Paul Meier

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: List and label the N observed lifetimes (whether to death or loss) in order of increasing magnitude, so that one has 0≤t 1ǐ≤t 2ǐ≤ … ≤t N ǐ. Then P(t)= II. [(N – r)/(N – r + 1)], where r assumes those values for which tr ≤t and for which tr ǐ measures the time to death. This estimate is the distribution, unrestricted as to form, which maximizes the likelihood of the observations. Other estimates that are discussed are the actuarial estimates (which are also products, but with the number of factors usually reduced by grouping); and reduced-sample (RS) estimates, which require that losses not be accidental, so that the limits of observation (potential loss times) are known even for those items whose deaths are observed. When no losses occur at ages less than t, the estimate of P(t) in all cases reduces to the usual binomial estimate, namely, the observed proportion of survivors.

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: List and label the N observed lifetimes (whether to death or loss) in order of increasing magnitude, so that one has 0≤t 1ǐ≤t 2ǐ≤ … ≤t N ǐ. Then P(t)= II. [(N – r)/(N – r + 1)], where r assumes those values for which tr ≤t and for which tr ǐ measures the time to death. This estimate is the distribution, unrestricted as to form, which maximizes the likelihood of the observations. Other estimates that are discussed are the actuarial estimates (which are also products, but with the number of factors usually reduced by grouping); and reduced-sample (RS) estimates, which require that losses not be accidental, so that the limits of observation (potential loss times) are known even for those items whose deaths are observed. When no losses occur at ages less than t, the estimate of P(t) in all cases reduces to the usual binomial estimate, namely, the observed proportion of survivors.

BACKGROUND: Implantable left ventricular assist devices have benefited patients with end-stage heart failure as a bridge to cardiac transplantation, but their long-term use for the purpose of enhancing survival and the quality of life has not been evaluated. METHODS: We randomly assigned 129 patients with end-stage heart failure who were ineligible for cardiac transplantation to receive a left ventricular assist device (68 patients) or optimal medical management (61). All patients had symptoms of New York Heart Association class IV heart failure. RESULTS: Kaplan-Meier survival analysis showed a reduction of 48 percent in the risk of death from any cause in the group that received left ventricular assist devices as compared with the medical-therapy group (relative risk, 0.52; 95 percent confidence interval, 0.34 to 0.78; P=0.001). The rates of survival at one year were 52 percent in the device group and 25 percent in the medical-therapy group (P=0.002), and the rates at two years were 23 percent and 8 percent (P=0.09), respectively. The frequency of serious adverse events in the device group was 2.35 (95 percent confidence interval, 1.86 to 2.95) times that in the medical-therapy group, with a predominance of infection, bleeding, and malfunction of the device. The quality of life was significantly improved at one year in the device group. CONCLUSIONS: The use of a left ventricular assist device in patients with advanced heart failure resulted in a clinically meaningful survival benefit and an improved quality of life. A left ventricular assist device is an acceptable alternative therapy in selected patients who are not candidates for cardiac transplantation.

BACKGROUND: Because left ventricular assist devices have recently been approved by the Food and Drug Administration to support the circulation of patients with end-stage heart failure awaiting cardiac transplantation, these devices are increasingly being considered as a potential alternative to biologic cardiac replacement. The Randomized Evaluation of Mechanical Assistance for the Treatment of Congestive Heart Failure (REMATCH) trial is a multicenter study supported by the National Heart, Lung, and Blood Institute to compare long-term implantation of left ventricular assist devices with optimal medical management for patients with end-stage heart failure who require, but do not qualify to receive cardiac transplantation. METHODS: We discuss the rationale for conducting REMATCH, the obstacles to designing this and other randomized surgical trials, the lessons learned in conducting the multicenter pilot study, and the features of the REMATCH study design (objectives, target population, treatments, end points, analysis, and trial organization). CONCLUSIONS: We consider what will be learned from REMATCH, expectations for expanding the use of left ventricular assist devices, and future directions for assessing clinical procedures.