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: The addition of enalapril to conventional therapy in patients with severe congestive heart failure can reduce mortality and improve symptoms, and the effect seems to be due to a reduction in death from progression of heart failure.
Abstract: To evaluate the influence of the angiotensin-converting enzyme inhibitor, enalapril (2.5 to 40 mg/day), on the prognosis of severe congestive heart failure, defined as New York Heart Association functional class IV, a double-blind study was undertaken in which 253 patients were randomized to receive either placebo (n = 126) or enalapril (n = 127) in addition to conventional treatment, including vasodilators. Follow-up averaged 188 days (range 1 day to 20 months). The reduction in crude mortality within 6 months (primary objective) was 40% in the enalapril-treated group (from 44 to 26%, p = 0.002) and within 1 year 31% (p = 0.001). By the end of the study, 68 subjects in the placebo group and 50 in the enalapril group had died--a reduction of 27% (p = 0.003). The entire reduction in total mortality (50%) was found in patients dying from progressive heart failure, whereas no difference was seen in the incidence of sudden cardiac death. There was a significant improvement in New York Heart Association classification in the enalapril group, together with a reduction in heart size and a reduced requirement for other heart failure medication. It is concluded that the addition of enalapril to conventional therapy in patients with severe congestive heart failure can reduce mortality and improve symptoms. The effect seems to be due to a reduction in death from progression of heart failure.
4,328 citations
TL;DR: Management of atrial fibrillation with the rhythm-control strategy offers no survival advantage over the rate- control strategy, and there are potential advantages, such as a lower risk of adverse drug effects, with the rate -control strategy.
Abstract: Background There are two approaches to the treatment of atrial fibrillation: one is cardioversion and treatment with antiarrhythmic drugs to maintain sinus rhythm, and the other is the use of rate-controlling drugs, allowing atrial fibrillation to persist. In both approaches, the use of anticoagulant drugs is recommended. Methods We conducted a randomized, multicenter comparison of these two treatment strategies in patients with atrial fibrillation and a high risk of stroke or death. The primary end point was overall mortality. Results A total of 4060 patients (mean [+/-SD] age, 69.7+/-9.0 years) were enrolled in the study; 70.8 percent had a history of hypertension, and 38.2 percent had coronary artery disease. Of the 3311 patients with echocardiograms, the left atrium was enlarged in 64.7 percent and left ventricular function was depressed in 26.0 percent. There were 356 deaths among the patients assigned to rhythm-control therapy and 310 deaths among those assigned to rate-control therapy (mortality at five years, 23.8 percent and 21.3 percent, respectively; hazard ratio, 1.15 [95 percent confidence interval, 0.99 to 1.34]; P=0.08). More patients in the rhythm-control group than in the rate-control group were hospitalized, and there were more adverse drug effects in the rhythm-control group as well. In both groups, the majority of strokes occurred after warfarin had been stopped or when the international normalized ratio was subtherapeutic. Conclusions Management of atrial fibrillation with the rhythm-control strategy offers no survival advantage over the rate-control strategy, and there are potential advantages, such as a lower risk of adverse drug effects, with the rate-control strategy. Anticoagulation should be continued in this group of high-risk patients.
3,988 citations
TL;DR: HR variability remained a significant predictor of mortality after adjusting for clinical, demographic, other Holter features and ejection fraction, and a hypothesis to explain this finding is that decreased HR variability correlates with increased sympathetic or decreased vagal tone, which may predispose to ventricular fibrillation.
Abstract: A high degree of heart rate (HR) variability is found in compensated hearts with good function, whereas HR variability can be decreased with severe coronary artery disease, congestive heart failure, aging and diabetic neuropathy. To test the hypothesis that HR variability is a predictor of long-term survival after acute myocardial infarction (AMI), the Holter tapes of 808 patients who survived AMI were analyzed. Heart rate variability was defined as the standard deviation of all normal RR intervals in a 24-hour continuous electrocardiogram recording made 11 +/- 3 days after AMI. In all patients demographic, clinical and laboratory variables were measured at baseline. Mean follow-up time was 31 months. Of all Holter variables measured, HR variability had the strongest univariate correlation with mortality. The relative risk of mortality was 5.3 times higher in the group with HR variability of less than 50 ms than the group with HR variability of more than 100 ms. HR variability remained a significant predictor of mortality after adjusting for clinical, demographic, other Holter features and ejection fraction. A hypothesis to explain this finding is that decreased HR variability correlates with increased sympathetic or decreased vagal tone, which may predispose to ventricular fibrillation.
3,902 citations
TL;DR: In this article, five subclasses defined by the estimated propensity score are constructed that balance 74 covariates, and thereby provide estimates of treatment effects using direct adjustment, and these subclasses are applied within sub-populations, and model-based adjustments are then used to provide estimates for treatment effects within these sub-population.
Abstract: The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates. Subclassification on an estimated propensity score is illustrated, using observational data on treatments for coronary artery disease. Five subclasses defined by the estimated propensity score are constructed that balance 74 covariates, and thereby provide estimates of treatment effects using direct adjustment. These subclasses are applied within sub-populations, and model-based adjustments are then used to provide estimates of treatment effects within these sub-populations. Two appendixes address theoretical issues related to the application: the effectiveness of subclassification on the propensity score in removing bias, and balancing properties of propensity scores with incomplete data.
3,860 citations
TL;DR: In this article, the authors studied whether prophylactic therapy with an implanted cardioverter-defibrillator, as compared with conventional medical therapy, would improve survival in this high-risk group of patients.
Abstract: Background Unsustained ventricular tachycardia in patients with previous myocardial infarction and left ventricular dysfunction is associated with a two-year mortality rate of about 30 percent. We studied whether prophylactic therapy with an implanted cardioverter–defibrillator, as compared with conventional medical therapy, would improve survival in this high-risk group of patients. Methods Over the course of five years, 196 patients in New York Heart Association functional class I, II, or III with prior myocardial infarction; a left ventricular ejection fraction <0.35; a documented episode of asymptomatic unsustained ventricular tachycardia; and inducible, nonsuppressible ventricular tachyarrhythmia on electrophysiologic study were randomly assigned to receive an implanted defibrillator (n = 95) or conventional medical therapy (n = 101). We used a two-sided sequential design with death from any cause as the end point. Results The base-line characteristics of the two treatment groups were similar. During...
3,843 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