coxsimtvc() R function from [simPH]

Simulate time-interactive quantities of interest from Cox Proportional Hazards models

coxsimtvc simulates time-interactive relative hazards, first differences, and hazard ratios from models estimated with coxph

using the multivariate normal distribution. These can be plotted with simGG.


coxsimtvc(
  obj,
  b,
  btvc,
  qi = "Relative Hazard",
  Xj = NULL,
  Xl = NULL,
  tfun = "linear",
  pow = NULL,
  nsim = 1000,
  from,
  to,
  by = 1,
  ci = 0.95,
  spin = FALSE,
  extremesDrop = TRUE
)

Arguments

obj: a coxph fitted model object with a time interaction.
b: the non-time interacted variable's name.
btvc: the time interacted variable's name.
qi: character string indicating what quantity of interest you would like to calculate. Can be 'Relative Hazard', 'First Difference', 'Hazard Ratio', 'Hazard Rate'. Default is qi = 'Relative Hazard'. If qi = 'First Difference'

or qi = 'Hazard Ratio' then you can set Xj and Xl.
Xj: numeric vector of fitted values for b. Must be the same length as Xl or Xl must be NULL.
Xl: numeric vector of fitted values for Xl. Must be the same length as Xj. Only applies if qi = 'First Difference' or qi = 'Hazard Ratio'.
tfun: function of time that btvc was multiplied by. Default is "linear". It can also be "log" (natural log) and "power". If tfun = "power" then the pow argument needs to be specified also.
pow: if tfun = "power", then use pow to specify what power the time interaction was raised to.
nsim: the number of simulations to run per point in time. Default is nsim = 1000.
from: point in time from when to begin simulating coefficient values
to: point in time to stop simulating coefficient values.
by: time intervals by which to simulate coefficient values.
ci: the proportion of simulations to keep. The default is ci = 0.95, i.e. keep the middle 95 percent. If spin = TRUE

then ci is the confidence level of the shortest probability interval. Any value from 0 through 1 may be used.
spin: logical, whether or not to keep only the shortest probability interval rather than the middle simulations. Currently not supported for hazard rates.
extremesDrop: logical whether or not to drop simulated quantity of interest values that are Inf, NA, NaN and $> 1000000$ for spin = FALSE or $> 800$ for spin = TRUE. These values are difficult to plot simGG and may prevent spin from finding the central interval.

Returns

a simtvc object

Details

Simulates time-varying relative hazards, first differences, and hazard ratios using parameter estimates from coxph models. Can also simulate hazard rates for multiple strata.

Relative hazards are found using:

RH = e^{\beta_{1} + \beta_{2}f(t)}RH = exp(\beta[1] + \beta[2] f(t))

where $f(t)$ is the function of time.

First differences are found using:

FD = (e^{(X_{j} - X_{l}) (\beta_{1} + \beta_{2}f(t))} - 1) * 100FD =(exp((X[j] - X[l])(\beta[1] + \beta[2]f(t)) - 1) * 100

where $X[j]$ and $X[l]$ are some values of $X$ to contrast.

Hazard ratios are calculated using:

FD = e^{(X_{j} - X_{l}) (\beta_{1} + \beta_{2}f(t))}FD = exp((X[j] - X[l])(\beta[1] + \beta[2]f(t))

When simulating non-stratifed time-varying harzards coxsimtvc uses the point estimates for a given coefficient $hat \beta[x]$ and its time interaction $hat \beta[xt]$

along with the variance matrix ( $hat V(hat \beta)$ ) estimated from a coxph model. These are used to draw values of $\beta[1]$ and $\beta[2]$ from the multivariate normal distribution $N(hat \beta, hat V (hat \beta))$ .

When simulating stratified time-varying hazard rates $H$ for a given strata $k$ , coxsimtvc uses:

H_{kxt} = \hat{\beta}_{k0t}e^{\hat{\beta_{1}} + \beta_{2}f(t)}H_{kxt} = hat \beta[k0t]exp(hat \beta[1] + \beta[2]f(t))

The resulting simulation values can be plotted using simGG.

Examples


## Not run:

# Load Golub & Steunenberg (2007) Data
data("GolubEUPData")

# Load survival package
library(survival)

# Expand data (not run to speed processing time, but should be run)
GolubEUPData <- SurvExpand(GolubEUPData, GroupVar = 'caseno',
                     Time = 'begin', Time2 = 'end', event = 'event')

# Create time interactions
BaseVars <- c('qmv', 'backlog', 'coop', 'codec', 'qmvpostsea', 'thatcher')
GolubEUPData <- tvc(GolubEUPData, b = BaseVars, tvar = 'end', tfun = 'log')

# Run Cox PH Model
M1 <- coxph(Surv(begin, end, event) ~ qmv + qmvpostsea + qmvpostteu +
                coop + codec + eu9 + eu10 + eu12 + eu15 + thatcher +
                agenda + backlog + qmv_log + qmvpostsea_log + coop_log +
                codec_log + thatcher_log + backlog_log,
            data = GolubEUPData, ties = "efron")

# Create simtvc object for Relative Hazard
Sim1 <- coxsimtvc(obj = M1, b = "qmv", btvc = "qmv_log",
                   tfun = "log", from = 80, to = 2000,
                   Xj = 1, by = 15, ci = 0.99, nsim = 100)

# Create simtvc object for First Difference
Sim2 <- coxsimtvc(obj = M1, b = "qmv", btvc = "qmv_log",
                 qi = "First Difference", Xj = 1,
                 tfun = "log", from = 80, to = 2000,
                 by = 15, ci = 0.95)

# Create simtvc object for Hazard Ratio
Sim3 <- coxsimtvc(obj = M1, b = "backlog", btvc = "backlog_log",
                  qi = "Hazard Ratio", Xj = c(191, 229),
                  Xl = c(0, 0),
                  tfun = "log", from = 80, to = 2000,
                  by = 15, ci = 0.5)
## End(Not run)

References

Gandrud, Christopher. 2015. simPH: An R Package for Illustrating Estimates from Cox Proportional Hazard Models Including for Interactive and Nonlinear Effects. Journal of Statistical Software. 65(3)1-20.

Golub, Jonathan, and Bernard Steunenberg. 2007. ''How Time Affects EU Decision-Making.'' European Union Politics 8(4): 555-66.

Licht, Amanda A. 2011. ''Change Comes with Time: Substantive Interpretation of Nonproportional Hazards in Event History Analysis.'' Political Analysis 19: 227-43.

King, Gary, Michael Tomz, and Jason Wittenberg. 2000. ''Making the Most of Statistical Analyses: Improving Interpretation and Presentation.'' American Journal of Political Science 44(2): 347-61.

Liu, Ying, Andrew Gelman, and Tian Zheng. 2013. ''Simulation-Efficient Shortest Probability Intervals.'' Arvix. https://arxiv.org/pdf/1302.2142v1.pdf.

coxsimtvc function