from IR-2. Under these assumptions, the observed trends provide a lower bound for the prevalence rate of use for illegal drugs. The upper bound depends on both the self-reported prevalence rates as well as the largest possible fraction of false negative reports, P.
The upper bound P on the fraction of false reports is not revealed by the data but instead must be known or assumed by the researcher. Suppose, for purposes of illustration, one knows that less than 30 percent of respondents give invalid self-reports of illegal drug use. In this case, the width of the bound on prevalence rates is 0.30, so that the data provide only modest information about the fraction of users. Consider, for instance, estimating the fraction of 12th graders using drugs in 1997. In total, 42.4 percent of respondents in the MTF reported consuming drugs during the year. If as many as 30 percent of respondents give false negative reports, the true fraction of users must lie between 42.4 and 72.4 percent.
Alternatively, one might consider setting this upper bound figure much lower than 30 percent. Suppose, for example, one is willing to assume that less than 5 percent of respondents provide invalid reports of drug use. In this case, the prevalence bounds from Equation 9 will be more informative. The estimated prevalence rate of use for 12th graders in 1997, for instance, must lie between [42.4, 47.4] percent.
Clearly, our ability to draw inferences on the prevalence rate of drug use in the United States depends directly on the magnitude of inaccurate reporting. Without better information, readers may differ in their opinions of the persuasiveness and plausibility of particular upper bound assumptions. A 30-point upper bound may be consistent with the inaccurate reporting rates found in DUF/ADAM, but whether arrestees are more or less likely to hide illegal activities is unknown.13 A 5-point upper bound may be consistent with the model-based results of Biemer and Witt (1996), but whether the model accurately measures the degree of inaccurate reporting is unknown.
Despite acknowledged uncertainty surrounding the level estimates, many continue to assert that the data do in fact reveal trends. What restrictions would need to be imposed to identify the trend or direction of
Two other arguments have been used to suggest that the inaccurate reporting rates from DUF/ADAM might be a conservative upper bound on misreporting in the national surveys. First, there is greater accuracy for annual prevalence of use for all drugs than for within-three-days use measures for stigmatized drugs such as cocaine. Second, survey techniques used in the DUF/ADAM are less advanced than in the national probability samples.