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We show that the preferred estimator equals a Greenwood\u2010type estimator that has been derived as a recursion formula using counting processes and martingales in a more general multistate framework. We also extend previous simulation studies on estimating the variance of the Aalen\u2013Johansen estimator in small samples to left\u2010truncated observation schemes, which may conveniently be handled within the counting processes framework. This investigation is motivated by a real data example on spontaneous abortion in pregnancies exposed to coumarin derivatives, where both competing risks and left\u2010truncation have recently been shown to be crucial methodological issues (Meister and Schaefer (2008), <jats:italic>Reproductive Toxicology<\/jats:italic> <jats:bold>26<\/jats:bold>, 31\u201335). Multistate\u2010type software and data are available online to perform the analyses. The Greenwood\u2010type estimator is recommended for use in practice.<\/jats:p>","DOI":"10.1002\/bimj.200900039","type":"journal-article","created":{"date-parts":[[2010,2,5]],"date-time":"2010-02-05T14:09:27Z","timestamp":1265378967000},"page":"126-137","source":"Crossref","is-referenced-by-count":53,"title":["A Note on Variance Estimation of the Aalen\u2013Johansen Estimator of the Cumulative Incidence Function in Competing Risks, with a View towards Left\u2010Truncated Data"],"prefix":"10.1002","volume":"52","author":[{"given":"Arthur","family":"Allignol","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Schumacher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan","family":"Beyersmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2010,2,17]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344198"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68560-1"},{"key":"e_1_2_8_4_1","first-page":"141","article-title":"An empirical transition matrix for non\u2010homogeneous Markov chains based on censored observations","volume":"5","author":"Aalen O.","year":"1978","journal-title":"Scandinavian Journal of Statistics"},{"key":"e_1_2_8_5_1","unstructured":"Allignol A.(2008).etm: Empirical Transition Matrix. 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