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## KEY CONCEPTS

KEY CONCEPTS

• When research involves time-related variables, such as survival and recurrence, we generally do not know the outcome for all patients at the time the study is published, so these outcomes are called censored.

• Observations are doubly censored when not all patients enter the study at the same time.

• An example of why special methods are needed to analyze survival data helps illustrate the logic behind them.

• Life table or actuarial methods were developed to show survival curves; although generally surpassed by Kaplan–Meier curves, they occasionally appear in the literature.

• Survival analysis gives patients credit for how long they have been in the study, even if the outcome has not yet occurred.

• The Kaplan–Meier procedure is the most commonly used method to illustrate survival curves.

• Estimates of survival are less precise as the time from entry into the study becomes longer, because the number of patients in the study decreases.

• Survival curves can also be used to compare survival in two or more groups.

• The logrank statistic is one of the most commonly used methods to learn if two curves are significantly different.

• The hazard ratio is similar to the odds ratio; the difference is that the hazard ratio compares risk over time, while the odds ratio examines risk at a given time.

• The Mantel–Haenszel statistic is also used to compare curves, not just survival curves.

• Several versions of the logrank statistic exist. The logrank statistic assumes that the risk of the outcome is the constant over time.

• The Mantel–Haenszel statistic essentially combines a number of 2 × 2 tables for an overall measure of difference.

• The hazard function gives the probability that an outcome will occur in a given period, assuming that the outcome has not occurred during previous periods.

• The intention-to-treat principle states that subjects are analyzed in the group to which they were assigned. It minimizes bias when there are treatment crossovers or dropouts.

## PRESENTING PROBLEMS

### Presenting Problem

Metastatic colorectal cancer may be treated by regorafenib alone or regorafenib in combination with chemotherapy. Lin et al (2018) studied the survival curves for patients on each treatment. They analyzed data from 61 patients that completed the study: 34 on regorafenib combined with chemotherapy and 27 received regorafenib alone.

The full article may be accessed here:

## PURPOSE OF THE CHAPTER

Many studies in medicine are designed to determine whether a new medication, a new treatment, or a new procedure will perform better than the one in current use. Although measures of short-term effects are of interest with efforts to provide more ...

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