Figure 3. Kaplan-Meier and Weibull estimates of survival from the time of presentation, each with 95 per cent confidence limits probability until the time tjj is given by
4.5. Non-parametric survival functions: effect of late entry
If a summary of the survival of patients with complex pulmonary atresia from birth (see Figure 1) is required, a second problem emerges since patients do not come under observation until presentation; this is a general issue in attempting to model the natural history of disease.19 How we handle left-truncation or late entry depends on our understanding of the reporting of events for the patients under study. If, for example, we are sure that an event occurring at any point of their life would be reported to us, whether or not the patient was under active follow-up, then we could assume surveillance started at birth and individuals would not enter the cohort late. Such a situation is only plausible in well-defined communities with efficient notification procedures, and as such is rarely an appropriate assumption. Otherwise, avoidance of bias requires that we only include information gathered from patients while they are actively under surveillance.
Because we would usually assume that if an event happened to a patient before they 'presented' we would have been unaware of it, patients should not contribute to our estimate of survival until their age at presentation. An extreme example occurs when we only have information about adult patients - we cannot use them to say anything about survival in childhood. However, just as in right-censoring, we would like to assume non-informative late entry,20 meaning that individuals who present at a certain age are essentially comparable with those of the same age already being followed up; the reasonableness of this assumption is discussed in Section 4.10(a).
4.6. Worked example of survival with late entry: survival from birth (corresponding to Figure 1)
We shall summarize the whole survival experience from birth of all patients with complex pulmonary atresia based on our small selected data set (Figure 1).
Table IV sets out to compare overall survival estimated when all patients are allowed to contribute to the risk set from birth with the curve prepared only allowing patients to contribute to the risk set from presentation; the first is as if a patient's period of observation as illustrated in Figure 1 was extrapolated backwards to birth (appropriate under the optimistic assumption that all events on these patients since birth would have been reported to us). In each case the formula from Section 4.4 is used, with the appropriate size of risk set. Figure 4 plots the estimated survival
Figure 3. Kaplan-Meier and Weibull estimates of survival from the time of presentation, each with 95 per cent confidence limits
Table IV. Survival estimates: entry time 'birth' contrasted to entry time 'presentation'
Analysis specification: inclusion criteria outcome time origin entry time censoring rule survival time period of observation whole survival experience of patients in the dataset all patients death birth entry: (a) at birth
(b) at presentation withdrawn at end of study birth to death or censored entry to death or censored dead 0
(b) agepres to agelast
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