Fit a landmark model using a last observation carried forward (LOCF) method for the longitudinal data

This function performs the two-stage landmarking analysis.

fit_LOCF_landmark(
  data_long,
  x_L,
  x_hor,
  covariates,
  covariates_time,
  k,
  cross_validation_df,
  individual_id,
  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)
covariates	Vector of character strings specifying the column names in data_long which correspond to the covariates
covariates_time	Vector of character strings specifying the column names in data_long which contain the times at which covariates were recorded. This should either be length 1 or the same length as covariates. In the latter case the order of elements must correspond to the order of elements in covariates.
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.
individual_id	Character string specifying the column name in data_long which contains the individual identifiers
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 calculating standard error of c-index and Brier score

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_survival, and prediction_error.

data has one row for each individual in the risk set at x_L and contains the value of the covariates at the landmark time x_L using the LOCF approach. 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 LOCF.

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 a function used within fit_LOCF_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. 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_LOCF_landmark.

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 time x_L (there is at least one observation for each of the predictors_LME and random_effects on or before x_L) and exited the study 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 datasets. 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_LOCF_longitudinal. See ?fit_LOCF_longitudinal more for information about this function. This function censors the individuals at the time horizon x_L and fits the survival model. 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.

Author

Isobel Barrott isobel.barrott@gmail.com

Examples

library(Landmarking)
data(data_repeat_outcomes)
data_model_landmark_LOCF <-
   fit_LOCF_landmark(
     data_long = data_repeat_outcomes,
     x_L = c(60, 61),
     x_hor = c(65, 66),
     covariates =
       c("ethnicity", "smoking", "diabetes", "sbp_stnd", "tchdl_stnd"),
     covariates_time =
       c(rep("response_time_sbp_stnd", 4), "response_time_tchdl_stnd"),
     k = 10,
     individual_id = "id",
     event_time = "event_time",
     event_status = "event_status",
     survival_submodel = "cause_specific"
   )
#> Warning: 887 individuals have been removed from the model building as they are not in the risk set at landmark age 60
#> Warning: 745 individuals have been removed from the model building as they are not in the risk set at landmark age 61
#> [1] "Fitting longitudinal submodel, landmark age 60"
#> [1] "Complete, landmark age 60"
#> [1] "Fitting survival submodel, landmark age 60"
#> Warning: Loglik converged before variable  2,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  2 ; coefficient may be infinite. 
#> [1] "Complete, landmark age 60"
#> [1] "Fitting longitudinal submodel, landmark age 61"
#> [1] "Complete, landmark age 61"
#> [1] "Fitting survival submodel, landmark age 61"
#> Warning: Loglik converged before variable  1,3 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> Warning: Loglik converged before variable  1,3,4 ; coefficient may be infinite. 
#> [1] "Complete, landmark age 61"