Role of survey response rates on valid inference: An application to HIV prevalence estimates

Background: Nationally-representative surveys suggest that females have a higher prevalence of HIV than males in most African countries. Unfortunately, these results are made on the basis of surveys with non-ignorable missing data. This study evaluates the impact that differential survey nonresponse rates between males and females can have on the point estimate of the HIV prevalence ratio of these two classifiers. Methods: We study 29 Demographic and Health Surveys (DHS) from 2001 to 2010. Instead of employing often used multiple imputation models with a Missing at Random assumption that may not hold in this setting, we assess the effect of ignoring the information contained in the missing HIV information for males and females through three proposed statistical measures. These measures can be used in settings where the interest is comparing the prevalence of a disease between two groups. The proposed measures do not utilize parametric models and can be implemented by researchers of any level. They are: (1) an upper bound on the potential bias of the usual practise of using reported HIV prevalence estimates that ignore subjects who have missing HIV outcomes. (2) Plausible range intervals to account for nonresponses, without any additional parametric modeling assumptions. (3) Prevalence ratio inflation factors to correct the point estimate of the HIV prevalence ratio, if estimates of nonresponders' HIV prevalences were known. Results: In 86% of countries, males have higher upper bounds of HIV prevalence than females, this is consonant with males possibly having higher infection rates than females. Additionally, 74% of surveys have a plausible range that crosses 1.0, suggesting a plausible equivalence between male and female HIV prevalences. Conclusions: It is quite reasonable to conclude that there is so much DHS nonresponse in evaluating the HIV status question, that existing data is plausibly generated by the situation where the virus is equally distributed between the sexes.