Estimate cumulative response rates (CRR) and test their equality between two groups

Description

Estimate cumulative response rates (CRR) and test their equality between two groups

Usage

CRR(
  t2PROGRESSION,
  STATUS_PROGRESSION,
  t2RESPONSE,
  STATUS_RESPONSE,
  TRT,
  time = NULL,
  alpha = 0.95
)

Arguments

Value

A list with following elements

• result0: a data matrix containing "time", "CRR estimates (group 0)", "standard error of CRR estimates (group 0)", "confidence interval of CRR (group 0)"

• result1: a data matrix containing "time", "CRR estimates (group 1)", "standard error of CRR estimates (group 1)", "confidence interval of CRR (group 1)"

• pvalue: the p-value from two group comparison

References

Gray, RJ. (1988) A class of K-sample tests for comparing the cumulative incidence of a competing risk, ANNALS OF STATISTICS, 16:1141-1154.

Aalen, O. (1978) Nonparametric estimation of partial transition probabilities in multiple decrement models, ANNALS OF STATISTICS, 6:534-545.

Examples

library(cmprsk)
n=100
set.seed(10)

# Generate the data

trt=rbinom(n, 1, 0.5)
error=rnorm(n)
tr=exp(rnorm(n)+error-trt*0.5+0.5)
tp=exp(rnorm(n)+error+trt*0.25)
tr[tp<tr]=Inf
tc=runif(n, 3, 8.5)
t2response=pmin(tr, tc)
delta_response=1*(tr<tc)
t2progression=pmin(tp, tc)
delta_progression=1*(tp<tc)

# Estimate the PBIR in two groups

fit=CRR(t2PROGRESSION=t2progression,
         STATUS_PROGRESSION=delta_progression,
         t2RESPONSE=t2response,
         STATUS_RESPONSE=delta_response,
         TRT=trt)

fit

# Plot the estimated PBIR by group

tt1=c(0, fit$result1$time)
CRR1=c(0, fit$result1$CRR)
B1=length(tt1)
tt1=rep(tt1, rep(2, B1))[-1]
CRR1=rep(CRR1, rep(2, B1))[-(2*B1)]
tt0=c(0, fit$result0$time)
CRR0=c(0, fit$result0$CRR)
B0=length(tt0)
tt0=rep(tt0, rep(2, B0))[-1]
CRR0=rep(CRR0, rep(2, B0))[-(2*B0)]
plot(range(c(fit$result1$time, fit$result0$time)),
     range(c(fit$result1$CRR, fit$result0$CRR)),
     xlab="time",  ylab="CRR",
     main="black: group 0; red: group 1", type="n")
lines(tt0, CRR0, col=1)
lines(tt1, CRR1, col=2)

Estimate the PBIR curve over a time window

Description

Estimate the PBIR curve over a time window

Usage

PBIR1(
  t2PROGRESSION,
  STATUS_PROGRESSION,
  t2RESPONSE,
  STATUS_RESPONSE,
  time = NULL,
  alpha = 0.95
)

Arguments

Value

a data matrix containing "time", "PBIR estimates", "standard errors of PBIR estimates", "confidence intervals of the PBIR"

References

Huang, B., Tian, L., Talukder, E., Rothenberg, M., Kim, DY., and Wei, LJ. (2018) Evaluating Treatment Effect Based on Duration of Response for a Comparative Oncology Study. JAMA Oncol, doi: 10.1001/jamaoncol.2018.0275

Huang, B., Tian, L., McCaw, Z., Luo, Talukder, E., X., Rothenberg, M., Xie, W., Choueiri, T., Kim, DY., & Wei, LJ. (2020). Analysis of Response Data for Assessing Treatment Effects in Comparative Clinical Studies. Ann Intern Med, doi: 10.7326/M20-0104.

Examples

library(survival)
n=100
set.seed(10)

# Generate the data

trt=rbinom(n, 1, 0.5)
error=rnorm(n)
tr=exp(rnorm(n)+error-trt*0.5+0.5)
tp=exp(rnorm(n)+error+trt*0.25)
tr[tp<tr]=Inf
tc=runif(n, 3, 8.5)
t2response=pmin(tr, tc)
delta_response=1*(tr<tc)
t2progression=pmin(tp, tc)
delta_progression=1*(tp<tc)

# Estimate the PBIR in two groups

fit1=PBIR1(t2PROGRESSION=t2progression[trt==1],
           STATUS_PROGRESSION=delta_progression[trt==1],
           t2RESPONSE=t2response[trt==1],
           STATUS_RESPONSE=delta_response[trt==1])

fit0=PBIR1(t2PROGRESSION=t2progression[trt==0],
           STATUS_PROGRESSION=delta_progression[trt==0],
           t2RESPONSE=t2response[trt==0],
           STATUS_RESPONSE=delta_response[trt==0])


# Plot the estimated PBIR by group

tt1=c(0, fit1$time)
PBIR1=c(0, fit1$PBIR)
B1=length(tt1)
tt1=rep(tt1, rep(2, B1))[-1]
PBIR1=rep(PBIR1, rep(2, B1))[-(2*B1)]
tt0=c(0, fit0$time)
PBIR0=c(0, fit0$PBIR)
B0=length(tt0)
tt0=rep(tt0, rep(2, B0))[-1]
PBIR0=rep(PBIR0, rep(2, B0))[-(2*B0)]
plot(range(c(fit1$time, fit0$time)), range(c(fit1$PBIR, fit0$PBIR)),
     xlab="time",  ylab="PBIR",
     main="black: group 0; red: group 1", type="n")
lines(tt0, PBIR0, col=1)
lines(tt1, PBIR1, col=2)

