Marschner I C
Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115.
Stat Med. 1994;13(19-20):1959-74. doi: 10.1002/sim.4780131908.
Estimation of HIV incidence by the method of back-projection typically uses data on the time of diagnosis of AIDS cases, together with known information about the incubation distribution of AIDS. This paper discusses back-projection using auxiliary data on AIDS cases, particularly the time of first positive HIV test. We discuss the possibility that certain types of auxiliary data, including time of first positive test, can be useful in back-projection because they provide extra information about the incubation period of AIDS cases. Under a back-projection model, theoretical efficiency calculations are given comparing back-projection with and without the time of first positive HIV test of AIDS cases. These calculations suggest that such data have the potential to significantly improve HIV incidence estimates, particularly in the recent past. Smoothed non-parametric estimates of both HIV incidence and time-dependent testing rates are described. These can be obtained using the EM algorithm, in conjunction with a smoothing step or a penalized likelihood. The benefit of these methods in practice needs to be assessed as such data become available.
通过反向推算方法估计艾滋病毒发病率通常使用艾滋病病例的诊断时间数据，以及有关艾滋病潜伏期分布的已知信息。本文讨论了使用艾滋病病例的辅助数据进行反向推算，特别是首次艾滋病毒检测呈阳性的时间。我们探讨了某些类型的辅助数据，包括首次检测呈阳性的时间，在反向推算中可能有用的可能性，因为它们提供了有关艾滋病病例潜伏期的额外信息。在反向推算模型下，给出了理论效率计算，比较了有和没有艾滋病病例首次艾滋病毒检测呈阳性时间的反向推算。这些计算表明，此类数据有可能显著改善艾滋病毒发病率估计，特别是在最近一段时间。描述了艾滋病毒发病率和随时间变化的检测率的平滑非参数估计。这些可以使用期望最大化（EM）算法，结合平滑步骤或惩罚似然来获得。随着此类数据的可得，需要评估这些方法在实际中的益处。
