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 analysis of censored failure times is considered in this paper, where the hazard function is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time.
Abstract: The analysis of censored failure times is considered. It is assumed that on each individual arc available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.
28,264 citations
Cites background from "Nonparametric Estimation from Incom..."
...The functions (7) and (8) are maximum-likelihood estimates in the family of all possible distributions (Kaplan and Meier, 1958)....
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...…A(u)du}= 1I7I j1-i (8) u aO t(i)K (i For uncensored ata this is the usual sample survivor function; some of the asymptotic properties of (8) are given by Kaplan and Meier (1958) and by Efron (1967) and can be used to adapt to the censored case tests based on sample cumulative distribution function....
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...Kaplan and Meier (1958) gave a comprehensive review of earlier work and many new results....
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TL;DR: Lifetime prevalence estimates are higher in recent cohorts than in earlier cohorts and have fairly stable intercohort differences across the life course that vary in substantively plausible ways among sociodemographic subgroups.
Abstract: Context Little is known about lifetime prevalence or age of onset of DSM-IV disorders. Objective To estimate lifetime prevalence and age-of-onset distributions of DSM-IV disorders in the recently completed National Comorbidity Survey Replication. Design and Setting Nationally representative face-to-face household survey conducted between February 2001 and April 2003 using the fully structured World Health Organization World Mental Health Survey version of the Composite International Diagnostic Interview. Participants Nine thousand two hundred eighty-two English-speaking respondents aged 18 years and older. Main Outcome Measures Lifetime DSM-IV anxiety, mood, impulse-control, and substance use disorders. Results Lifetime prevalence estimates are as follows: anxiety disorders, 28.8%; mood disorders, 20.8%; impulse-control disorders, 24.8%; substance use disorders, 14.6%; any disorder, 46.4%. Median age of onset is much earlier for anxiety (11 years) and impulse-control (11 years) disorders than for substance use (20 years) and mood (30 years) disorders. Half of all lifetime cases start by age 14 years and three fourths by age 24 years. Later onsets are mostly of comorbid conditions, with estimated lifetime risk of any disorder at age 75 years (50.8%) only slightly higher than observed lifetime prevalence (46.4%). Lifetime prevalence estimates are higher in recent cohorts than in earlier cohorts and have fairly stable intercohort differences across the life course that vary in substantively plausible ways among sociodemographic subgroups. Conclusions About half of Americans will meet the criteria for a DSM-IV disorder sometime in their life, with first onset usually in childhood or adolescence. Interventions aimed at prevention or early treatment need to focus on youth.
17,213 citations
TL;DR: Amplification of the HER-2/neu gene was a significant predictor of both overall survival and time to relapse in patients with breast cancer, and had greater prognostic value than most currently used prognostic factors in lymph node-positive disease.
Abstract: The HER-2/neu oncogene is a member of the erbB-like oncogene family, and is related to, but distinct from, the epidermal growth factor receptor. This gene has been shown to be amplified in human breast cancer cell lines. In the current study, alterations of the gene in 189 primary human breast cancers were investigated. HER-2/neu was found to be amplified from 2- to greater than 20-fold in 30% of the tumors. Correlation of gene amplification with several disease parameters was evaluated. Amplification of the HER-2/neu gene was a significant predictor of both overall survival and time to relapse in patients with breast cancer. It retained its significance even when adjustments were made for other known prognostic factors. Moreover, HER-2/neu amplification had greater prognostic value than most currently used prognostic factors, including hormonal-receptor status, in lymph node-positive disease. These data indicate that this gene may play a role in the biologic behavior and/or pathogenesis of human breast cancer.
11,597 citations
TL;DR: Efficient methods of analysis of randomized clinical trials in which the authors wish to compare the duration of survival among different groups of patients are described.
Abstract: Part I of this report appeared in the previous issue (Br. J. Cancer (1976) 34,585), and discussed the design of randomized clinical trials. Part II now describes efficient methods of analysis of randomized clinical trials in which we wish to compare the duration of survival (or the time until some other untoward event first occurs) among different groups of patients. It is intended to enable physicians without statistical training either to analyse such data themselves using life tables, the logrank test and retrospective stratification, or, when such analyses are presented, to appreciate them more critically, but the discussion may also be of interest to statisticians who have not yet specialized in clinical trial analyses.
8,334 citations
TL;DR: Blockade of aldosterone receptors by spironolactone, in addition to standard therapy, substantially reduces the risk of both morbidity and death among patients with severe heart failure.
Abstract: Background and Methods Aldosterone is important in the pathophysiology of heart failure. In a double-blind study, we enrolled 1663 patients who had severe heart failure and a left ventricular ejection fraction of no more than 35 percent and who were being treated with an angiotensin-converting–enzyme inhibitor, a loop diuretic, and in most cases digoxin. A total of 822 patients were randomly assigned to receive 25 mg of spironolactone daily, and 841 to receive placebo. The primary end point was death from all causes. Results The trial was discontinued early, after a mean follow-up period of 24 months, because an interim analysis determined that spironolactone was efficacious. There were 386 deaths in the placebo group (46 percent) and 284 in the spironolactone group (35 percent; relative risk of death, 0.70; 95 percent confidence interval, 0.60 to 0.82; P<0.001). This 30 percent reduction in the risk of death among patients in the spironolactone group was attributed to a lower risk of both death from prog...
7,861 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