coxsimPoly: Simulate quantities of interest for a range of values for a polynomial nonlinear effect from Cox Proportional Hazards models

Description

coxsimPoly simulates quantities of interest for polynomial covariate effects estimated from Cox Proportional Hazards models. These can be plotted with simGG.

Usage

coxsimPoly(obj, b = NULL, qi = "Relative Hazard", pow = 2, Xj = NULL,
  Xl = NULL, nsim = 1000, ci = 0.95, spin = FALSE,
  extremesDrop = TRUE)

Arguments

obj

a coxph class fitted model object with a polynomial coefficient. These can be plotted with simGG.

character string name of the coefficient you would like to simulate. To find the quantity of interest using only the polynomial and not the polynomial + the linear terms enter the polynomial created using I, e.g.

quantity of interest to simulate. Values can be "Relative Hazard", "First Difference", "Hazard Ratio", and "Hazard Rate". The default is qi = "Relative Hazard". If qi = "Hazard Rate"

pow

numeric polynomial used in coxph.

Xj

numeric vector of fitted values for b to simulate for.

Xl

numeric vector of values to compare Xj to. If NULL,
then it is authomatically set to 0.

nsim

the number of simulations to run per value of Xj. Default
is nsim = 1000.

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

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

`Value`

a simpoly class object.

`Details`

Simulates quantities of interest for polynomial covariate effects.
For example if a nonlinear effect is modeled with a second order
polynomial--i.e. $\beta_{1}x_{i} + \beta_{2}x_{i}^{2}$--we can once again draw $n$ simulations from the
multivariate normal distribution for both $\beta_{1}$ and
$\beta_{2}$. Then we simply calculate quantities of interest
for a range of values and plot the results as before. For example, we find
the first difference for a second order polynomial with:
$$%\triangle h_{i}(t) = (\mathrm{e}^{\beta_{1}x_{j-1} +
\beta_{2}x_{j-l}^{2}} - 1) * 100$$
where $x_{j-l} = x_{j} - x_{l}$.
Note, you must use I to create the polynomials.

`References`

Keele, Luke. 2010. ''Proportionally Difficult: Testing for
Nonproportional Hazards in Cox Models.'' Political Analysis 18(2): 189-205.
Carpenter, Daniel P. 2002. ''Groups, the Media, Agency Waiting Costs, and
FDA Drug Approval.'' American Journal of Political Science 46(3): 490-505.
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.
http://arxiv.org/pdf/1302.2142v1.pdf.

`See Also`

simGG, survival, strata,
and coxph

`Examples`

Run this code# Load Carpenter (2002) data
data("CarpenterFdaData")

# Load survival package
library(survival)

# Run basic model
M1 <- coxph(Surv(acttime, censor) ~ prevgenx + lethal + deathrt1 +
            acutediz + hosp01  + hhosleng + mandiz01 + femdiz01 +
            peddiz01 + orphdum + natreg + I(natreg^2) +
            I(natreg^3) + vandavg3 + wpnoavg3 +
            condavg3 + orderent + stafcder, data = CarpenterFdaData)

# Simulate simpoly First Difference
Sim1 <- coxsimPoly(M1, b = "natreg", qi = "First Difference",
                pow = 3, Xj = seq(1, 150, by = 5), nsim = 100)

# Simulate simpoly Hazard Ratio with spin probibility interval
Sim2 <- coxsimPoly(M1, b = "natreg", qi = "Hazard Ratio",
              pow = 3, Xj = seq(1, 150, by = 5), spin = TRUE)
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