Reduced Piecewise Exponential Estimate/Test Software

Description

This reduced piecewise exponential survival software implements the likelihood ratio test and backward elimination procedure in Han, Schell, and Kim (2012, 2014), and Han et al. (2016). Inputs to the program can be either times when events/censoring occur or the vectors of total time on test and the number of events. Outputs of the programs are times and the corresponding p-values in the backward elimination. Details about the model and implementation are given in Han et al. 2014. This program can run in R version 3.2.2 and above.

References

[1] Han, G., Schell, M. J., and Kim, J. (2012) “Comparing Two Exponential Distributions Using the Exact Likelihood Ratio Test," Statistics in Biopharmaceutical Research, 4(4), 348-356.

[2] Han, G., Schell, M. J., and Kim, J. (2014) “Improved Survival Modeling in Cancer Research Using a Reduced Piecewise Exponential Approach," Statistics in Medicine, 33(1), 59-73.

[3] Han, G., Schell, M., Zhang, H., Zelterman, D., Pusztai, L., Adelson, K., and Hatzis, C. (2016) “Testing Violations of the Exponential Assumption in Cancer Clinical Trials with Survival Endpoints," Biometrics, DOI: 10.1111/biom.12590; PMID: 27669414.

[4] Adelson, K. B., Ramaswamy, B., Sparano, J. A., Christos, P. J., Wright, J. J., Raptis, G., Han, G., Villalona-Calero, M., Ma, C., Hershman, D., Baar, J., Klein, P., Cigler, T., Budd, T., Novik, Y., Tan, A.R., Tannenbaum, S., Goel, A., Levine, E., Shapiro, C. L., Andreopoulou, E., Naughton, M., Kalinsky, K., Waxman, S., Germain, D. (2016) “Randomized Phase II Trial of Fulvestrant Alone or in Combination with Bortezomib in Hormone Receptor-Positive Metastatic Breast Cancer Resistant to Aromatase Inhibitors: A New York Cancer Consortium Trial," Nature Partner Journals Breast Cancer, Volume 2, Article ID 16037, DOI: 10.1038/npjbcancer.2016.37.

[5] Simon GR, Extermann M, Chiappori A, Williams C, Begum M, Haura RKE, Ismail-Khan R, Schell M, Antonia SJ, Bepler G. Phase 2 trial of docetaxel and gefitinib in the first-line treatment of patients with advanced stage non-small cell lung cancer (NSCLC) who are 70 years of age or older. Cancer 2008; 112:2021–2029.

[6] Hatzis, C., Pusztai, L., Valero, V., Booser, D. J., Esserman, L., Lluch, A., et al. (2011). A genomic predictor of response and survival following taxane-anthracycline chemotherapy for invasive breast cancer. The Journal of the American Medical Association 305, 1873–1881.

RPEXE main function

Description

This is the RPEXE main function taking inputs including time, censoring, change-point candidates, order restriction, criticl value, and display position. This function produces the RPEXE estimate. The prediction of the survival probability will be made on 100 equally spaced time points within the range of the event times based on the piecewise exponential estimate determined by all the changepoints.

Usage

RPEXEv1_2(times,censoring,cuttimes=NULL, monotone=0, criticalp=-1, pos = 0)

Arguments

Value

times: event/censoring times taking out from the backward elimination pvalues: p-values corresponding to "times" times_c: significant change-points pvalues_c: critical p-values that are smaller than the critical p-value trend: trend information struct: structure information for multiple order restrictions changet: change-point time of trend for umbrella alternatives.

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
RPEXEv1_2(t1, c1, monotone = 1,criticalp=0.05, pos = 0)

Bisection algorithm in Beta distribution

Description

Running bisection algorithm to search for a2, the minimizer of (log((a2)^dea1*(1-a2)^dea2-delta))^2

Usage

bisec(delta, dea1, dea2, upbd, lowbd)

Arguments

Value

a2

Examples

bisec(-74.4824, 33, 98, 1, 0.252)

RPEXE_fitting

Description

A breast cancer clinical trial dataset in Adelson et al. (2016).

Usage

data(data2)

Details

• first column - times : time to event

• second column - censor : censoring status; 0=censored, 1=event.

• third column - group : labels the single agent arm and combination arm

References

[1] Adelson, K. B., Ramaswamy, B., Sparano, J. A., Christos, P. J., Wright, J. J., Raptis, G., Han, G., Villalona-Calero, M., Ma, C., Hershman, D., Baar, J., Klein, P., Cigler, T., Budd, T., Novik, Y., Tan, A.R., Tannenbaum, S., Goel, A., Levine, E., Shapiro, C. L., Andreopoulou, E., Naughton, M., Kalinsky, K., Waxman, S., Germain, D. (2016) “Randomized Phase II Trial of Fulvestrant Alone or in Combination with Bortezomib in Hormone Receptor-Positive Metastatic Breast Cancer Resistant to Aromatase Inhibitors: A New York Cancer Consortium Trial," Nature Partner Journals Breast Cancer, Volume 2, Article ID 16037, DOI: 10.1038/npjbcancer.2016.37.