Estimate and compare PBIR curves from two groups over a time window

Description

Estimate and compare PBIR curves from two groups over a time window

Usage

PBIR2(
  t2PROGRESSION,
  STATUS_PROGRESSION,
  t2RESPONSE,
  STATUS_RESPONSE,
  TRT,
  time = NULL,
  alpha = 0.95
)

Arguments

Value

a data matrix containing "time", "estimated differences in PBIR (treatment-control)", "standard errors of estimated PBIR differences", "confidence intervals of the PBIR difference"

References

Huang, B., Tian, L., Talukder, E., Rothenberg, M., Kim, DY., and Wei, LJ. (2018) Evaluating Treatment Effect Based on Duration of Response for a Comparative Oncology Study. JAMA Oncol, doi: 10.1001/jamaoncol.2018.0275

Huang, B., Tian, L., McCaw, Z., Luo, Talukder, E., X., Rothenberg, M., Xie, W., Choueiri, T., Kim, DY., & Wei, LJ. (2020). Analysis of Response Data for Assessing Treatment Effects in Comparative Clinical Studies. Ann Intern Med, doi: 10.7326/M20-0104.

Examples

library(survival)
n=100
set.seed(10)

# Generate the data

TRT=trt=rbinom(n, 1, 0.5)

error=rnorm(n)
tr=exp(rnorm(n)+error-trt*0.5+0.5)
tp=exp(rnorm(n)+error+trt*0.25)
tr[tp<tr]=Inf
tc=runif(n, 3, 8.5)

t2response=pmin(tr, tc)
delta_response=1*(tr<tc)
t2progression=pmin(tp, tc)
delta_progression=1*(tp<tc)

# Estimate the difference in PBIR
# the analysis is truncated at time 8, which is slightly smaller than the largest follow-up time

fit=PBIR2(t2PROGRESSION=t2progression,
          STATUS_PROGRESSION=delta_progression,
          t2RESPONSE=t2response,
          STATUS_RESPONSE=delta_response,
          TRT=trt)


# Plot the estimated differnece in PBIR

tt=fit$time
diff=fit$diff
low=fit$ci.low
up=fit$ci.up

tt=c(0, tt)
diff=c(0, diff)
low=c(0, low)
up=c(0, up)
B=length(tt)

tt=rep(tt, rep(2, B))[-1]
diff=rep(diff, rep(2, B))[-(2*B)]
low=rep(low, rep(2, B))[-(2*B)]
up=rep(up, rep(2, B))[-(2*B)]

plot(range(c(fit$time, 0)), range(c(low, up)),
     xlab="time", ylab="difference in PBIR",
     lwd=2, type="n")
lines(tt, diff, lwd=2, col=3)
lines(tt, low,  col=2)
lines(tt, up, col=2)
lines(range(fit$time), rep(0, 2), col=4, lty=4)

Estimate mean duration of response

Description

Estimate mean duration of response

Usage

mduration(
  t2PROGRESSION,
  STATUS_PROGRESSION,
  t2RESPONSE,
  STATUS_RESPONSE,
  time.max = -1
)

Arguments

Details

The mean duration of response restricted within a time window is also the area under the PBIR curve over the same time window. The estimated mean duration can be viewed as a global summary of the PBIR curve. One may compare the mean duration of response between two groups, which is also a global comparison between two PBIR curves.

Value

A list with following elements

• meandor.est: the restricted mean DOR estimate

• meandor.se: the standard error of the esimated DOR

• time.truncation: the truncation time point used in DOR.

References

Huang, B., Tian, L., Talukder, E., Rothenberg, M., Kim, DY., and Wei, LJ. (2018) Evaluating Treatment Effect Based on Duration of Response for a Comparative Oncology Study. JAMA Oncol, doi: 10.1001/jamaoncol.2018.0275

Huang, B., Tian, L., McCaw, Z., Luo, Talukder, E., X., Rothenberg, M., Xie, W., Choueiri, T., Kim, DY., & Wei, LJ. (2020). Analysis of Response Data for Assessing Treatment Effects in Comparative Clinical Studies. Ann Intern Med, doi: 10.7326/M20-0104.

Examples

library(survival)
n=100
set.seed(10)

# Generate the data

error=rnorm(n)
tr=exp(rnorm(n)+error+0.5)
tp=exp(rnorm(n)+error)
tr[tp<tr]=Inf
tc=runif(n, 3, 8.5)
t2response=pmin(tr, tc)
delta_response=1*(tr<tc)
t2progression=pmin(tp, tc)
delta_progression=1*(tp<tc)

# Estimate the mean duration of response (point estimator and its standard error)

fit=mduration(t2PROGRESSION=t2progression,
              STATUS_PROGRESSION=delta_progression,
              t2RESPONSE=t2response,
              STATUS_RESPONSE=delta_response,
              time.max=8)

fit