In survival analysis, deviations from proportional hazards may sometimes be explained by unaccounted random heterogeneity, or frailty. This paper recalls the literature on omitted covariates in survival analysis and shows in a case study how unstably frailty models might behave when asked to account for unobserved heterogeneity in standard survival analysis with no replications per heterogeneity unit. Accelerated failure time modelling seems to avoid these difficulties and also to yield easily interpretable results. We propose that it would be advantageous to upgrade the accelerated failure time approach alongside the hazard modelling approach to survival analysis.