Model verification/validation applies the metrics of prediction error (e.g. area under curve), information criterion (e.g. Akaike, Bayesian, deviance), model uncertainty (e.g. substitution, portioning, leave-one-out/K-fold cross-validation), and numerical convergence. However, censoring and non-respondents cause uncertainty in follow-up studies and surveys. When missing at completely random (MACR) is not true, empirical result verification is problematic. Thus, emphasis should be given on ways to illustrate ignorance related to missing values. OBJECTIVES: To present a possibility interval (PI) and its relation to Wald confidence intervals (CI) and Jeffreys Bayesian credibility intervals (CrI; Beta 0.5, 0.5 a priori) in 9 artificial samples of 1000 individuals (prevalence of e.g. drug utilization 10%-50%; ignorance due to censoring/non-responding 5%-25%). METHODS: The epistemic uncertainty is considered here as sampling ignorance. The conjunctive set of points comprised in an interval of minimum necessary level (NL) and maximum possibility level (PL) constitute a PI (i.e. where the "true" mean must be conditional to sample's representativeness). Firstly, in possibility quantification, certainty sources (e.g. certain observations) are determined. Secondly, the dominant possibility factors causing ignorance are identified. Thirdly, NL and PL bounds are established for parameters representing the outcome/model. RESULTS: The NL and PL of PI depict the depth of ignorance. In the artificial samples of e.g. 1000 potential drug users, PI overlapping was related to the levels of prevalence and ignorance. If e.g. 10% difference in prevalence is observed between compared groups, 15% ignorance constitutes a threshold for inference change. In a case of 50% prevalence with ignorance between approximately 5%-10%, PIs were visually in substitutive relation to CIs and CrIs. In other cases, PIs provide complementary information. CONCLUSIONS: The complementary information provided by PIs is important with higher (e.g.>10%) censoring levels and, most importantly, if MACR does not hold or the prevalence of research subject is very different from 50%.