MRsurv (version 0.2)

MRsurvival: Multiplicative-regression model to compare the risk factors between a reference and relative populations.

Description

Compute a MRS model to compare the risk factors between a reference and a relative population.

Usage

MRsurvival(time.ref, status.ref, cov.rel, data.rel, cox.ref, cov.ref, init, B)

Arguments

time.ref

The column name of the data frame data.rel, in which the time of follow-up of each individual is collected.

status.ref

The column name of the data frame data.rel, in which the indicator of event at the end of follow-up is collected (1 if the event is observed and 0 if right censoring).

cov.rel

The column(s) name(s) of the data frame declared in data.rel in order to declare the explicative variable included in the multiplicative relative model.

data.rel

A data frame with the variables (columns) of the individuals (raw) of the relative sample.

cox.ref

The results of the Cox model performed in the reference sample, i.e an object obtained by the coxph function.

cov.ref

The column(s) name(s) of the data frame data.rel in order to declare the explicative variable corresponding to those included in the Cox model cox.ref. Please, note that the order of these variables is important and have to be similar with the order in cox.ref.

init

A vector with the same length than cov.rel with the initial values for the parameters to be optimized.

B

The number of iterations of the bootstrap resampling.

Value

matrix.coef

A matrix containing the parameters estimations at each of the B iterations.

estim.coef

A numerical vector containing the mean of the previous estimation

lower95.coef

A numerical vector containing the lower bounds of the 95% confidence intervals.

upper95.coef

A numerical vector containing the upper bounds of the 95% confidence intervals.

Details

We proposed here an adaptation of a multiplicative-regression model for relative survival to study the heterogeneity of risk factors between two groups of patients. Estimation of parameters is based on partial likelihood maximization and Monte-Carlo simulations associated with bootstrap re-sampling yields to obtain the corresponding standard deviations. The expected hazard ratios are obtained by using a PH Cox model.

References

Andersen P, Borch-Johnsen K, Deckert T, Green A, Hougaard P, Keiding N, Kreiner S. A cox regression model for the relative mortality and its application to diabetes mellitus survival data. Biometrics Dec 1985; 41(4):921-932.

K. Trebern-Launay, M. Giral, J. Dantal and Y. Foucher. Comparison of the risk factors effects between two populations: two alternative approaches illustrated by the analysis of first and second kidney transplant recipients. BMC Med Res Methodol. 2013 Aug 6;13:102.

Examples

# import and attach both samples
data(FTR.data)
data(STR.data)

# We reduce the dimension to save time for this example (CRAN policies)
STR.data <- STR.data[1:100,]

# Compute the Cox model in the reference sample (FTR)
cox.FTR<-coxph(Surv(Tps.Evt, Evt)~ ageR2cl + sexeR, data=FTR.data)
summary(cox.FTR)


# Compute the multiplicative relative model (STR)
mrs.STR <- MRsurvival(time.ref="Tps.Evt", status.ref="Evt",
 cov.rel=c("ageR2cl", "Tattente2cl"),
 data.rel=STR.data, cox.ref=cox.FTR, cov.ref=c("ageR2cl", "sexeR"),
 init=c(0,0), B=5)
  # Of course, choose B>>5 for real applications
  
# The values at each iteration
mrs.STR$matrix.coef

# The parameters estimations (mean of the values)
mrs.STR$estim.coef 
apply(mrs.STR$matrix.coef, FUN="mean", MARGIN=2)

# The 95% confidence intervals
cbind(mrs.STR$lower95.coef, mrs.STR$upper95.coef)