JAMA Breast cancer

Description

A dataset containing predictions for chemo-censitivity and pathological response from Hatzis (2011)

Usage

data(df)

Details

• validate: Validation status

• drfs: Censoring status; 0=censored, 1=event.

• drfs.time: Time to event or censoring

• er.status: ER status, P=positive, N=negative

• chemo.pred: Prediction for chemo sensitivity from the ACES predictor, sensitive or insensitive

• pre.N: Prediction of nodal status

• pCR.RD: pathological complete response (pCR) or residual disease (RD)

• pre.grade: prediction of tumor grade

• pre.T: T stage prediction

• dlda30: DLDA30 prediction for the pathological response.

References

[1] Hatzis, C., Pusztai, L., Valero, V., Booser, D. J., Esserman, L., Lluch, A., et al. (2011). A genomic predictor of response and survival following taxane-anthracycline chemotherapy for invasive breast cancer. The Journal of the American Medical Association 305, 1873–1881.

P-value for the two exponential comparison in Han et al.(2012)

Description

This function computes the exact p-value from the likelihood ratio test

Usage

exact_pvalue(ttot1,ttot2,dea1,dea2,mono)

Arguments

Value

a2: Beta distribution quantile computed using bisec.R pval: p-value

Examples

exact_pvalue(1, 302.04, 2, 25, 1)

Log likelihood from the gamma distribution

Description

A function computing the log likelihood from the gamma distribution under an order restriction reduction

Usage

gamllik(structtime,structttot,structdeaths,time_die,ttot,deaths)

Arguments

Value

log of the likelihood

Examples

time_die <- c(0.05,0.08,0.38,0.41,0.64)
ttot <- c(9.2,5.8,52.1,5.8,40.0)
deaths <- c(1,1,1,1,1)
structtime <- c(0.05,0.64)
structttot <- c(9.2, 40.0)
structdeaths = c(1, 5)
gamllik(structtime,structttot,structdeaths,time_die,ttot,deaths)

Kaplan-Meier curve

Description

This function plots the Kaplan-Meier curve without returning outputs

Usage

km(time, censor, plotcens)

Arguments

Value

Kaplan-Meier curve only

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
km(t1,c1,0)

Kaplan-Meier curve

Description

This function plots the Kaplan-Meier curve without returning outputs

Usage

km_blacksolid(time, censor, plotcens)

Arguments

Value

Kaplan-Meier curve only

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
km_blacksolid(t1,c1,0)

Comparing two Kaplan Meier curves in one plot

Description

The function compares two Kaplan Meier curves in one plot

Usage

km_combine(x1, x2, pos = 0)

Arguments

Value

A combined Kaplan Meier curve

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
t2 <- c(1,3,5,4,8,10,9,11)
c2 <- c(0,0,0,0,1,0,0,0)
x1<-cbind(t1,c1)
x2<-cbind(t2,c2)
km_combine(x1,x2)
km_combine(x1,x2,pos=1)

Plot a Kaplan Meier curve in log scale

Description

The function plots a Kaplan Meier curve in log scale

Usage

km_log(time, censor, plotcens)

Arguments

Value

A Kaplan Meier curve in log scale

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
km_log(t1,c1,0)

Plot a Kaplan Meier curve in red

Description

The function plots a Kaplan Meier curve in red

Usage

km_red(time, censor, plotcens)

Arguments

Value

A red Kaplan Meier curve

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
km_red(t1,c1,0)

Plot a Kaplan Meier curve in red solid line

Description

The function plots a Kaplan Meier curve in red solid line

Usage

km_redsolid(time, censor, plotcens)

Arguments

Value

A red solid Kaplan Meier curve

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
km_redsolid(t1,c1,0)

Obtain values for Kaplan-Meier plotting

Description

Obtain values for Kaplan-Meier plotting

Usage

kmvalue(x)

Arguments

Value

Values used for Kaplan-Meier plotting

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
x1<-cbind(t1,c1)
kmvalue(x1)

Example data for loopcut_onestep

Description

Example data for loopcut_onestep

Usage

data(loopcut_onestep_data)

Change-point p-values with backward elimination

Description

A function that iterates to compute the p-values from the backward elimination procedure (Han et al. 2014)

Usage

loopcuts(time,censor,cuttimes,mono)

Arguments

Value

the times in the backward elimination procedure and the corresponding p-values for each change-point in the iteration

Examples

data(loopcuts_t_c)
data(loopcuts_cut)
time = loopcuts_t_c[,1]
censor = loopcuts_t_c[,2]
loopcuts(time, censor, loopcuts_cut, 1)

Example data for loopcuts_cuttimes

Description

Example data for loopcuts_cuttimes

Usage

data(loopcuts_cut)

Change-point p-values at given time points

Description

This function computes the p-values at the current time points in input "time"

Usage

loopcuts_onestep(time,censor,cuttimes,mono)

Arguments

Value

P-values at for all time points in "time"

Examples

data(loopcuts_t_c)
time = loopcuts_t_c[,1]
censor = loopcuts_t_c[,2]
loopcuts_onestep(time, censor, 28.03013699, 1)

Example data for loopcut_times_censoring

Description

Example data for loopcut_times_censoring

Usage

data(loopcuts_t_c)

Change-point p-values with backward elimination under umbrella alternative order restriction

Description

A function that iterates to compute the p-values from the backward elimination procedure (Han et al. 2014) with umbrella alternative order restriction.

