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Bigsby has written extensively on American theatre, and in particular has published widely on the playwright Arthur Miller. His books on Miller include, "Arthur Miller &amp; Company" (1990), "The Cambridge Companion to Arthur Miller" (1997), "Arthur Miller: A Critical Study" (2005), and "Remembering Arthur Miller" (2005). In November 2008, Bigsby published the first volume of his biography of Miller, based on boxes of papers Miller made available to him before he died in 2005, as well as countless interviews and conversations during a friendship with the playwright that lasted over three decades. The second volume appeared three years later. The biography was serialised in "The Daily Telegraph" and was "Book of the Week" on BBC Radio 4.