Nonparametric Estimation from Incomplete Observations
01 Jun 1958-Journal of the American Statistical Association (Taylor & Francis Group)-Vol. 53, Iss: 282, pp 457-481
TL;DR: In this article, the product-limit (PL) estimator was proposed to estimate the proportion of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t).
Abstract: In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss). Losses may be either accidental or controlled, the latter resulting from a decision to terminate certain observations. In either case it is usually assumed in this paper that the lifetime (age at death) is independent of the potential loss time; in practice this assumption deserves careful scrutiny. Despite the resulting incompleteness of the data, it is desired to estimate the proportion P(t) of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t). The observation for each item of a suitable initial event, marking the beginning of its lifetime, is presupposed. For random samples of size N the product-limit (PL) estimate can be defined as follows: L...
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TL;DR: None of four chemotherapy regimens offered a significant advantage over the others in the treatment of advanced non-small-cell lung cancer.
Abstract: Background We conducted a randomized study to determine whether any of three chemotherapy regimens was superior to cisplatin and paclitaxel in patients with advanced non–small-cell lung cancer. Methods A total of 1207 patients with advanced non–small-cell lung cancer were randomly assigned to a reference regimen of cisplatin and paclitaxel or to one of three experimental regimens: cisplatin and gemcitabine, cisplatin and docetaxel, or carboplatin and paclitaxel. Results The response rate for all 1155 eligible patients was 19 percent, with a median survival of 7.9 months (95 percent confidence interval, 7.3 to 8.5), a 1-year survival rate of 33 percent (95 percent confidence interval, 30 to 36 percent), and a 2-year survival rate of 11 percent (95 percent confidence interval, 8 to 12 percent). The response rate and survival did not differ significantly between patients assigned to receive cisplatin and paclitaxel and those assigned to receive any of the three experimental regimens. Treatment with cisplatin...
4,781 citations
TL;DR: Cetuximab has clinically significant activity when given alone or in combination with irinotecan in patients with ir inotecans-refractory colorectal cancer.
Abstract: background The epidermal growth factor receptor (EGFR), which participates in signaling pathways that are deregulated in cancer cells, commonly appears on colorectal-cancer cells. Cetuximab is a monoclonal antibody that specifically blocks the EGFR. We compared the efficacy of cetuximab in combination with irinotecan with that of cetuximab alone in metastatic colorectal cancer that was refractory to treatment with irinotecan. methods We randomly assigned 329 patients whose disease had progressed during or within three months after treatment with an irinotecan-based regimen to receive either cetuximab and irinotecan (at the same dose and schedule as in a prestudy regimen [218 patients]) or cetuximab monotherapy (111 patients). In cases of disease progression, the addition of irinotecan to cetuximab monotherapy was permitted. The patients were evaluated radiologically for tumor response and were also evaluated for the time to tumor progression, survival, and side effects of treatment. results The rate of response in the combination-therapy group was significantly higher than that in the monotherapy group (22.9 percent [95 percent confidence interval, 17.5 to 29.1 percent] vs. 10.8 percent [95 percent confidence interval, 5.7 to 18.1 percent], P=0.007). The median time to progression was significantly greater in the combination-therapy group (4.1 vs. 1.5 months, P<0.001 by the log-rank test). The median survival time was 8.6 months in the combination-therapy group and 6.9 months in the monotherapy group (P=0.48). Toxic effects were more frequent in the combinationtherapy group, but their severity and incidence were similar to those that would be expected with irinotecan alone. conclusions Cetuximab has clinically significant activity when given alone or in combination with irinotecan in patients with irinotecan-refractory colorectal cancer.
4,625 citations
TL;DR: In this paper, a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups is presented. The tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest.
Abstract: In this paper, for right censored competing risks data, a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups. The tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest. Asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory. It is proposed that weight functions very similar to those for the $G^p$ tests from ordinary survival analysis be used. Simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples.
4,469 citations
TL;DR: There was a significant AF-sex interaction: AF diminished the female advantage in survival and AF remained significantly associated with excess mortality, with about a doubling of mortality in both sexes in subjects free of valvular heart disease and preexisting cardiovascular disease.
