Example
We use the sample example from the introductory vignette to joineRML using the heart valve data.
We analyse only the records with case-complete data for heart valve gradient (grad) and left ventricular mass index (lvmi):
Further to that, we only select the first 50 individuals to speed up these examples:
set.seed(12345)
fit <- mjoint(
formLongFixed = list(
"grad" = log.grad ~ time + sex + hs,
"lvmi" = log.lvmi ~ time + sex
),
formLongRandom = list(
"grad" = ~ 1 | num,
"lvmi" = ~ time | num
),
formSurv = Surv(fuyrs, status) ~ age,
data = list(hvd, hvd),
timeVar = "time"
)## Running multivariate LMM EM algorithm to establish initial parameters...## Finished multivariate LMM EM algorithm...## EM algorithm has converged!## Calculating post model fit statistics...tidy method
The tidy method returns a tidy dataset with model estimates.
## # A tibble: 3 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 age 0.137 0.0661 2.07 0.0382
## 2 gamma_1 2.90 3.74 0.776 0.438
## 3 gamma_2 3.69 3.37 1.10 0.273By default the tidy method returns the estimated coefficients for the survival component of the joint model; however, it is possible to extract each component by setting the component argument:
## # A tibble: 7 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept)_1 2.52 0.163 15.4 1.07e-53
## 2 time_1 0.00959 0.0310 0.309 7.57e- 1
## 3 sex_1 0.0336 0.230 0.146 8.84e- 1
## 4 hsStentless valve_1 0.0823 0.198 0.416 6.77e- 1
## 5 (Intercept)_2 4.99 0.0829 60.2 0.
## 6 time_2 0.0260 0.0129 2.02 4.36e- 2
## 7 sex_2 -0.197 0.209 -0.941 3.47e- 1It is also possible to require confidence intervals to be calculated by setting conf.int = TRUE, and modify the confidence level by setting the conf.level argument:
## # A tibble: 3 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 age 0.137 0.0661 2.07 0.0382
## 2 gamma_1 2.90 3.74 0.776 0.438
## 3 gamma_2 3.69 3.37 1.10 0.273## # A tibble: 3 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 age 0.137 0.0661 2.07 0.0382
## 2 gamma_1 2.90 3.74 0.776 0.438
## 3 gamma_2 3.69 3.37 1.10 0.273The standard errors reported by default are based on the empirical information matrix, as in mjoint. It is of course possible to use bootstrapped standard errors as follows:
bSE <- bootSE(fit, nboot = 100, safe.boot = TRUE, progress = FALSE)
tidy(fit, boot_se = bSE, conf.int = TRUE)The results of this example are not included as it would take too long to run for CRAN.
The tidy method is useful for custom plotting (e.g. forest plots) of results from joineRML models, all in a tidy framework:
library(ggplot2)
out <- tidy(fit, conf.int = TRUE)
ggplot(out, aes(x = term, y = estimate, ymin = conf.low, ymax = conf.high)) +
geom_point() +
geom_errorbar()
augment method
The augment method returns a dataset with added predictions from the joint model. In particular, population-level and individual-level fitted values and residuals are added to the data frame returned by the method:
preds <- augment(fit)
head(preds[, c("num", "log.grad", ".fitted_grad_0", ".fitted_grad_1", ".resid_grad_0", ".resid_grad_1")])## # A tibble: 6 x 6
## num log.grad .fitted_grad_0 .fitted_grad_1 .resid_grad_0 .resid_grad_1
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 2.30 2.60 2.42 -0.301 -0.114
## 2 1 2.30 2.64 2.45 -0.337 -0.149
## 3 1 2.30 2.65 2.46 -0.346 -0.158
## 4 2 2.64 2.58 2.45 0.0563 0.188
## 5 2 2.20 2.59 2.46 -0.394 -0.263
## 6 2 2.48 2.60 2.47 -0.116 0.0152head(preds[, c("num", "log.lvmi", ".fitted_lvmi_0", ".fitted_lvmi_1", ".resid_lvmi_0", ".resid_lvmi_1")])## # A tibble: 6 x 6
## num log.lvmi .fitted_lvmi_0 .fitted_lvmi_1 .resid_lvmi_0 .resid_lvmi_1
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 4.78 4.99 4.75 -0.213 0.0298
## 2 1 4.78 5.09 4.87 -0.308 -0.0869
## 3 1 4.92 5.11 4.90 -0.189 0.0265
## 4 2 4.74 5.16 4.83 -0.413 -0.0827
## 5 2 4.70 5.18 4.86 -0.483 -0.157
## 6 2 5.06 5.21 4.89 -0.149 0.174We can plot the resulting predictions for four distinct individuals:
out <- preds[preds$num %in% c(26, 36, 227, 244), ]
ggplot(out, aes(x = time, colour = num)) +
geom_line(aes(y = log.grad, linetype = "Measured")) +
geom_line(aes(y = .fitted_grad_1, linetype = "Fitted")) +
labs(linetype = "Type", colour = "ID", y = "Aortic gradient")
glance method
The glance method allows extracting summary statistics from the joint model:
## # A tibble: 1 x 5
## sigma2_1 sigma2_2 AIC BIC logLik
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.517 0.158 342. 374. -153.This allows comparing competing models easily. Say for instance that we fit a second model with only random intercepts:
set.seed(67890)
fit2 <- mjoint(
formLongFixed = list(
"grad" = log.grad ~ time + sex + hs,
"lvmi" = log.lvmi ~ time + sex
),
formLongRandom = list(
"grad" = ~ 1 | num,
"lvmi" = ~ 1 | num
),
formSurv = Surv(fuyrs, status) ~ age,
data = list(hvd, hvd),
timeVar = "time"
)## Running multivariate LMM EM algorithm to establish initial parameters...## Finished multivariate LMM EM algorithm...## EM algorithm has converged!## Calculating post model fit statistics...We can go ahead and compare the models in terms of AIC and BIC:
## # A tibble: 1 x 5
## sigma2_1 sigma2_2 AIC BIC logLik
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.517 0.158 342. 374. -153.## # A tibble: 1 x 5
## sigma2_1 sigma2_2 AIC BIC logLik
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.516 0.173 342. 369. -156.