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Drug Use Among U.S. Workers: Prevalence & Trends by Occupation and Industry |
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Appendix B: Analytic Methods
1. Prevalence Estimates
In order to obtain accurate estimates of the percentage of reported illicit drug use and heavy alcohol use, the weighted percentage is used. A weight, based on specific sampling criteria,5 was assigned to each respondent and indicates how many members of the target population he or she represents. The sum of these weights equals the estimated population size. Therefore, the percentage of full-time workers who reported current illicit drug use indicates the percentage of the estimated population size, and not merely the percentage of actual respondents. SUDAAN 6.3, a software package designed for the analysis of surveys which utilize a complex sampling design (such as the NHSDA), was used to compute the prevalence estimates and their accompanying standard errors.
2. Suppression Rule
As in other SAMHSA publications which use NHSDA data, estimates with low precision are not reported. The criterion used for suppressing estimates is based on the relative standard error (RSE). The RSE is defined as the ratio of the standard error of the estimate over the estimate. For this report, as well as others, the log transformation of the proportion estimate is used to calculate the RSE. Specifically, percentages are suppressed if
RSE[-ln(p)] > 0.175 when p< 0.5
or
RSE[-ln(1-p)] > 0.175 when p< 0.5
For computational purposes, this is equivalent to
SE(p)/p > 0.175 when p< 0.5 -ln(p)
or
SE(p)/(1-p) > 0.175 when p< 0.5 -ln(1-p)
where SE(p) equals the standard error estimate of p. The log transformation of p is used to provide a more balanced treatment of measuring the quality of small, large, and intermediate p values. The switch to (1-p) for p greater than 0.5 provides a symmetric suppression rule across the range of possible p values.
3. Statistical Significance of Differences
This section describes the methods used to compare prevalence estimates when they are stratified (e.g., by gender or marital status; see Tables 4.1-4.4) within the occupation and industry categories. Normally, the observed difference between estimates is evaluated in terms of statistical significance. This term refers to the probability that a difference as large as that observed would occur due to random error in the estimates if there were no difference in the prevalence for the population groups being compared. The significance of a particular difference referred to in the above text is at the 0.05 probability level. However, the reader may wish to compare prevalence estimates from two groups for which significance of the difference is not reported.
For comparing percentage estimates for two groups, the following test statistic (referred to as the z statistic) is used:
z = (p1 - p2) divided by the square root of Var(p1) + var(p2) - 2*cov(p1, p2)
where:
p1 = estimated proportion from first group
p2 = estimated proportion from second group
var(p1) = variance estimate for p1
var(p2) = variance estimate for p2
cov(p1,p2) = estimate of covariance of p1 and p2
Under the null hypothesis of no difference in percentages, z is asymptotically distributed as a normal random variable; calculated values of z may, therefore, be referred to the unit normal distribution to determine the corresponding probability level (i.e., p value). Two multiplied by the covariance is subtracted in the denominator of the above formula since there is a small positive covariance between the estimates due to the individuals who share sampling units.
4. Direct Age Adjustment used in Tables 4.3 and 4.4
As with many studies that compare population attributes by marital status, the NHSDA indicates that respondents who are married tend to be significantly older than those who are unmarried (either never married, divorced, or separated). Since older people are also less likely overall to report illicit drug and heavy alcohol use, one runs the risk of attributing an association between age and drug use to marital status in this type of analysis. Therefore, the estimates in Tables 4.3 and 4.4 were age-adjusted through a statistical procedure known as direct standardization. This procedure eliminates differences in the age composition between the two marital status groups in each occupation and industry. Thus, differences in the percentage of illicit drug or heavy alcohol use between the married and unmarried respondents in each respective category are not attributable to age.
Direct standardization uses a standard population to derive the age-adjusted estimates. The standard population used in Tables 4.3 and 4.4 is the combined NHSDA 1991-1993 sample of full-time workers ages 18-49. The age distribution is estimated as the weighted proportion of respondents in the following age groups: 18-25 (16 percent), 26-34 (33.4 percent), and 35-49 (50.6 percent). The formula for direct standardization is:
m1 = [Sum maPa]/P
or
Sum ma(Pa/P)
where ma = da/Pa = age-specific drug or alcohol prevalence in a given marital status group, Pa is the standard population in each age group, and P or Sum Pa is the total standard population.6 Each age-specific estimate is multiplied by the proportion of the standard population in each group. The result, in effect, controls for the effects of age on the estimated prevalence of illicit drug and heavy alcohol use between the marital status groups within occupations and industries.
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