Table 4.

Selected papers describing methods for addressing common issues arising in the analysis of time-to-event data when there is missing covariate data

Consideration	Some recommended references
Missing data (general)
General recommendations	[6]	Sterne et al.: Recommendations for missing data and multiple imputation
Simple imputation	[36]	Zhang: Mean, median, mode, regression imputations
Complete-case bias considerations	[37]	Bartlett et al.: When CC is valid
	[38]	Carpenter & Kenward: When CC is valid
Multiple imputation
Number of imputations to use	[15]	White et al.: at least the percentage of incomplete cases
	[39]	von Hippel: two-stage quadratic rule
Covariate selection procedures	[32]	Wood et al.: Repeated use of Rubin’s rules or stacking approach
	[40]	Morris et al.: Adapted for MFP including selection procedure and functional form
Non-linear effects	[40]	Morris et al.: Adapted for MFP including selection procedure and functional form
	[41]	Seaman et al.: recommend just another variable (JAV) approach
Using a Cox model	[3]	White & Royston: inclusion of Nelson-Aalen estimate and event indicator in imputation model
	[4]	Bartlett & Seaman: full conditional specification adjusting for the analysis model of choice
Testing the Proportional hazards assumption and modelling time-varying effects of covariates	[5]	Keogh & Morris: adapting White & Royston and Bartlett & Seaman approaches for time-varying effects
Time-dependent covariates	[42]	De Silva et al.: Investigating performance of two-fold fully conditional specification for time-dependet covariates
	[43]	Moreno-Betancur et al.: Use of joint modelling for time-dependent covariates
Time-to-event features not concerning missing data
Functional form	[44]	Sauerbrei et al.: multivariable fractional polynomial time i.e. MFP in survival setting accounting for time-varying effects
	[45]	Buchholz & Sauerbrei: comparison of procedures for assessing time-varying effects and functional form
	[46]	Heinzl & Kaider: Using cubic spline functions to assess functional form
	[47]	Wynant & Abrahamowicz: Importance of assessing time-varying effects and functional form
	[48]	Abrahamowicz & MacKenzie: Joint estimation of time-varying effects and functional form using splines
Covariate selection procedures	[44]	See above
	[49]	Yan & Huang: Assessing time-varying effects using an adaptive lasso method
Testing the Proportional hazards assumption	[35]	Austin: Assessing power of tests to assess proportional hazards assumption
	[50]	Bellera et al.: Recommend assessing proportional hazards assumption and inclusion of time-varying effects where necessary
	[51]	Abrahamowicz et al.: use of regression splines to model time-varying effects
	[52]	Hess: use of cubic splines to model time-varying effects
Time-varying effects	[44]	See above
	[45]	See above
	[46]	See above
	[47]	See above
	[48]	See above
	[49]	See above
	[50]	See above
	[52]	See above
General study considerations
Categorising of covariates	[53]	MacCallum et al.: Discussion on dichotomising continuous covariates
Non-linear effects	[54]	Royston & Sauerbrei: Text book providing overview of model selection with a focus on MFP procedures
	[33]	Harrell: Text book providing overview of strategies for regression modelling
Covariate selection procedures	[54]	See above
	[55]	Heinze et al.: Review of methods for covariate selection

MFP: Multivariable fractional polynomials