Table 3 Summary of single-stage models used to incorporate longitudinal data in survival models

Cox model, N = 25 (62.5) [18, 19, 21, 25, 28, 29, 32, 34,35,36, 38, 39, 41,42,43, 45, 47, 49,50,51, 53,54,55,56,57]

Continuous, Categorical

Time to event

Baseline only, N = 7 (17.5) [18, 21, 24, 43, 50, 53, 54]

Continuous, N = 6 (15.0) [18, 21, 43, 50, 53, 54]

Categorised, N = 2 (5.0) [24, 54]

To clinically relevant time point to be used for prediction

PH

Simple method

Dependence between measurement times is ignored

Continuous

Time to event

Change from baseline, N = 3 (7.5) [28, 35, 38]

To incorporate change over time

PH; Change is linear

Incorporates more than one time point

Only looks at pairs of time points

Continuous

Time to event

Slope calculated manually, N = 3 (7.5) [25, 29, 32]

To incorporate constant change in the survival model

PH; Change is linear

Incorporates more than one time point

Only looks at pairs of time points

Continuous

Time to event

Average (categorized before use),^a N = 1 (2.5) [36]

To incorporate the average change over time

PH; Constant between time points; Change is linear

Incorporates the average impact over time

Interpretation unclear

Continuous, Categorical

Time to event

Time-dependent covariate, N = 6 (15.0) [39, 42, 45, 47, 49, 51, 55]

To incorporate change in exposure variable over time

PH; Change is constant between two consecutive time points; Longitudinal data are measured without error

Incorporates time-varying measures over the follow-up period

Computationally slower as compared to time-fixed covariates; Computationally infeasible if the longitudinal outcome is measured at different time points for different individuals; Interpretation is difficult; Can lead to great overfitting of the data; must be used with caution

Continuous

Time to event

Summary measures(Standard deviation, number of drops between observations), N = 1 (2.5) [19]

To incorporate variability summaries of the longitudinal data

PH

Incorporates variability of measures into the model

Summary measures fairly specific to dataset

Continuous, Categorical

Time to event

Change in category between first and last time-point categorized, N = 2 (5.0) [34, 41]

Change in continuous variable between time points categorized with manually defined cut-offs, N = 1 (2.5) [56]

To summarise trajectories in an interpretable way

PH

Results interpretable

Groups manually selected based on data which could lead to bias

Hierarchical Cox model to adjust for multiple studies, N = 1 (2.5) [20]

Continuous

Time to event

Continuous measurements categorized. Multiple time points also categorised as consistent/non-consistent, N = 1 (2.5) [20]

To summarise trajectories in an interpretable way adjusting for combining multiple studies

PH

Results interpretable; Adjusts for use of multiple studies

Groups manually selected based on data which could lead to bias

Logistic Regression, N = 3 (7.5) [30, 31, 48]

Continuous

Binary

Baseline only, N = 1 (2.5) [31]

Allows clinically relevant time point to be used for prediction

Not applicable

Simple method

Dependence between measurement times is ignored

Categorical

Binary

Separate time points, N = 1 (2.5) [30]

To include all predictive values in model

Not applicable

Simple method

Caution needed for multicollinearity

Continuous

Binary

Summaries of repeated measures

• Standard deviation

• Mean

• Mean change from baseline

• Average daily risk range^b

• Range

N = 1 (2.5) [48]

Includes different measures of variation

Not applicable

Simple method

Interpretation of different summary measures non-trivial

GEE - logit link N = 2 (5.0) [17, 27]

Continuous

Binary

Non-linear relationships considered through piecewise models or splines, N = 1 (2.5) [17]

To attempt to include a variety of shapes of relationships in the model using data from all time points

Not applicable

Includes all measured values of longitudinal variable with various relationships with risk

Splines harder to interpret; Produces population averages not individual predictions

Continuous

Binary

Multiple time points, N = 1 (2.5) [27]

To include values and change at all time points

Not applicable

Includes all measured values of longitudinal variable

Produces population averages not individual predictions

GEE – log link, N = 2 (5.0) [22, 37]

Continuous

Rates

Multiple time points, N = 1 (2.5) [37]

Multiple time points categorized as stable, increasing (in the second or third time point), decreasing, unstable, N = 1 (2.5) [22]

To include all time points in predicting rates

Not applicable

Includes all measured values of longitudinal variable

Produces population averages not individual predictions

Poisson regression, N = 2 (5.0) [23, 26]

Continuous

Rates

Baseline only, N = 2 (5.0) [23, 26]

To enable modelling of baseline rate

Not applicable

Enables modelling of baseline rate in a parametric manner

Dependence between measurement times is ignored

Linear Mixed Effects model, N = 4 (10.0) [33, 44, 46, 96]

Continuous, categorical

Continuous

Repeated measures, N = 4 (10.0) [33, 44, 46, 96]

To predict changes over time

Random effects are independent of covariates

Includes all measured values of longitudinal variable

None

Fixed effects linear regression, N = 1 (2.5) [52]

Continuous, categorical

Continuous

The variable is transformed by subtracting patient-level mean to remove between patient variation. N = 1 (2.5) [52]

To predict changes over time

Not applicable

Includes all measured values of longitudinal variable; Relaxes assumption of independence of random effects from covariates; Computationally very easy to fit compared with mixed effects models

Lower statistical efficiency than mixed effects models