Fix Random Slope Model Link Parameter

[gowerc]

Currently it looks like the link parameter to the random slope model isn't working. As in its credible intervals are massive even with reasonably large amounts of data. This may just be the nature of the model but it may also indicate a bug in the code. Needs to be investigated and resolved.

example code:

devtools::load_all(export_all = FALSE)

# Fully specified model
jm <- JointModel(
    longitudinal_model = LongitudinalRandomSlope(),
    link = LinkRandomSlope(),
    survival_model = SurvivalWeibullPH()
)

jlist <- simulate_joint_data(
    n = 1000,
    max_time = 2000,
    lambda_cen = 1 / 9000,
    beta_cat = c(
        "A" = 0,
        "B" = -0.1,
        "C" = 0.5
    ),
    beta_cont = 0.3,
    lm_fun = sim_lm_random_slope(
        intercept = 30,
        sigma = 3,
        slope = 2,
        z_sigma = 0.2,
        phi = 0.02
    ),
    os_fun = sim_os_weibull(
        lambda = 1 / 300,
        gamma = 0.97
    )
)

dat_os <- jlist$os
dat_lm <- jlist$lm |>
    dplyr::filter(time %in% c(1, 50, 100, 150, 200, 250, 300)) |>
    dplyr::arrange(time, pt)

stan_data <- as_stan_data(dat_os, dat_lm, ~ cov_cat + cov_cont)

dir.create(path = file.path("local"), showWarnings = FALSE)
mp <- sampleStanModel(
    jm,
    data = stan_data,
    iter_sampling = 1000,
    iter_warmup = 1000,
    chains = 1,
    parallel_chains = 1,
    exe_file = file.path("local", "full")
)

[gowerc]

Recommendations from @danielinteractive were to check the following:

• Run multiple chains and see if they are all converging
• Check the traceplots to see that they are stable
• Run with different sample sizes (50, 100, 1000) and see if the credible intervals are shrinking

[gowerc]

Phi with true value of 0.1

for 800 / 1600 / 4000 patients respectively:

variable       mean   median      sd     mad       q5      q95  rhat
link_lm_phi  0.132    0.133   3.49e-2 3.46e-2  0.0756   0.188   1.00
link_lm_phi  0.0881   0.0886  2.48e-2 2.46e-2  0.0458   0.127   1.01 
link_lm_phi  0.117    0.117   1.57e-2 1.49e-2  0.0898   0.142   1.00

Seems to be working exactly as expected now will close