Paraskevi Peristera: Computing crude and net probabilities in the analysis of multiple causes of failure: Illustration with cohabitation and marriage as competing risks in family initiation

Analysis of survival data with competing risks require an understanding of three types of probabilities of experiencing the event due to a specific cause: the crude probability - the probability of experiencing the event due to a specific cause in the presence of all other causes acting in a population; the partial crude probability - the probability of experiencing the event due to a specific cause when another cause (or causes) is eliminated from the population; and the net probability - the probability of experiencing the event due to a specific cause if that cause is the only cause in effect in the population. The net and partial crude probabilities cannot be estimated directly, but only through their relations with the crude probability. In this work, we adapt Chiang’s (1968; 1991) estimation procedure to family initiation among Swedish men where informal cohabitation and formal marriage are treated as competing risks. We illustrate the issues by estimating crude and net probabilities of marriage and investigate in which ages marriage gains more if cohabitation was eliminated and vice-versa. The resulting estimates may be of value in answering whether informal cohabitation is a prelude to marriage or a permanent substitute to it.