Impact of independence assumption for joint predictor distributions prior to data collection

Investigate the impact of assuming conditional independence among core predictors when only marginal distributions are available and the joint correlations are unknown during sample size planning, including how this assumption affects individual-level uncertainty intervals and classification instability in clinical prediction models.

Background

When planning studies before data are available, the joint distribution of predictors may be unknown. The authors suggest a pragmatic initial assumption of conditional independence among predictors to simulate synthetic data for their sample size approach.

They explicitly acknowledge that the consequences of this assumption need further investigation to understand its effect on the precision and robustness of individual-level predictions.

References

In situations in advance of data collection, the joint distribution of predictors may be difficult to gauge and assuming predictors are independent may be a pragmatic approach; the impact of that needs further research but it forms a starting point.

— A decomposition of Fisher's information to inform sample size for developing fair and precise clinical prediction models -- part 1: binary outcomes  (2407.09293 - Riley et al., 2024) in Section 6 (Discussion)

Observed joint MIC profiles for the five drugs were unavailable; each five-drug row was a synthetic pairing of values from published marginal distributions. Cross-drug dependence was imposed through a Gaussian copula at prespecified correlation levels and was not estimated from observed joint data. Therefore, the analysis cannot establish whether elevated MIC values for different drugs occur jointly in individual isolates.

— Copula-Based Reconstruction and Clustering of Coccidioides Minimum Inhibitory Concentration Profiles  (2608.19722 - Wasco et al., 20 Aug 2026) in Section 4.1, Limitations