Abstract: Background—Atrial fibrillation (AF) causes substantial morbidity. It is uncertain whether AF is associated with excess mortality independent of associated cardiac conditions and risk factors. Methods and Results—We examined the mortality of subjects 55 to 94 years of age who developed AF during 40 years of follow-up of the original Framingham Heart Study cohort. Of the original 5209 subjects, 296 men and 325 women (mean ages, 74 and 76 years, respectively) developed AF and met eligibility criteria. By pooled logistic regression, after adjustment for age, hypertension, smoking, diabetes, left ventricular hypertrophy, myocardial infarction, congestive heart failure, valvular heart disease, and stroke or transient ischemic attack, AF was associated with an OR for death of 1.5 (95% CI, 1.2 to 1.8) in men and 1.9 (95% CI, 1.5 to 2.2) in women. The risk of mortality conferred by AF did not significantly vary by age. However, there was a significant AF-sex interaction: AF diminished the female advantage in survi...
4,390 citations
TL;DR: Cardiac resynchronization results in significant clinical improvement in patients who have moderate-to-severe heart failure and an intraventricular conduction delay.
Abstract: Background Previous studies have suggested that cardiac resynchronization achieved through atrial-synchronized biventricular pacing produces clinical benefits in patients with heart failure who have an intraventricular conduction delay. We conducted a double-blind trial to evaluate this therapeutic approach. Methods Four hundred fifty-three patients with moderate-to-severe symptoms of heart failure associated with an ejection fraction of 35 percent or less and a QRS interval of 130 msec or more were randomly assigned to a cardiac-resynchronization group (228 patients) or to a control group (225 patients) for six months, while conventional therapy for heart failure was maintained. The primary end points were the New York Heart Association functional class, quality of life, and the distance walked in six minutes. Results As compared with the control group, patients assigned to cardiac resynchronization experienced an improvement in the distance walked in six minutes (+39 vs. +10 m, P=0.005), functional clas...
4,329 citations
References
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24 May 1950
919 citations
"Nonparametric Estimation from Incom..." refers methods in this paper
...Berkson and Gage [3] have called it the "ad-hoc" method....
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...[4] Berkson, J., and Gage, R. P., "Survival curve for cancer patients following treatment," Journal of the American Statistical Association, 47 (1952), 501-15....
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...[31 Berkson, J., and Gage, R. P., "Calculation of survival rates for cancer," Proceedings of the Staff Meetings of the Mayo Clinic, 25 (1950), 270-86....
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TL;DR: A simple function, in terms of two physically meaningful parameters, has been evolved, which fits survivorship data very well and can be used to compare succinctly the mortality of two groups, different in respect of treatment, type of cancer, or other characteristics.
Abstract: On the basis of experience with calculated survivorships of patients following treatment for cancer, a simple function, in terms of two physically meaningful parameters, has been evolved, which fits such survivorship data very well. These two parameters can be used to compare succinctly the mortality of two groups, different in respect of treatment, type of cancer, or other characteristics. The parameters are c (“cured”), which represents the proportion of the population which is subject only to “normal” death rates, and β, which is the death rate from the cancer, to which the rest of the population [not “cured,” (1–c)] is subject. Thus if one treatment is characterized by c 1 = 0.30, β 1 = 0.25, another by c 2 = 0.20, β 2 = 0.15, this could be interpreted as meaning that while the first treatment “cured” a larger proportion of the population than did the second treatment, it did not ameliorate the deaths attributable to cancer in the patients not cured as much as did the second treatment. If l T...
785 citations
TL;DR: The rationale and statistical techniques employed in the analysis of some failure data obtained from operations performed by machines and people are summarized and the agreement between theory and data is evaluated.
Abstract: This paper summarizes the rationale and statistical techniques employed in the analysis of some failure data obtained from operations performed by machines and people. These data are compared to frequency distributions arising from either an exponential or a normal theory of failure. The agreement between theory and data is evaluated.
419 citations