Table 4:
Missing data rates in pre- and post-intervention risk variables, and resulting variance inflationa in estimates of (i) pre-intervention prevalence, (ii) post-intervention prevalence, and (iii) pre-to-post-intervention prevalence change.
| Pre-intervention | Post-intervention | Pre-to-post change | |||
|---|---|---|---|---|---|
| Missing rate | Variance inflation | Missing rate | Variance inflation | Variance inflation | |
| Site 1 (n=185) | |||||
| Specific risky behaviors: | |||||
| buy drug pre-loaded | 21.1% | 36.8% | |||
| give syringe to dealer | 20.0% | 34.1% | |||
| give syringe to partnerb | 58.9% | 52.4% | |||
| give syringe to middle personb | 61.1% | 49.7% | |||
| front- or back-loading | 14.6% | 33.5% | |||
| using common container | 23.2% | 31.4% | |||
| using used cooker, cotton or water | 26.5% | 33.5% | |||
| Composite outcome variables of risky behaviors inc: | |||||
| drug acquisition | 52.4% | 2.07 | 50.3% | 1.51 | 2.11 |
| drug injection | 23.2% | 1.17 | 37.3% | 1.37 | 1.30 |
| drug acquisition/injection | 31.9% | 1.33 | 44.9% | 1.48 | 1.45 |
| Site 1 sensitivity analysis sample leaving out those lost to follow-up (n=141) | |||||
| Specific risky behaviors: | |||||
| buy drug pre-loaded | 21.3% | 17.0% | |||
| give syringe to dealer | 19.1% | 13.5% | |||
| give syringe to partnerb | 57.4% | 37.6% | |||
| give syringe to middle personb | 58.9% | 34.0% | |||
| front- or back-loading | 14.2% | 12.8% | |||
| using common container | 23.4% | 9.9% | |||
| using used cooker, cotton or water | 27.7% | 12.8% | |||
| Composite outcome variables of risky behaviors inc: | |||||
| drug acquisition | 52.5% | 1.86 | 34.8% | 1.19 | 1.73 |
| drug injection | 21.3% | 1.14 | 17.7% | 1.14 | 1.16 |
| drug acquisition/injection | 31.2% | 1.29 | 27.7% | 1.18 | 1.26 |
| Site 2 (n=161) | |||||
| Specific risky behaviors: | |||||
| buy drug pre-loaded | 9.9% | 18.6% | |||
| give syringe to dealer | 7.5% | 18.0% | |||
| give syringe to partnerb | 25.5% | 26.1% | |||
| give syringe to middle personb | 24.8% | 26.1% | |||
| front- or back-loading | 5.6% | 14.3% | |||
| using common container | 10.6% | 21.1% | |||
| using used cooker, cotton or water | 8.7% | 16.1% | |||
| Composite outcome variables risky behavior inc: | |||||
| drug acquisition | 17.4% | 1.30 | 23.0% | 1.11 | 1.21 |
| drug injection | 6.8% | 1.07 | 16.1% | 1.12 | 1.11 |
| drug acquisition/injection | 6.8% | 1.16 | 17.4% | 1.11 | 1.14 |
| Site 3 (n=160) | |||||
| Specific risky behaviors: | |||||
| buy drug pre-loaded | 8.8% | 8.1% | |||
| give syringe to dealer | 4.4% | 5.0% | |||
| give syringe to partnerb | 13.1% | 14.4% | |||
| give syringe to middle personb | 13.8% | 14.4% | |||
| front- or back-loading | 11.9% | 7.5% | |||
| using common container | 6.3% | 6.9% | |||
| using used cooker, cotton or water | 3.8% | 5.0% | |||
| Composite outcome variables of risky behavior inc: | |||||
| drug acquisition | 12.5% | 1.72 | 14.4% | 2.03 | 1.99 |
| drug injection | 11.9% | 1.08 | 8.1% | 1.04 | 1.12 |
| drug acquisition/injection | 10.6% | 1.73 | 12.5% | 2.02 | 2.18 |
| Site 4 (n=170) | |||||
| Specific risky behaviors: | |||||
| buy drug pre-loaded | 12.9% | 18.8% | |||
| give syringe to dealer | 10.6% | 16.5% | |||
| give syringe to partnerb | 35.3% | 41.2% | |||
| give syringe to middle personb | 38.8% | 41.2% | |||
| front- or back-loading | 7.1% | 15.9% | |||
| using common container | 14.1% | 20.6% | |||
| using used cooker, cotton or water | 11.2% | 19.4% | |||
| Composite outcome variables of risky behavior inc: | |||||
| drug acquisition | 25.9% | 1.80 | 32.9% | 1.19 | 1.48 |
| drug injection | 10.6% | 1.12 | 17.6% | 1.10 | 1.11 |
| drug acquisition/injection | 15.3% | 1.47 | 23.5% | 1.15 | 1.31 |
Variance inflation is the factor by which the variance (= squared standard error) of the estimator is inflated as a result of uncertainty due to missing data. This table reports variance inflation in estimating: (i) pre-intervention prevalence, (ii) post-intervention prevalence, and (iii) pre-to-post prevalence change (see estimates in Table 5). Note that this variance inflation factor = 1/(1-FMI) where FMI is the fraction of missing information, defined as the ratio of between variance (variance of the estimate across the imputed datasets) to the sum of between variance and average within variance (variance of the estimate within each dataset). We choose to directly report variance inflation because FMI, a variance partition measure, is often mixed with missing data rate.
At all the four sites, the two items giving syringe to partner and giving syringe to middle person (to get drug) suffer from higher missing rates than other items due to a flawed skip pattern in the questionnaire.
The composite outcome variables inherit missingness from the specific risky behaviors variables in the original data. The missingness in the two questionnaire items mentioned in noteb leads to higher missing rates in the first composite variable, risky behavior in drug acquisition, which to some extent carries into the last composite variable, risky behavior in drug acquisition/injection. Note that a missing value on a composite variable does not imply complete missing information on that value. For example, the composite variable risky behavior in drug acquisition variable is based on four specific risky behavior variables. If three of these component variables are 0 and one is missing, then we have partial information on the composite variable even though it is missing; such information is incorporated in the imputed data.