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

General recommendations

Sterne et al.: Recommendations for missing data and multiple imputation

Simple imputation

Zhang: Mean, median, mode, regression imputations

Complete-case bias considerations

Bartlett et al.: When CC is valid

Carpenter & Kenward: When CC is valid

Number of imputations to use

White et al.: at least the percentage of incomplete cases

von Hippel: two-stage quadratic rule

Covariate selection procedures

Wood et al.: Repeated use of Rubin’s rules or stacking approach

Morris et al.: Adapted for MFP including selection procedure and functional form

Non-linear effects

Morris et al.: Adapted for MFP including selection procedure and functional form

Seaman et al.: recommend just another variable (JAV) approach

Using a Cox model

White & Royston: inclusion of Nelson-Aalen estimate and event indicator in imputation model

Bartlett & Seaman: full conditional specification adjusting for the analysis model of choice

Testing the Proportional hazards assumption and modelling time-varying effects of covariates

Keogh & Morris: adapting White & Royston and Bartlett & Seaman approaches for time-varying effects

Time-dependent covariates

De Silva et al.: Investigating performance of two-fold fully conditional specification for time-dependet covariates

Moreno-Betancur et al.: Use of joint modelling for time-dependent covariates

Functional form

Sauerbrei et al.: multivariable fractional polynomial time i.e. MFP in survival setting accounting for time-varying effects

Buchholz & Sauerbrei: comparison of procedures for assessing time-varying effects and functional form

Heinzl & Kaider: Using cubic spline functions to assess functional form

Wynant & Abrahamowicz: Importance of assessing time-varying effects and functional form

Abrahamowicz & MacKenzie: Joint estimation of time-varying effects and functional form using splines

Covariate selection procedures

See above

Yan & Huang: Assessing time-varying effects using an adaptive lasso method

Testing the Proportional hazards assumption

Austin: Assessing power of tests to assess proportional hazards assumption

Bellera et al.: Recommend assessing proportional hazards assumption and inclusion of time-varying effects where necessary

Abrahamowicz et al.: use of regression splines to model time-varying effects

Hess: use of cubic splines to model time-varying effects

Time-varying effects

See above

See above

See above

See above

See above

See above

See above

See above

Categorising of covariates

MacCallum et al.: Discussion on dichotomising continuous covariates

Non-linear effects

Royston & Sauerbrei: Text book providing overview of model selection with a focus on MFP procedures

Harrell: Text book providing overview of strategies for regression modelling

Covariate selection procedures

See above

Heinze et al.: Review of methods for covariate selection