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Nonparametric estimation from queues arising in staggered entry clinical trials. (English) Zbl 0661.62033

Applied mathematics and computing, Trans. 5th Army Conf., West Point, NY 1987, ARO Rep. 88-1, 589-596 (1988).
[For the entire collection see Zbl 0649.00009.]
In clinical trials with staggered entries and fixed duration of study, patients enter at random epochs and are put on test. The objective is to study survival times from a principal cause A, but factors such as end of study or patient withdrawal make it impossible to observe the survival times (censoring).
We consider two different situations. (1) For some patients death may actually be from a cause other than A, say B (competing risks). It is desired to study the survival times associated with both causes A and B. (2) A certain number m (\(\geq 1)\) treatments are available and each entering patient is diagnosed and assigned to one of these treatments. The objective is to study the survival times from cause A under these treatments. These problems are formulated in terms of queueing models, for which it is desired to obtain nonparametric estimates of service time distributions.
We investigate an infinite server model to study case (1) and an m- station model for case (2). The input in both models is a point process. We observe the system over a finite time-interval [0,t], with t fixed. The data collected consist of the arrival epochs, service times of the customers who arrive during [0,t], with some of the service times partially observed, and (in Model 2) delays experienced by them before service. Our estimators are martingale estimators, for which we establish consistency and weak convergence (as \(t\to \infty)\) of the normalized difference to a Gaussian process. We present the results for Model 1. Work on Model 2 is in progress.

MSC:

62G05 Nonparametric estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)

Citations:

Zbl 0649.00009