Ronald Syme's The Roman Revolution, our upcoming chat subject, makes extensive use of prosopography (from prosopon, the Greek word for "character" or "person," together with graphein, the Greek verb "to write"), as defined by G.W. Bowersock:
"the cumulative study of the careers of individual people as a means of escaping from a more abstract, impressionistic, and doctrinaire historiography."
Dictionaries describe it as "a study that identifies and relates a group of persons or characters within a particular historical or literary context," or "a collection of biographical sketches used by social and political historians studying a particular historical period."
Bingley steered me to the OCD, which has probably the best definition and description in the context of Roman history I have seen. While Syme seems to be the first one in the English-speaking world to use this method, he followed German predecessors, Friedrich Münzer, E. Groag, and the first edition of Prosopographia Imperii Romani,* begun in 1897. Another well-known practitioner was H.H. Scullard. The method has its detractors and skeptics, but the OCD entry argues for "sophisticated and flexible use."
The OCD includes a small bibliography. I found plenty of citations online of L. Stone, 'Prosopography' at Daedalus, 1971, but cannot find access to the actual paper. Of the other four articles listed, I found only Prosopography: Payoffs and Pitfalls, T. F. Carney, Phoenix > Vol. 27, No. 2 (Summer, 1973), pp. 156-179, at JSTOR (limited access).
There is also Syme's rather pricey The Augustan Aristocracy, of which several reviews can be found on JSTOR.
* The Prosopographia Imperii Romani (PIR) is a dictionary of names containing the biographical data of Roman officials. The prosopography's main objective is to present a comprehensive listing of the ruling classes in the Roman Empire in its early and high stages. It covers the period starting with the Battle of Actium in 31 BC, which saw the final establishment of a monarchic system in Rome, and ends with the reign of Diocletian (284-305). To date, some 15.000 persons have been registered. The PIR is published entirely in Latin.