# Using FLORAL for survival models with longitudinal microbiome data

    library(FLORAL)
    library(dplyr)
    library(patchwork)
    library(survival)
    set.seed(8192024)

In this vignette, we illustrate how to apply `FLORAL` to fit a Cox model with longitudinal microbiome data. Due to limited availability of public data sets with survival information, we use simulated data for illustrative purposes.

## Data simulation

We will use the built-in simulation function `simu()` to generate longitudinal compositional features and the corresponding time-to-event. The underlying methodology used for the simulation is based on a piece-wise exponential distribution as described by Hendry 2014.

By default, the first 10 features out of the 500 features simulated below are associated with the time-to-event.

    simdat <- simu(n=200, # sample size
                   p=500, # number of features
                   model="timedep",
                   pct.sparsity = 0.8, # proportion of zeros
                   rho=0, # feature-wise correlation
                   longitudinal_stability = TRUE # choose to simulate longitudinal features with stable trajectories
    )

With the simulated data, the log-ratio lasso Cox model with time-dependent features can be fitted by running the following function. Here we provide a detailed description on each arguments:

- First of all, please use `longitudinal = TRUE` such that the algorithm would use the appropriate method to handle longitudinal data.
- The feature matrix input `x` should be the count matrix where rows specify samples and columns specify features.
- The vector of IDs of subjects/patients corresponding to the rows of `x` should be input as `id`.
- The vector of sample collection times corresponding to the rows of `x` should be input as `tobs`.
- The `Surv` object (`Surv(time,status)`) of unique patients should be input as `y`. Please note that the survival data should be sorted with respect to the IDs specified in `id`.

    fit <- FLORAL(x=simdat$xcount,
                  y=Surv(simdat$data_unique$t,simdat$data_unique$d),
                  family="cox",
                  longitudinal = TRUE,
                  id = simdat$data$id,
                  tobs = simdat$data$t0,
                  progress=FALSE,
                  plot=TRUE)

    fit$selected
    #> $min
    #> [1] "taxa1"   "taxa2"   "taxa27"  "taxa366" "taxa37"  "taxa5"   "taxa6"
    #> [8] "taxa8"   "taxa9"
    #>
    #> $`1se`
    #> [1] "taxa1" "taxa5" "taxa6" "taxa8" "taxa9"
    #>
    #> $min.2stage
    #> [1] "taxa1"   "taxa2"   "taxa27"  "taxa366" "taxa37"  "taxa5"   "taxa6"
    #> [8] "taxa8"   "taxa9"
    #>
    #> $`1se.2stage`
    #> [1] "taxa1" "taxa5" "taxa6" "taxa8" "taxa9"

The list of selected features is saved in `fit$selected` as shown above.

To appropriately prepare the data in practice, we have the following recommendations:

- Start with patient metadata which includes survival data (time and status), sorting the metadata by patient IDs. Extract time and status variables for the `Surv` object for input as `y`.
- Curate the microbiome feature data matrix, sorted by patient IDs and time of sample collection. Save the patient ID and time of sample collection vectors for `id` and `tobs`. Save the feature table for input as `x`.