Evaluation research using log-linear analysis of contingency tables

Abstract

Followup outcomes during a 3-year period after termination from treatment in the Drug Abuse Reporting Program (DARP) were analyzed for a sample of clients admitted to treatment in 1969-1972. Log-linear models were used to predict treatment outcomes in the first 6 months after DARP and to describe changes in drug use patterns across the 3-year followup period. In the prediction model analyses, age and race (black or white) were used to predict patterns of illicit drug use, return to treatment, and any employment in the first 6 months after leaving DARP treatment (Time 1). Under one set of causal assumptions (the recursive model), drug use in Time 1 was also considered a predictor of treatment and employment in Time 1, and treatment in Time 1 was considered a predictor of employment in Time 1. An alternative, nonrecursive, model was also analyzed in which it was assumed that drug use, treatment, and employment in Time 1 were reciprocally related to each other. In general the final recursive and nonrecursive prediction models selected included the same effects and were interpreted using expected odds and odds ratios. With one exception, all two-variable associations were found to be significant; the exception was that age was found to be independent of employment in Time 1. The only higher-order effect (or interaction) found to be significant indicated that age was a moderator of the association between drug use pattern and treatment reentry in Time 1. Log-linear models were also used to describe the changes in the pattern of drug use from Time 1 to Time 3 (the last 6 month of the 3-year followup period). These models were fit to two groups of persons--those who returned to drug abuse treatment between Time 1 and Time 3, and those who did not. Models of change found to be useful in describing these changes in drug use patterns included symmetry plus trend and quasi-independence. Among persons who changed their pattern of drug use from Time 1 to Time 3, the Time 3 pattern of drug use was independent of the pattern in Time 1. The symmetry-plus-trend model indicated that there was a favorable trend toward complete abstinence from drugs among persons who returned to treatment as well as those who did not. Persons who returned to treatment, however, were much more likely to show a favorable trend than were those who did not return to treatment. These analyses served to illustrate several limitations and advantages of log-linear analysis of contingency tables. The major limitation encountered was the difficulty of analyzing large contingency tables, even with a relatively large sample size. The major advantage brought out by these analyses was the capability of log-linear analysis to conduct a detailed, almost microscopic examination of associations within a small set of categorical variables.