coxsimtvc: Simulate time-interactive quantities of interest from Cox...
In simPH: Simulate and Plot Estimates from Cox Proportional Hazards Models

Description Usage Arguments Details Value References See Also Examples

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
)

`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.

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 = exp(β[1] + β[2] f(t))

where f(t) is the function of time.

First differences are found using:

FD = (exp((X[j] - X[l])(β[1] + β[2]f(t)) - 1) * 100

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

Hazard ratios are calculated using:

FD = exp((X[j] - X[l])(β[1] + β[2]f(t))

When simulating non-stratifed time-varying harzards coxsimtvc uses the point estimates for a given coefficient hat β[x] and its time interaction hat β[xt] along with the variance matrix (hat V(hat β)) estimated from a coxph model. These are used to draw values of β[1] and β[2] from the multivariate normal distribution N(hat β, hat V (hat β)).

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

H_{kxt} = hat β[k0t]exp(hat β[1] + β[2]f(t))

The resulting simulation values can be plotted using simGG.

a simtvc object

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.

simGG, survival, strata, and coxph

## 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)