Simulate and Plot Estimates from Cox Proportional Hazards Models.

simPH

Christopher Gandrud

Please report any bugs to:

https://github.com/christophergandrud/simPH/issues

simPH is an R package for simulating and plotting quantities of interest (relative hazards, first differences, and hazard ratios) for linear coefficients, multiplicative interactions, polynomials, penalised splines, and non-proportional hazards, as well as stratified survival curves from Cox Proportional Hazard models.

For more information plus examples, please see the description paper in the Journal of Statistical Software.

To cite the paper please use:

@article{simPH_JSS,
    author = {Christopher Gandrud},
    title = {simPH: An R Package for Illustrating Estimates from Cox
        Proportional Hazard Models Including for Interactive and Nonlinear
        Effects},
    journal = {Journal of Statistical Software},
    year = {2015},
    volume = {65},
    issue = {3},
    pages = {1--20}
}

Functions

The package includes the following functions:

Simulation Functions

• coxsimLinear: a function for simulating relative hazards, first differences, hazard ratios, and hazard rates for linear, non-time interacted covariates from Cox Proportional Hazard models.

• coxsimtvc: a function for simulating time interactive hazards (relative hazards, first differences, and hazard ratios) for covariates from Cox Proportional Hazard models. The function will calculate time-interactive hazard ratios for multiple strata estimated from a stratified Cox Proportional Hazard model.

• coxsimSpline: a function for simulating quantities of interest from penalised splines using multivariate normal distributions. Currently does not support simulating hazard rates from stratified models. Note: be extremely careful about the number of simulations you ask the function to find. It is very easy to ask for more than your computer can handle.

• coxsimPoly: a function for simulating quantities of interest for a range of values for a polynomial nonlinear effect from Cox Proportional Hazard models.

• coxsimInteract: a function for simulating quantities of interest for linear multiplicative interactions, including marginal effects and hazard rates.

Plotting Functions

Results from these functions can be plotted using the simGG method. The syntax and capabilities of simGG varies depending on the sim object class you are using:

• simGG.simlinear: plots simulated linear time-constant hazards using ggplot2.

• simGG.simtvc: uses ggplot2 to graph the simulated time-varying relative hazards, first differences, hazard ratios or stratified hazard rates.

• simGG.simspline: uses ggplot2 to plot quantities of interest from simspline objects, including relative hazards, first differences, hazard ratios, and hazard rates.

• simGG.simpoly: uses ggplot2 to graph the simulated polynomial quantities of interest.

• simGG.siminteract: uses ggplot2 to graph linear multiplicative interactions.

Additional styling

Because in almost all cases simGG returns a ggplot2 object, you can add additional aesthetic attributes in the normal ggplot2 way. See the ggplot2 documentation for more details.

Misc.

• SurvExpand: a function for converting a data frame of non-equal interval continuous observations into equal interval continuous observations. This is useful to do before creating time interactions.

  • See also the SurvSetup package for additional functions to set up your data for survival analysis.

• tvc: a function for creating time interactions. Currently supports 'linear', natural 'log', and exponentiation ('power').

• setXl: a function for setting valid Xl values given a sequence of fitted Xj values. This makes it more intuitive to find hazard ratios and first differences for comparisons between some Xj fitted values and Xl values other than 0.

• ggfitStrata: a function to plot fitted stratified survival curves estimated from survfit using ggplot2. This function builds on the survival package's plot.survfit function. One major advantage is the ability to split the survival curves into multiple plots and arrange them in a grid. This makes it easier to examine many strata at once. Otherwise they can be very bunched up.

• MinMaxLines: a function for summarising the constricted intervals from the simulations, including the median, upper and lower bounds and the middle 50% of these intervals.

Installation

The package is available on CRAN and can be installed in the normal R way.

Tip

Before running the simulation and graph functions in this package carefully consider how many simulations you are about to make. Especially for hazard rates over long periods of time and with multiple strata, you can be asking simPH to run very many simulations. This will be computationally intensive.

Sources

Simulating Parameter Estimates

For more information about simulating parameter estimates to make interpretation of results easier see:

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.

Stratified Cox PH

For more information about stratified Cox PH models see:

Box-Steffensmeier, Janet M, and Suzanna De Boef. 2006. “Repeated Events Survival Models: the Conditional Frailty Model.”Statistics in Medicine 25(20): 3518–33.

Shortest Probability Intervals

To learn more about shortest probability intervals (and also for the source of the code that made this possible in simPH) see:

Liu, Y., Gelman, A., & Zheng, T. (2015). "Simulation-efficient Shortest Probablility Intervals."Statistics and Computing 25:809-819.

Also good: Hyndman, R. J. (1996). "Computing and Graphing Highest Density Regions."The American Statistician, 50(2): 120–126.

Interpreting Interactions

For more information about interpreting interaction terms:

Brambor, Thomas, William Roberts Clark, and Matt Golder. 2006. “Understanding Interaction Models: Improving Empirical Analyses.”Political Analysis 14(1): 63–82.

The Olden Days

For an example of how non-proportional hazard results were often presented before simPH see (some of the problems I encountered in this paper were a major part of why I developed this package):

Gandrud, Christopher. 2013. “The Diffusion of Financial Supervisory Governance Ideas.”Review of International Political Economy. 20(4): 881-916.

Future Plans

I intend to expand the quantities of interest that can be simulated and graphed for Cox PH models. I am also currently working on functions that can simulate and graph hazard ratios estimated from Fine and Gray competing risks models.

I am also working on a way to graph hazard ratios with frailties.

Licensed under GPL-3