When the design effect is unknown: sensitivity of logistic regression and survival models to DEFF misspecification in complex surveys

Abstract Complex survey data are often released with limited information about the sampling design, which constrains the use of standard design-based variance estimation methods. In such settings, researchers often use normalized sampling weights adjusted by a design effect (DEFF) as a pragmatic alternative. This paper investigates the inferential consequences of misspecifying the DEFF in regression models for complex survey data. Using data from the Portuguese Fertility Survey and the U.S. National Survey on Drug Use and Health, we conduct a sensitivity analysis of logistic regression and Cox proportional hazards models under a range of DEFF values. Two analytical strategies are considered: (i) model selection under different DEFF assumptions, and (ii) fixed-model comparisons where DEFF-adjusted analyses are contrasted with benchmark approaches based on replicate weights or Taylor linearization, when available. Results show that incorrect DEFF specification substantially affects standard errors, statistical significance, and the selection of covariates and interactions, while discrimination and global model fit measures remain largely unchanged. These findings highlight the risk of drawing substantively different conclusions from models that appear well-fitted when DEFF values are misspecified. The study reinforces the need to interpret DEFF-based adjustments as inferential sensitivity tools, highlighting how variance misspecification propagates to hypothesis testing, interaction detection, and substantive interpretation in applied regression models.