Introduction to Splus Program pmtd

 

The Splus program pmtd can be used for numeric calculation of the statistical quantities discussed in the paper "Statistical Properties of The Traditional Algorithm-based Designs for Phase I Cancer Clinical Trials " by Yong Lin and Weichung Joe shih. The program was written by the authors and are available in http://www2.umdnj.edu/~linyo. There are three arguments in the program as described below:

ptox = the vector of the probability of toxicity at each dose level.
design = c(A, B, C, D, E) where A, B, C, D, E are the parameters in the general A+B design.
deescalate = 0 if the design is without dose de-escalation;
                = 1 if the design is with dose de-escalation.

Consider a 3+6 design with dose de-escalation and with parameter C=D=E=1. Assume that the probabilities of toxicity at each dose level are 0.05, 0.1, 0.15, 0.2 and 0.3. The Splus command

pmtd(c(.05,.1,.15,.2,.3), c(3,6,1,1,1), 1)

will give the statistical quantities discussed in the paper for this design. The following is the output from Splus:

> pmtd(c(.05,.1,.15,.2,.3),c(3,6,1,1,1),1)

$Design:
A B C D E
3 6 1 1 1

$Deescalate:
[1] T

$summary1:

1 2 3 4 5
Prob. of Tox.: 0.050 0.100 0.150 0.200 0.300
Prob. of MTD: 0.157 0.245 0.243 0.160 0.146
Exp. # of Pat.: 4.684 5.652 5.560 4.333 2.093
Exp. # of Tox.: 0.234 0.565 0.834 0.867 0.628
% of Pat.: 20.983 25.318 24.910 19.413 9.375


$summary2:

Target Toxicity Level: 0.125
Prob. that MTD < dose 1: 0.048
Exp. All Pat.: 22.322
 Exp. All Tox.: 3.128
Exp. All Tox. Rate: 0.140

Notice that since the probability of the last dose n (n=5 in our example) being chosen as MTD is 0, for convenience we have used the notation P(MTD = dose n) to mean P(MTD >= dose n) in the above output.

From the output, we see that most likely dose level 2 and 3 will be declared as MTD (with probability of 0.245 and 0.243, respectively). The target toxicity level is 0.125. The expected overall toxicity rate is 14%. On average, we expect to treat 22-23 patients and observe 3-4 incidences of DLT.

The following Splus output is for the same configuration except that the design is without dose de-escalation.

> pmtd(c(.05,.1,.15,.2,.3),c(3,6,1,1,1),0)

$Design:
A B C D E
3 6 1 1 1

$Deescalate:
[1] F

$summary1:

1 2 3 4 5
Prob. of Tox.: 0.050 0.100 0.150 0.200 0.300
Prob. of MTD: 0.136 0.216 0.234 0.224 0.146
Exp. # of Pat.: 3.812 4.266 4.065 3.209 2.093
Exp. # of Tox.: 0.191 0.427 0.610 0.642 0.628
% of Pat.: 21.853 24.453 23.304 18.394 11.996

$summary2:

Target Toxicity Level: 0.134
Prob. that MTD < dose 1: 0.043
Exp. All Pat.: 17.445
  Exp. All Tox.: 2.497
Exp. All Tox. Rate: 0.143

In this case, we see that most likely dose level 3 or 4 will be declared as MTD (with probability of 0.234 and 0.224, respectively). The target toxicity level is 0.134. The expected overall toxicity rate is 14.3%. On average, we expect to treat 17-18 patients and observe 2-3 incidences of DLT.

 

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Last Updated: 10/5/00