Simple random sampling is an assumption when using fit statistics to fit latent class (LC) models to data. However, LC models are often fit to datasets collected through complex survey sampling methods that may result in inaccurate estimates of standard errors, parameter estimates and fit statistics. This study examined how various comparison tests functioned for latent class models when using complex survey data. The motivation for this research is the issue of reported drug use patterns and whether changes in drug use have occurred over time. This issue was investigated using reported drug use data from the National Household Survey on Drug Abuse (NHSDA) for 1979 and 1988. Monte Carlo simulations were used to determine how well the various model comparison statistics (chi-square, AIC, BIC, RIC and Wald statistic) functioned for a variety of complex sample designs. In addition, a simulation based on the NHSDA data was used to answer the research question: Do patterns of reported drug use show change over time? The model comparison statistics were most accurate when sample sizes were large and item-specific error rates were low. Intraclass correlation, an indicator of how similar individuals are within the same cluster, appeared to have little effect on the accuracy of the model comparison statistics. Statistics were not as accurate when sampling from unequally weighted groups. The chi-square statistics and AIC were recommended for use with complex survey data based on their high rates of accuracy. More caution was recommended when using BIC and RIC. Results indicated that reported drug use patterns changed between 1979 and 1988. Most patterns of reported drug use increased slightly, with the exception of respondents characterized by alcohol and tobacco use alone that decreased substantially.