Edward L. Kaplan

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.

Soft-tissue infections are common, generally of mild to modest severity, and are easily treated with a variety of agents. An etiologic diagnosis of simple cellulitis is fre-quently difficult and generally unnecessary for patients with mild signs and symptoms of illness. Clinical as-sessment of the severity of infection is crucial, and sev-eral classification schemes and algorithms have been proposed to guide the clinician [1]. However, most clinical assessments have been developed from either retrospective studies or from an author’s own “clinical experience, ” illustrating the need for prospective studies with defined measurements of severity coupled to man-agement issues and outcomes. Until then, it is the recommendation of this com-mittee that patients with soft-tissue infection accom-

There is concern that group A streptococci, which have caused less serious infections in developed countries in recent decades, may be acquiring greater virulence. We describe 20 patients from the Rocky Mountain region who had group A streptococcal infections from 1986 to 1988 that were remarkable for the severity of local tissue destruction and life-threatening systemic toxicity. Among the 20 patients (median age, 36), necrotizing fasciitis with or without myositis was the most common soft-tissue infection (55 percent). Nineteen patients (95 percent) had shock, 16 (80 percent) had renal impairment, and 11 (55 percent) had acute respiratory distress syndrome. The mortality rate was 30 percent. All patients but 1 had positive tissue cultures for Streptococcus pyogenes; 12 had positive blood cultures. Most of the patients had no underlying disease; 2 used intravenous drugs. Strains of group A beta-hemolytic streptococci isolated from 10 patients were not of a single M or T type; however, 8 of the 10 strains produced pyrogenic exotoxin A (scarlet fever toxin A, a classic erythrogenic toxin), which has rarely been observed in recent years. From our study of this cluster of severe streptococcal infections with a toxic shock-like syndrome, we conclude that in our region, more virulent group A streptococci have reappeared that produce the pyrogenic toxin A associated with scarlet fever.