1 General Information

This reduced piecewise exponential survival software implements the likelihood ratio test and backward elimination procedure in Han, Schell, and Kim (2012^[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.], 2014^[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.]), and Han et al. (2016^[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.]). 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. Adelson (2016^[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.]) also mentioned the application of the method. This program can run in R version 3.2.2 and above.

2 Inputs and Outputs

2.1 Inputs

This software has one driver files RPEXEv1_2.R. Inputs to RPEXEv1_2.R include

2.2 Outputs

3 Example with dataset data2

3.1 Load data and extract variables

times = data2[,1]
censor = data2[,2]
group = data2[,3]

ID_nan = which(is.na(times))
times = times[-ID_nan] 
censor = censor[-ID_nan]
group = group[-ID_nan]
armsA_ID = which(group == 1)
armsB_ID = which(group == 2)

3.2 Plot the data

# figure(1): Kaplan Meier curve of Arm A without indicating censored points 
km(times[armsA_ID], censor[armsA_ID], 0)
# figure(2): Kaplan Meier curve of armA with censored points indicated
km_red(times[armsA_ID], censor[armsA_ID], 1)
# figure(3): Kaplan Meier curve of armB without indicating censored points 
km(times[armsB_ID], censor[armsB_ID], 0)
# figure(4): Kaplan Meier curve of Arm B with censored points indicated
km_red(times[armsB_ID], censor[armsB_ID], 0)

3.3 Plot the KME in the paper

# figure(5) : Combined plot of both armA and armB 
x1 = cbind(times[armsA_ID], censor[armsA_ID])
x2 = cbind(times[armsB_ID], censor[armsB_ID])

3.4 The reduced piecewise exponential analysis

# Fit the rpexe with monotonic order restriction;
pexeoutA     =  RPEXEv1_2(times[armsA_ID],censor[armsA_ID], monotone = 1,criticalp = 0.05)

pexeoutB     =  RPEXEv1_2(times[armsB_ID],censor[armsB_ID],monotone = 1,criticalp = 0.05)

# combined
pexeout = RPEXEv1_2(times,censor,monotone = 1,criticalp = 0.05)

3.5 Additional analysis

Given the RPEXE estimates, using the total time on test and number of events to compare the two arms where the hazard rates are costant.

# Calculate the ttot and n from a), 0-2.777, b), 2.777-8.959, c), 8,959-end;





ttotA1 = 0
ttotA2 = 0
ttotA3 = 0
dA1 = 0
dA2 = 0
dA3 = 0
for (i in 1:length(time_dieA))
  if ( time_dieA[i]<=2.777)
    ttotA1 = ttotA1+ttotA[i]
    dA1    = dA1+deathsA[i]
  }else if (time_dieA[i]<=8.959)
    ttotA2 = ttotA2+ttotA[i]
    dA2    = dA2+deathsA[i]
  } else 
    ttotA3 = ttotA3+ttotA[i]
    dA3    = dA3+deathsA[i]

ttotB1 = 0
ttotB2 = 0
ttotB3 = 0
dB1 = 0
dB2 = 0
dB3 = 0
for (i in 1:length(time_dieB))
  if ( time_dieB[i]<=2.777)
    ttotB1 = ttotB1+ttotB[i]
    dB1    = dB1+deathsB[i]
  }else if (time_dieB[i]<=8.959)
    ttotB2 = ttotB2+ttotB[i]
    dB2    = dB2+deathsB[i]
  } else 
    ttotB3 = ttotB3+ttotB[i]
    dB3    = dB3+deathsB[i]

Compute the test statistic and p-value. Show the p-values

# Test the two side hypothesis;

# Two-sided test
# first piece
a11 = result[1]
p11 = result[2]
# second piece
a12 = result[1]
p12 = result[2]
# third piece
a13 = result[1]
p13 = result[2]

# One-sided test
# first piece
a21 = result[1]
p21 = result[2]
# second piece
a22 = result[1]
p22 = result[2]
# third piece
a23 = result[1]
p23 = result[2]


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RPEXE.RPEXT documentation built on July 1, 2020, 6:02 p.m.