• 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 Problem 1

Lung cancer is the leading cause of cancer deaths in men and in women between the ages of 15 and 64 years of age. Small-cell lung cancer accounts for 20–25% of all cases of lung cancer. At the time of diagnosis, 40% of the patients with small-cell cancer have disease confined to the thorax (limited disease) and 60% have metastases outside of the thorax (extensive disease). Current standard chemotherapy for extensive disease using a combination of cisplatin and etoposide yields a median survival of 8–10 months and a 2-year survival rate of 10%. Preliminary studies using a combination of cisplatin with irinotecan resulted in a median survival of 13.2 months. For this reason, Noda and colleagues (2002) at the Japan Clinical Oncology Group conducted a prospective, randomized clinical trial to compare irinotecan plus cisplatin with etoposide plus cisplatin. The primary endpoint was overall survival. Secondary endpoints included rates of complete and overall response. A complete response was defined as the disappearance of all clinical and radiologic evidence of a tumor ...

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