PROPHET StatGuide: Examining life table results to detect assumption violations

The problems detectable from the life table results themselves are generally related to problems due to lack of data.

Examining results for a life table analysis:

• Lack of independence of censoring: lack of independence of censoring
• Effects of grouping: problems caused by the time intervals used
• Many censored values: problems caused by a large number of censored values
• Special problems with small sample sizes
• Graphical results

Lack of independence of censoring:

Although the grouped nature of the data can mask systematic patterns in the censoring, you may be able to spot very strong patterns. For example, if there are many values censored earlier in the experiment rather than later, there may have been a change of conditions during the experiment. (For example, one physician may have withdrawn referred patients early on while other doctors did not.) If there was a relatively large number of censored values in a single interval, then the censorings may be related. (For example, a physician transfers to another hospital, and all referred patients suddenly leave the study.)

A common problem with a survival analysis experiment studying medical treatments is that patients who do not do well one or more of the treatments must be withdrawn from the study, so that sicker patients may be more likely to have censored survival times.

Effects of grouping:

One sign of potential problems with grouping is that the number of intervals is either so small that the assumption of constant survival rate within each time interval is unlikely to hold, or so large that the number of subjects in an interval drops to a small number. A common rule of thumb is: If the number of intervals can not be at least 8 to 10 without creating intervals with very small sample sizes, the life table results may not be reliable.

Many censored values:

If there are many censored values, the life table table estimates become less reliable, and the estimated variances may be considerably smaller than the actual variances. If many subjects are left alive at the end of the study, the study may simply not have continued long enough to give reliable estimates.

If many subjects are censored at approximately the same time, the possibility of a common cause should be considered. This would violate the assumption of independence of censoring and survival times.

Small sample sizes:

Small sample sizes tend to lead to small numbers of subjects within an interval, exacerbating the effects of grouping. High censoring rates also reduce the effective sample size. If the final interval(s) of a study contain only a few subjects, the life table estimates for those intervals are not reliable, and should not be given much weight.

Graphical results:

The graphs of the survival functions can point to possible parametric models for the life table survival data. Because the life table data are grouped, a plot will either be a step function or a piecewise linear graph connecting values at the midpoint of each interval. However, it is often possible to get an approximate idea of the shape of the underlying curve.

If the (negative) exponential model is appropriate, the graph of the log of the survival function (or the cumulative hazard function, which is -log(survival function)), against time should look like a straight line passing through the origin. If the Weibull distribution is appropriate, a graph of the log of the log of the survival function (or the log of the cumulative hazard function) against the log of time should look like a straight line.

If the plot of the hazard function against time is a horizontal line (constant hazard), then the survival distribution is likely to be negative exponential. A hazard function that starts at 0 at time 0, increases to a maximum value and then decreases (like an inverted bathtub) suggests the possibility of a log-normal or log-logistic survival distribution. A monotonically increasing hazard function may suggest a Poisson survival function.

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Last modified: February 20, 1997