simKHCE: Simulate a kidney disease 'hce' dataset

In hce: Design and Analysis of Hierarchical Composite Endpoints

Simulate a kidney disease hce dataset

Description

Simulate a kidney disease hce dataset, capturing eGFR (Estimated Glomerular Filtration Rate) progression over time, along with a competing and dependent terminal event: KFRT (Kidney Failure Replacement Therapy)

Usage

simKHCE(
  n,
  CM_A,
  CM_P = -4,
  n0 = n,
  TTE_A = 1000,
  TTE_P = TTE_A,
  fixedfy = 2,
  Emin = 20,
  Emax = 100,
  sigma = NULL,
  Sigma = 3,
  m = 10,
  theta = -0.4605,
  phi = 0,
  two_meas = c("no", "base", "postbase", "both"),
  df_sigma = Inf
)

Arguments

n	sample size in the active treatment group.
CM_A	annualized eGFR slope in the active group.
CM_P	annualized eGFR slope in the control group.
n0	sample size in the control treatment group.
TTE_A	event rate per year in the active group for KFRT.
TTE_P	event rate per year in the placebo group for KFRT.
fixedfy	length of follow-up in years.
Emin	lower limit of eGFR at baseline.
Emax	upper limit of eGFR at baseline.
sigma	within-patient standard deviation.
Sigma	between-patient standard deviation.
m	number of equidistant visits.
theta	coefficient of dependence of eGFR values and the risk of KFRT.
phi	coefficient of proportionality (between 0 and 1) of the treatment effect. The case of 0 corresponds to the uniform treatment effect.
two_meas	determines whether to use duplicate measurements at baseline and/or at fixedfy. The default is to use a single measurement.
df_sigma	degrees of freedom for the measurement error distribution. The default Inf gives normal measurement errors; must be more than 2.

Details

The default setting is TTE_A = TTE_P because, conditional on eGFR level, the treatment effect does not influence the event rate of KFRT. In this model, the effect of treatment on KFRT operates entirely through its impact on eGFR decline.

Let CM_A and CM_P be denoted by \beta_A and \beta_P, respectively. Let TTE_A and TTE_P be denoted by \lambda_A and \lambda_P, respectively. Let theta be denoted by \theta, phi by \phi, sigma by \sigma, Sigma by \Sigma, and df_sigma by \nu.

The parameters TTE_A and theta are chosen so that when GFR is 15, the event rate is 1 per patient per year, and when GFR is 25, the event rate is 0.01 per patient per year. These parameter values are obtained by solving

\lambda_g \exp(\theta \cdot \mathrm{GFR}) = \mathrm{rate}

for the group-specific baseline rate \lambda_g and \theta. When the observed eGFR is above 30, the event rate is set to a very low value (10e-7), while when the observed eGFR is below or equal to 7, the event rate is set to a very high value (10e5). This ensures that patients with observed low eGFR values always experience KFRT, while those with high eGFR values do not.

By default, the within-patient standard deviation, sigma, is set to NULL. When left as NULL, sigma is calculated as

\sigma_{ij} = \sqrt{0.67 \cdot \mu_{ij}},

where \mu_{ij} denotes the predicted eGFR for patient i at visit j. This yields time-dependent measurement variability, with lower predicted eGFR values corresponding to lower variability. In the implementation, to prevent the variance from becoming negative or too small, the quantity 0.67 \cdot \mu_{ij} is truncated below at 0.1 before taking the square root.

When df_sigma = Inf (the default), measurement errors are normally distributed:

\varepsilon_{ij} \sim N(0, \sigma_{ij}^2).

When df_sigma is finite and greater than 2, measurement errors follow a Student t distribution with heavier tails:

\varepsilon_{ij} = \sigma_{ij}\sqrt{\frac{\nu - 2}{\nu}} T_{\nu},

where \nu = df_sigma and T_{\nu} is a standard t random variable with \nu degrees of freedom. This scaling preserves the same time-dependent standard deviation defined by sigma, so that

\mathrm{Var}(\varepsilon_{ij}) = \sigma_{ij}^2.

Given the overall effect Delta and the placebo progression rate CM_P, a fully uniform (purely additive) treatment effect—meaning the same average effect applies to all patients regardless of baseline progression—is implemented by setting \phi = 0 and

\beta_A = \Delta + \beta_P.

A fully proportional treatment effect—no additive component, the effect scales with the baseline rate—is implemented by setting

\beta_A = \beta_P

and

\phi = \frac{\Delta}{|\beta_P|}.

A more relativistic intermediate effect (half additive and half proportional) is obtained by setting

\phi = \frac{\Delta}{2|\beta_P|}

and

\beta_A = \frac{\Delta}{2} + \beta_P.

The kidney hierarchical composite endpoint is defined in the following order: (1) Kidney Failure Replacement Therapy (KFRT); (2) Sustained eGFR < 15; (3) Sustained 57 percent or more decline in eGFR; (4) Sustained 50 percent or more decline in eGFR; (5) Sustained 40 percent or more decline in eGFR; and (6) Change in eGFR. In practice, because KFRT is frequently initiated when true eGFR is very low, sustained eGFR < 15 events are rarely observed.

If two_meas is not "no", a second measurement is generated using the same latent baseline eGFR and subject-specific slope, but with an independent measurement error draw from the same distribution as above. The two measurements are then averaged at baseline when two_meas = "base", at the final visit when two_meas = "postbase", or at both baseline and the final visit when two_meas = "both". This implementation preserves correlation between the duplicate measurements because they share the same underlying true trajectory.

See Also

simHCE() for a general function of simulating hce datasets.

Examples

# Example - Specifying the most important variables
set.seed(2022)
## The overall treatment effect
Delta <- 0.75
## The placebo progression rate
CM_P <- - 4.5
## Intermediate effect (half additive and half proportional)
delta <- Delta/2
CM_A <- delta + CM_P 
phi <- Delta / (2*abs(CM_P))
L <- simKHCE(n = 1000, CM_A = CM_A, CM_P = CM_P, 
fixedfy = 4, Emin = 25, Emax = 75, phi = phi)
dat <- L$HCE
calcWO(dat)

hce documentation built on May 13, 2026, 9:06 a.m.