fit_LME_landmark {Landmarking}

Fit a landmarking model using a linear mixed effects (LME) model for the longitudinal submodel

Description

This function performs the two-stage landmarking analysis.

Usage

fit_LME_landmark(
  data_long,
  x_L,
  x_hor,
  fixed_effects,
  random_effects,
  fixed_effects_time,
  random_effects_time,
  individual_id,
  k,
  cross_validation_df,
  random_slope_in_LME = TRUE,
  random_slope_as_covariate = TRUE,
  standardise_time = FALSE,
  lme_control = nlme::lmeControl(),
  event_time,
  event_status,
  survival_submodel = c("standard_cox", "cause_specific", "fine_gray"),
  b
)

Arguments

data_long

Data frame or list of data frames each corresponding to a landmark age x_L (each element of the list must be named the value of x_L it corresponds to). Each data frame contains repeat measurements data and time-to-event data in long format.

x_L

Numeric specifying the landmark time(s)

x_hor

Numeric specifying the horizon time(s)

fixed_effects

Vector of character strings specifying the column names in data_long which correspond to the fixed effects

random_effects

Vector of character strings specifying the column names in data_long which correspond to the random effects

fixed_effects_time

Character string specifying the column name in data_long which contains the time at which the fixed effects were recorded

random_effects_time

Vector of character strings specifying the column names in data_long which contain the times at which repeat measures were recorded. This should either be length 1 or the same length as random_effects. In the latter case the order of elements must correspond to the order of elements in random_effects.

individual_id

Character string specifying the column name in data_long which contains the individual identifiers

k

Integer specifying the number of folds for cross-validation. An alternative to setting parameter cross_validation_df for performing cross-validation; if both are missing no cross-validation is used.

cross_validation_df

List of data frames containing the cross-validation fold each individual is assigned to. Each data frame in the list should be named according to the landmark time x_L that they correspond. Each data frame should contain the columns individual_id and a column cross_validation_number which contains the cross-validation fold of the individual. An alternative to setting parameter k for performing cross-validation; if both are missing no cross-validation is used.

random_slope_in_LME

Boolean indicating whether to include a random slope in the LME model

random_slope_as_covariate

Boolean indicating whether to include the random slope estimate from the LME model as a covariate in the survival submodel.

standardise_time

Boolean indicating whether to standardise the time variables (fixed_effects_time and random_effects_time) by subtracting the mean and dividing by the standard deviation (see Details section for more information)

lme_control

Object created using nlme::lmeControl(), which will be passed to the control argument of the lme function

event_time

Character string specifying the column name in data_long which contains the event time

event_status

Character string specifying the column name in data_long which contains the event status (where 0=censoring, 1=event of interest, if there are competing events these are labelled 2 or above).

survival_submodel

Character string specifying which survival submodel to use. Three options: the standard Cox model i.e. no competing risks ("standard_cox"), the cause-specific regression model ("cause_specific"), or the Fine Gray regression model ("fine_gray")

b

Integer specifying the number of bootstrap samples to take when calcluating standard error of c-index and Brier score

Details

Firstly, this function selects the individuals in the risk set at the landmark time x_L. Specifically, the individuals in the risk set are those that have entered the study before the landmark age (there is at least one observation for each of the fixed_effects andrandom_effects on or before x_L) and exited the study on after the landmark age (event_time is greater than x_L).

Secondly, if the option to use cross validation is selected (using either parameter k or cross_validation_df), then an extra column cross_validation_number is added with the cross-validation folds. If parameter k is used, then the function add_cv_number randomly assigns these folds. For more details on this function see ?add_cv_number. If the parameter cross_validation_df is used, then the folds specified in this data frame are added. If cross-validation is not selected then the landmark model is fit to the entire group of individuals in the risk set (this is both the training and test dataset).

Thirdly, the landmark model is then fit to each of the training data. There are two parts to fitting the landmark model: using the longitudinal data and using the survival data. Using the longitudinal data is the first stage and is performed using fit_LME_longitudinal. See ?fit_LME_longitudinal more for information about this function. Using the survival data is the second stage and is performed using fit_survival_model. See ?fit_survival_model more for information about this function.

Fourthly, the performance of the model is then assessed on the set of predictions from the entire set of individuals in the risk set by calculating Brier score and C-index. This is performed using get_model_assessment. See ?get_model_assessment more for information about this function.

Value

List containing containing information about the landmark model at each of the landmark times. Each element of this list is named the corresponding landmark time, and is itself a list containing elements: data, model_longitudinal, model_LME, model_LME_standardise_time, model_survival, and prediction_error.

data has one row for each individual in the risk set at x_L and contains the value of the fixed_effects using the LOCF approach and predicted values of the random_effects using the LME model at the landmark time x_L. It also includes the predicted probability that the event of interest has occurred by time x_hor, labelled as "event_prediction". There is one row for each individual.

model_longitudinal indicates that the longitudinal approach is LME.

model_LME contains the output from the lme function from package nlme. For a model using cross-validation, model_LME contains a list of outputs with each element in the list corresponds to a different cross-validation fold. prediction_error contains a list indicating the c-index and Brier score at time x_hor and their standard errors if parameter b is used. For more information on how the prediction error is calculated please see ?get_model_assessment which is the function used to do this within fit_LME_landmark.

model_LME_standardise_time contains a list of two objects mean_response_time and sd_response_time if the parameter standardise_time=TRUE is used. This is the mean and standard deviation use to normalise times when fitting the LME model.

model_survival contains the outputs from the survival submodel functions, including the estimated parameters of the model. For a model using cross-validation, model_survival will contain a list of outputs with each element in the list corresponding to a different cross-validation fold. model_survival contains the outputs from the function used to fit the survival submodel, including the estimated parameters of the model. For a model using cross-validation, model_survival contains a list of outputs with each element in the list corresponding to a different cross-validation fold. For more information on how the survival model is fitted please see ?fit_survival_model which is the function used to do this within fit_LME_landmark.

prediction_error contains a list indicating the c-index and Brier score at time x_hor and their standard errors if parameter b is used.

Author(s)

Isobel Barrott [e-mail]

Examples

library(Landmarking)
data(data_repeat_outcomes)
data_model_landmark_LME <-
  fit_LME_landmark(
    data_long = data_repeat_outcomes,
    x_L = c(60, 61),
    x_hor = c(65, 66),
    k = 10,
    fixed_effects = c("ethnicity", "smoking", "diabetes"),
    fixed_effects_time = "response_time_sbp_stnd",
    random_effects = c("sbp_stnd", "tchdl_stnd"),
    random_effects_time = c("response_time_sbp_stnd", "response_time_tchdl_stnd"),
    individual_id = "id",
    standardise_time = TRUE,
    lme_control = nlme::lmeControl(maxIter = 100, msMaxIter = 100),
    event_time = "event_time",
    event_status = "event_status",
    survival_submodel = "cause_specific"
  )