Jewell N P
Division of Biostatistics, University of California, Berkeley 94720.
Stat Med. 1994;13(19-20):2081-95. doi: 10.1002/sim.4780131917.
In many epidemiologic studies of human immunodeficiency virus (HIV) disease, interest focuses on the distribution of the length of the interval of time between two events. In many such cases, statistical estimation of properties of this distribution is complicated by the fact that observation of the times of both events is subject to intervalcensoring so that the length of time between the events is never observed exactly. Following DeGruttola and Lagakos, we call such data doubly-censored. Jewell, Malani and Vittinghoff showed that, with certain assumptions and for a particular doubly-censored data structure, non-parametric maximum likelihood estimation of the interval length distribution is equivalent to non-parametric estimation of a mixing distribution. Here, we extend these ideas to various other kinds of doubly-censored data. We consider application of the methods to various studies generated by investigations into the natural history of HIV disease with particular attention given to estimation of the distribution of time between infection of an individual (an index case) and transmission of HIV to their sexual partner.
在许多关于人类免疫缺陷病毒（HIV）疾病的流行病学研究中，关注点集中在两个事件之间时间间隔长度的分布上。在许多此类情况下，由于对两个事件发生时间的观察都受到区间删失的影响，以至于两个事件之间的时间长度从未被精确观测到，这使得对该分布特性的统计估计变得复杂。遵循德格鲁托拉和拉加科斯的说法，我们称此类数据为双重删失数据。朱厄尔、马拉尼和维廷霍夫表明，在某些假设条件下且针对特定的双重删失数据结构，区间长度分布的非参数最大似然估计等同于混合分布的非参数估计。在此，我们将这些想法扩展到其他各类双重删失数据。我们考虑将这些方法应用于对HIV疾病自然史调查所产生的各种研究中，特别关注个体（索引病例）感染HIV到将其传播给性伴侣之间时间分布的估计。