Usage

loopcuts_umbrella(time,censor,cuttimes,mono)

Arguments

Value

the times in the backward elimination procedure and the corresponding p-values for each change-point in the iteration

Examples

data(loopcuts_t_c)
data(loopcuts_umbrella_cuttimes_mono)
time = loopcuts_t_c[,1]
censor = loopcuts_t_c[,2]
cuttimes = loopcuts_umbrella_cuttimes_mono[,1]
mono = loopcuts_umbrella_cuttimes_mono[,2]
loopcuts_umbrella(time, censor, cuttimes, mono)

Example data for loopcut_umbrella

Description

Example data for loopcut_umbrella

Usage

data(loopcuts_umbrella_cuttimes_mono)

PAVA order restriction under decreasing failure rate (DFR)

Description

This function imposes the PAVA DFR order restriction by eliminating change-points violating the restriction

Usage

pava_dfr(time_die,ttot,deaths)

Arguments

Value

time2: the event times after PAVA ttot2: the corresponding ttot deaths2 the corresponding number of deaths

Examples

data(pava_dfrd)
t_d = pava_dfrd[,1]
t = pava_dfrd[,2]
d = pava_dfrd[,3]
pava_dfr(t_d, t, d)

Example data for pava

Description

Example data for pava

Usage

data(pava_dfrd)

PAVA order restriction under increasing failure rate (IFR)

Description

This function imposes the PAVA IFR order restriction by eliminating change-points violating the restriction

Usage

pava_ifr(time_die,ttot,deaths)

Arguments

Value

time2 the event times after PAVA ttot2 the corresponding ttot after PAVA deaths2 the corresponding number of deaths after PAVA

Examples

data(pava_dfrd)
t_d = pava_dfrd[,1]
t = pava_dfrd[,2]
d = pava_dfrd[,3]
pava_ifr(t_d, t, d)

RPEXE estimate given change-points

Description

This function estimates the survival probability at tx when a piecewise exponential distribution is fitted to (times,cens) cens = 0 for censored, cens = 1 for uncensored. the change point is tchange and lamest is the estimated parameters

Usage

pexeest(times, cens, tchange, tx)

Arguments

Value

quan survival probability lamest Lambda estimates for time periods divided by the change-points

Examples

data(pexeest_times_censoring)
data(t100)
times = pexeest_times_censoring[,1]
cens = pexeest_times_censoring[,2]
pexeest(times, cens, 28.03014, t100)

Example data for pexeest_times_censoring

Description

Example data for pexeest_times_censoring

Usage

data(pexeest_times_censoring)

None Small Cell Lung cancer data

Description

A dataset non-small-cell lung cancer trial data from Simon et al. (2011)

Usage

data(simple)

Details

• first column - censor : censoring status; 0=censored, 1=event.

• second column - times : time to event

References

[1] Simon GR, Extermann M, Chiappori A, Williams C, Begum M, Haura RKE, Ismail-Khan R, Schell M, Antonia SJ, Bepler G. Phase 2 trial of docetaxel and gefitinib in the first-line treatment of patients with advanced stage non-small cell lung cancer (NSCLC) who are 70 years of age or older. Cancer 2008; 112:2021–2029.

Example data for pexeest_tx

Description

Example data for pexeest_tx

Usage

data(t100)

total time on test

Description

Function 'totaltest' computes total-time-on-test.

Usage

totaltest(time,censor)

Arguments

Value

time_die time points where events occur (in ascending order) ttot total time on test corresponding to each time point in "time_die" deaths number of death corresponding to each time point in "time_die"

Examples

t1 <- c(2,3,4,5.5,7,10,12,15)
c1 <- c(0,0,1,0,0,1,0,0)
totaltest(t1,c1)

Umbrella alternative.

Description

Using the umbrella alternative to merge certain entries to make the sequence of ttot/deaths to increase then decrease or to decrease then increase. Note that the pava function imposes non-decreasing or non-increasing order. This function directly uses function pava().

Usage

umbrella(time_die,ttot,deaths,indi)

Arguments

Value

time2 == the merged time_die after the umbrealla alternative order restriction; struct == a structure saves the partition information; label == a note about how the failure rate varies; indx == the position where the change point value is.

Examples

data(pava_dfrd)
t_d = pava_dfrd[,1]
t = pava_dfrd[,2]
d = pava_dfrd[,3]
umbrella(t_d, t, d, 2)