Pepper obtained bounds on prevalence (Appendix D). The lower bound results if prevalence among nonrespondents equals that among respondents. The upper bound results if all nonrespondents use illegal drugs. True prevalence is within these bounds. Using data from MTF, Pepper found that annual prevalence for 12th graders lies between 29 and 40 percent in 1991 and between 42 and 51 percent in 1997. Thus, the data place prevalence within about a 10 percentage point range. The estimates imply that prevalence increased in the 1990s, although the magnitude of the increase is not revealed. In particular, from 1991 to 1997, prevalence increased by at least 2 percentage points (from 40 to 42 percent) and may have increased by as much as 22 points (from 29 to 51 percent).

Using data from the NHSDA, Pepper found that annual prevalence for adolescents ages 12 to 17 was between 13 and 35 percent in 1991 and between 19 and 39 percent 1997. Thus, the data restrict the prevalence rate to a 20 percentage point range. The direction of any trend is not revealed. Prevalence might have fallen by 16 percentage points (from 35 to 19 percent) or increased by 26 percentage points (from 13 to 39 percent). Thus, in the absence of additional information, the NHSDA data are uninformative about the direction of even large changes over this period.

The direction and magnitude of the change in prevalence can be identified if one makes sufficiently strong assumptions about drug use among nonrespondents. The magnitude is identified if one assumes that prevalence is the same among respondents and nonrespondents. The direction is identified if one assumes that prevalence among nonrespondents did not decrease by too much. In the NHSDA data on 12- to 17-year-olds, Pepper found that true prevalence increased from 1991 to 1997 under the assumption that prevalence among nonrespondents did not decrease by more than 18 percentage points during this period. This assumption may be acceptable to many observers, but it cannot be verified or refuted empirically using any data of which the committee is aware. Thus, potentially strong though possibly plausible assumptions are required to estimate the direction of the trend of prevalence, whereas weaker assumptions suffice to bound prevalence levels.

School Nonresponse and Replacement in MTF. School nonresponse is a particularly troubling source of uncertainty in estimates obtained from MTF data. MTF asks schools to participate in its study, and students are sampled from the participating schools. Each year, between 30 and 50 percent of the selected schools decline to participate, in which case a similar school (in terms of size, geographic area, and other characteristics) is recruited as a replacement. If a 30 to 50 percent nonresponse rate were incorporated into the bounds described earlier, then the MTF data would not identify the direction of even the largest changes in prevalence. This problem does not arise if the decision of a school to participate in MTF is



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