (which you can’t know) may be within the confidence intervals at some time points and outside the confidence intervals at other time points.

It is possible (however, not with Prism) to compute the true confidence bands for survival curves, and these are wider than the confidence intervals shown above. In other words, confidence bands that are 95% certain to contain the entire survival curve at all time points are wider than confidence intervals for individual time points.

When analyzing survival data, Prism simply ignores any rows with X=0. The logic is simple. If alternative treatments begin at time zero, then a death at the moment treatment begins provides no information to help you decide which of two treatments is better. There is no requirement that X be an integer. If a death occurs half a day into treatment, and X values are tabulated in days, simply enter 0.5 for the elapsed time of observation for this subject.

Some fields (pediatric leukemia is one) do consider events at time zero to be valid. These studies do not simply track death, but track time until recurrence of the disease. But disease cannot recur until it first goes into remission. In the case of some pediatric leukemia trials, the treatment begins 30 days before time zero. Most of the patients are in remission at time zero. Then the patients are followed until death or the recurrence of the disease. But what about subjects who never go into remission? Some investigators consider these to be events at time zero. Some programs take into account the events at time zero, so the Kaplan-Meier survival curve starts with a survival probability of less than 100%. If 10% of the patients in one treatment group never went into remission, the survival curve would begin at Y=90% instead of 100%.

We have no changed Prism to account for events that occur at time zero for the following reasons:

•We have seen no scientific papers, and no textbooks, that explain what it means to analyze deaths at time zero. It seems far from standard

•It seems wrong to combine the answers to two very different questions in one survival curve: What fraction of patients go into remission? How long do those in remission stay in remission?

•If we included data with X=0, we are not sure that the results of the survival analysis (median survival times, hazard ratios, P values, etc.) would be meaningful

The fundamental problem is this: Survival analysis utilizes data expressed as the time that elapses prior to the occurrence of an event of interest. Often this event is earth. Often it is some other well-defined event that can only occur once per subject. Moreover, this event is defined to be something that could - in theory - occur to every participant in the trial given enough time. With these pediatric leukemia trials, the event is defined to be recurrence of the disease. But, of course, the disease cannot recur unless it first went into remission. So the survival analysis is really being used to track time elapsed until the occurrence of the second of two distinct events. That leads to the problem of how to analyze the data from patients who never go into remission (the first event never happens).

We are willing to reconsider our decision to ignore (rather than analyze) survival data entered with X=0. If you think we made the wrong decision, please let us know. Provide references if possible.

There is a simple workaround if you really want to analyze your data so deaths at time zero bring down the starting point below 100%. Simply enter some tiny value other than zero. For example, enter these values as X=0.000001. An alternative is to enter the data with X=0, and then use Prism’s transform analysis with this user-defined transformation:

X=IF(X=0, 0.000001, X)

In the results of this analysis, all of the X=0 values will be converted to X=0.000001. From that results table, click Analyze and choose Survival analysis.

Prism uses the Kaplan-Meier product limit method to compute survival probability. This is a standard method. The only trick is in accounting for censored observations.

Consider a simple example. You start with 16 individuals. Two were censored before the first event at 15 months. Because these two individuals were not considered to be in the “at risk” population when the first event occurred, they are not included in the survival probability calculations. Thus, the survival probability drops at 15 months from 100% (16/16=100%) down to 92.86% (13/14=92.86%). The denominator of 14 indicates that the number of individuals in the “at risk” population was only 14 after removing the two that were previously censored.

Seven more individuals were censored before the next event at 93 months. So of those that survived more than 15 months, we know that 83.3% (5/6=83.3%) were alive after 93 months. But this is a relative drop. To know the percent of people alive at 0 months who are still alive after 93 months, you must multiply 92.86% (the percentage of survival at the time of the first event) by 83.3% (the percentage of survival at the time of the second event) to get 77.38%. This is the survival probability that Prism would report at 93 months. This is why the Kaplan-Meier method is also referred to as the product limit method. More details on this method can be found on this page.