Conditional distribution of Y|T for a mixed continuous/ordinal (Gaussian-copula) joint model, if no competing risk – biomarker-value prediction

Copula-aware counterpart to conditionalYTBio(), used by dynamicPredictionBio() whenever long_fit_all$biomarker_type contains at least one "ordinal" biomarker (see longitudinalSubCopula()). Both a continuous and an ordinal bio_i target are supported: for an ordinal bio_i, Y_all is expected to already be the vector of candidate category labels (the fitted factor's levels(), in threshold order) rather than a numeric grid – see compute_bio_marker_step(), which builds that vector and translates the result back into integer category codes for its caller. No branching is actually needed here: build_conditional_design_copula() already looks up each row of biomarker bio_i (historical and the candidate row assigned below) generically via long_fit_all$biomarker_type[bio_i], bracketing an ordinal row's latent score between its category's cumulative-link thresholds instead of matching it to an exact value – exactly the same mechanism already used for every other ordinal biomarker's observed history in the joint density. Assigning a candidate label into data_it_Y's ordinal factor column (below) therefore evaluates the same mixed_density_prob_copula() box probability as any other ordinal row would, with no separate code path required.

Unlike conditionalYTBio() – which can evaluate mvtnorm::dmvnorm() once per l_i across every Y_all candidate in one vectorized call, because the multivariate-normal density does not need re-normalizing per candidate – here each candidate value in Y_all changes the conditional block's mean/covariance (see mixed_density_prob_copula()) and therefore requires its own mvtnorm::pmvnorm() evaluation. This makes the copula path in this function O(patients * length(l_i) * length(Y_all)) Monte-Carlo box probability evaluations, rather than one dmvnorm() call per patient/l_i – keep bandcount3 modest for mixed fits with a continuous bio_i (an ordinal bio_i's Y_all length is fixed at its category count, not controlled by bandcount3 at all).

Usage

conditionalYTBioCopula(
  Y_all,
  time_new,
  bio_i,
  data_predict_all,
  long_fit_all,
  l_i,
  survival_variable,
  time_variable,
  survival_variable_all,
  survival_trans_function
)

Arguments

time_new

Prediction time add horizon

bio_i

Biomarker used to do prediction

data_predict_all

This involves a collection of data.frame objects for dynamic prediction, each corresponding to a distinct longitudinal outcome. These data frames should contain the variables specified in long_sub_fixed and long_sub_random. Utilizing a list structure allows for the incorporation of multiple longitudinal outcomes, each potentially following different measurement protocols. In instances where all longitudinal outcomes are recorded at identical time points across patients, a singular data.frame object may be used in a list. It is presumed that each data frame is structured in a long format.

long_fit_all

Outputs from the model fitting process using the nlme package, encompassing the results and parameters obtained from the analysis.

l_i

A vector of time points to calculate the conditional probability.

survival_variable

Time-to-event outcomes variable name.

time_variable

The name of time variable in linear mixed model.

survival_variable_all

The name of the transformed time-to-event outcomes variable.

survival_trans_function

The transformation function used for time-to-event outcomes, in the order of survival_variable_all.