An ad hoc method for dual adjusting for measurement errors and nonresponse bias for estimating prevalence in survey data: Application to Iranian mental health survey on any illicit drug use.

Purpose The prevalence estimates of binary variables in sample surveys are often subject to two systematic errors: measurement error and nonresponse bias. A multiple-bias analysis is essential to adjust for both biases. Methods In this paper, we linked the latent class log-linear and proxy pattern-mixture models to adjust jointly for measurement errors and nonresponse bias with missing not at random mechanism. These methods were employed to estimate the prevalence of any illicit drug use based on Iranian Mental Health Survey data. Results After jointly adjusting for measurement errors and nonresponse bias in this data, the prevalence (95% confidence interval) estimate of any illicit drug use changed from 3.41 (3.00, 3.81)% to 27.03 (9.02, 38.76)%, 27.42 (9.04, 38.91)%, and 27.18 (9.03, 38.82)% under "missing at random," "missing not at random," and an intermediate mode, respectively. Conclusions Under certain assumptions, a combination of the latent class log-linear and binary-outcome proxy pattern-mixture models can be used to jointly adjust for both measurement errors and nonresponse bias in the prevalence estimation of binary variables in surveys.