Jefford, Clayton N. "Did Ignatius of Antioch Know the Didache?" in Jefford, Clayton (editor). The Didache in Context: essays on its text, history, and transmission. Leiden: Brill, 1995, 330-351.
Jefford immediately grants that chronological and geographical information are salient factors in an analysis of literary influence, and that we know relatively little of either in the case of the Didache (Jefford 1995, 331). Yet the evidence for the Didache being in existence prior to Ignatius' death about 120 C.E. is fairly persuasive, and Antioch, the home of Ignatius, is a strong contender for the place of composition of the Didache. Jefford then notes that there has been virtually no study of a relationship between Ignatius and the Didache, and that on the surface of Ignatius' wriitings there is no strong suggestion of one (Jefford 1995, 332). To proceed with his evaluation, Jefford considers how Ignatius used his sources of information (Jefford 1995, 332). When Ignatius draws from the Old T estament, he may provide a quotation of the Septuagint, which he normally introduces with "as it is written" (Jefford 1995, 333). He makes some clear allusions as well, without the introduction. Jefford concludes that Ignatius' use of Hebrew texts is not frequent or rigorous (Jefford 1995, 335).
Ignatius uses themes and occasional phrases from Luke's account of the post-resurrection apperance of Jesus, as well as numerous phrases and concepts preserved in John (Jefford 1995, 336-337). However, Ignatius uses ideas and language which connect with Matthew in a relatively systematic way (Jefford 1995, 338-339). His use of Matthew is not through quotations but mostly through allusions and the construction of arguments which work in the same way as those of Matthew. Jefford notes that Ignatius uses the same procedure in his references to Pauline ideas (Jefford 1995, 340).
Ignatius tends to use early Christian traditions in much the same way, through citing an idea, then drawing a conclusion from that idea. Jefford provides three examples of this process (Jefford 1995, 341).
Jefford, having concluded that Ignatius applied information known to him, often by allusions, proceeds to consider Ignatius' possible knowledge of the Didache. Ignatius did speak in terms of a dualistic world, with a way of life and a way of death, similar to the Didache's Two Ways material (Jefford 1995, 343). Ignatius urges reception and compliance to bishops, a theme applied to prophets in the Didache. In both instances the speaker of God's Word is to be received "as the Lord" and to be shown high levels of respect (Jefford 1995, 344). Both the Didachist and Ignatius refer to the shared Lord's table as bearing food of immortality. Jefford notes that the term used for immortality is rarely used, but is used in the same way by both authors (Jefford 1995, 345). Both authors view society as bearing heirarchies which parallel the positional levels of authority described of the Godhead. Jefford takes this to be significant, even though the human heirarchy referred to differs (Jefford 1995, 346). In both authors there is a clear need to evaluate the teachings which are brought to the community (Jefford 1995, 346). Both authors are clear that worship centers around the Lord's Day, and both use a specific and rarely used term (κυριακή) for it (Jefford 1995, 347). Finally, both authors make specific reference to appointing leaders "worthy of the Lord." Jefford finds they use the language in very similar ways. (Jefford 1995, 348).
Jefford concludes that while it is not possible to prove that Ignatius knew the Didache, it is certainly reasonable to expect that he knew some of the material for it or which was adapted for use in it (Jefford 1995, 350).