Survival analysis was used to assess likelihood as well as timing of substance involvement, separately for each substance use variable (alcohol use, alcohol intoxication, cigarette use, regular smoking, cannabis use, and other illicit drug use). In preliminary descriptive analyses, cumulative failure curves were estimated using the Kaplan-Meier survivor function (Kaplan and Meier, 1958), with log-rank tests to identify significant differences in equality of survivor functions by race/ethnicity. While monozygotic (MZ) twinning occurs at random, dizygotic (DZ) twining has been linked to both maternal age and socioeconomic status (Bulmer, 1970); thus, to identify limitations to the generalizability of twin data, log-ranks tests were also conducted for zygosity. Cox proportional hazards regression was used to examine risk of substance involvement without and with adjustment for control variables. The Efron approximation (Efron, 1977) was applied for survival ties. Because age of onset of AD is available from parent self-report only, parental alcoholism was modeled as a time-invariant predictor. Parental separation was modeled as time-varying to ensure onset before or at the same time as initiation of substance involvement. This was achieved using person-year
