surrosurv {surrosurv}

Fit and print the models for evaluating the surrogacy strength of a candidate surrogate endpoint

Description

The function surrosurv fits (all or a subset of) statistical models to evaluate a surrogate endpoint S for a given true endpoint T, using individual data from a meta-analysis of randomized controlled trials.

Usage

surrosurv(data,
          models = c('Clayton', 'Plackett', 'Hougaard',
                     'Poisson I', 'Poisson T', 'Poisson TI', 'Poisson TIa'),
          intWidth = NULL,  nInts = 8,
          cop.OPTIMIZER = "bobyqa",
          poi.OPTIMIZER = "bobyqa",
          verbose = TRUE,
          twoStage = FALSE,
          keep.data = TRUE)

## S3 method for class 'surrosurv'
predict(object, models = names(object), exact.models, ...)

## S3 method for class 'surrosurv'
print(x, silent = FALSE, 
      digits = 2, na.print = "-.--", ...)
          
## S3 method for class 'predictSurrosurv'
print(x, n = 6, ...)
          
## S3 method for class 'surrosurv'
plot(x, ...)

## S3 method for class 'predictSurrosurv'
plot(x, models = names(x), exact.models,
                      pred.ints = TRUE,
                      show.ste = TRUE,
                      surro.stats = TRUE, 
                      xlab, ylab, 
                      xlim, ylim, mfrow, main, ...)

Arguments

data

A data.frame with columns

• trialref, the trial reference

• trt, the treatment arm (-0.5 or 0.5)

• id, the patient id

• timeT, the value of the true endpoint T

• statusT, the censoring/event (0/1) indicator of the true endpoint T

• timeS, the value of the surrogate endpoint S

• statusS, the censoring/event (0/1) indicator of the surrogate endpoint S

models

For surrosurv(), the models should be fitted/plotted/predicted. Possible models are: Clayton copula (unadjusted and adjusted), Plackett copula (unadjusted and adjusted), Hougaard copula (unadjusted and adjusted), Poisson (with individual-level heterogeneity only, with trial-level heterogeneity only, with both individual- and trial-level heterogeneity, with both individual- and trial-level heterogeneity and with random per-trial intercept).

exact.models

If TRUE, plots or predictions are generated only for the elements of x which match exactly any of models. If exact.models = TRUE, partial matching is used. By default, exact.models = TRUE if all the models match exactly any of the names(x) (or names(object)) and exact.models = FALSE otherwise.

intWidth

the width of time intervals for data Poissonization (see poissonize)

nInts

the number of time intervals for data Poissonization (see poissonize)

cop.OPTIMIZER

the optimizer for copula models (see optimx)

poi.OPTIMIZER

the optimizer for Poisson models (see optimx)

verbose

should the function print out the model being fitted

twoStage

should the parameters of the baseline hazard functions fixed to their marginal estimates (Shih and Louis, 1995)

keep.data

should the data object be kept as attribute of the returned results? (this is needed for confint.surrosurv())

x, object

The fitted models, an object of class surrosurv

silent

Should the results be return for storing without printing them?

digits, na.print, xlab, ylab, xlim, ylim, main, ...

other parameters for print or plot

mfrow

the number of rows and columns for displaying the plots (see par). If missing, the default is computed using the function n2mfrow

n

the number of rows to print

pred.ints

Should the prediction intervals be plotted?

show.ste

Should the surrogate threshold effect be showed?

surro.stats

Should the surrogacy statistics be showed?

Details

Three copula models can be fit: Clayton (1978), Plackett (1965), and Hougaard (1986). For all of them the linear regression at the second step is computed both via simple LS regression and via a linear model adjusted for measurement error of the log-hazard ratios estimated at the first step. This adjusted model is the one described by Burzykowski et al. (2001), which relies on the results by van Houwelingen et al. (2002).

The mixed Poisson models that can be fit are used to estimate parameters of mixed proportional hazard models, as described for instance by Crowther et al (2014). The statistical details are provided in Rotolo et al (WP).

The function predict() returns the estimated values of the log-hazard ratios on the true and the surrogate endpoints. The list of the prediction functions (for all the models) is available as attr(predict.surrosurv(...), 'predf').

Value

The fitted models, an object of class surrosurv.

Author(s)

NA

References

Burzykowski T, Molenberghs G, Buyse M et al. Validation of surrogate end points in multiple randomized clinical trials with failure time end points. Journal of the Royal Statistical Society C 2001; 50:405–422. doi: 10.1111/1467-9876.00244

Clayton DG. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 1978; 65:141–151. doi: 10.1093/biomet/65.1.141

Crowther MJ, Riley RD, Staessen JA, Wang J, Gueyffier F, Lambert PC. Individual patient data meta-analysis of survival data using Poisson regression models. BMC Medical Research Methodology 2012; 12:34. doi: 10.1186/1471-2288-12-34.

Gasparrini A, Armstrong B, Kenward MG. Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine 2012; 31:3821–39. doi: 10.1002/sim.5471

Hougaard P. A class of multivariate failure time distributions. Biometrika 1986; 73:671–678. doi: 10.1093/biomet/73.3.671

Plackett RL. A class of bivariate distributions. Journal of the America Statistical Association 1965; 60:516–522. doi: 10.1080/01621459.1965.10480807

Rotolo F, Paoletti X, Burzykowski T, Buyse M, Michiels S. A Poisson approach for the validation of failure time surrogate endpoints in individual patient data meta-analyses. Statistical Methods in Medical Research 2017; In Press. doi: 10.1177/0962280217718582

Shih JH, Louis TA. Inferences on the Association Parameter in Copula Models for Bivariate Survival Data. Biometrics 1995; 51:1384–1399. doi: 10.2307/2533269

van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Statistics in Medicine 2002; 21:589–624. doi: 10.1002/sim.1040

Examples

  set.seed(150)
  data <- simData.re(N = 20, ni = 250,
                     R2 = 0.8, kTau = 0.4,
                     alpha = log(0.95), beta = log(0.85),
                     censorA = 15 * 365.25)
  library(survival)
  par(mfrow = 1:2)
  plot(survfit(Surv(timeS, statusS) ~ trt, data = data), lty = 1:2, 
       xscale = 365.25, main = 'Progression-Free Survival\n(S)', col = 2)
  plot(survfit(Surv(timeT, statusT) ~ trt, data = data), lty = 1:2,
       xscale = 365.25, main = 'Overall Survival\n(T)')
       
  ## Not run: 
    # Long computation time!
    surrores <- surrosurv(data, verbose = TRUE)
    convergence(surrores)
    surrores
  
## End(Not run)
  
  # Advanced GASTRIC data
  ## Not run: 
    # Long computation time!
    data('gastadv')
    allSurroRes <- surrosurv(gastadv, c('Clayton', 'Poisson'), verbose = TRUE)
    convergence(allSurroRes)
    allSurroRes
    predict(allSurroRes)
    plot(allSurroRes)
  
## End(Not run)