DEMONSTRATION II
Suppose we wish to design a 5 year clinical trial with accrual taking place uniformly during the first three years. The control group failure rate is 0.10 per year, while the treatment group rates vary from year to year: .04 for the first year, .08 each for the second and third year and .10 each for the last two years. The candidate statistics are logrank and Peto-Prentice statistics. For the noncompliance or crossover rates, assume that there is a constant drop-in rate of 3 percent per year and the drop-out rates are 10 percent for the first year and 5 percent each for the last four years. Also assume that there is 5 percent of loss to follow-up in each group for the 5 year period. Suppose interim analysis is carried out at 1, 1.5, 2, 2.5, , 4.5 and 5 years, and the Lan-DeMets approach with the O'Brien-Fleming spending function is adopted. The total sample size is 900 patients. We demonstrate how the program dssp2.exe can be used to determine the power at the above specified alternative.
First we modify the sample input file dssp2.inp. The modified sample input file
exam5.inp can be found on this Web page. Since we have selected the Lan-DeMets method, on
line 11 of the input file, we change the number to 2. On line 14, we change the output
file name to "exam5.log". On line 20, we change the number to 9 since we are
planning 9 interim analyses. On line 23, the 9 scheduled times of interim analyses are
specified: they are 1 1.5 2 2.5 3 3.5 4 4.5 5. We specify on line 26 that we are going to
simulate 2 statistics. On line 30, we specify the rhos of the statistics, and input 0 1; 0
is the rho of the logrank and 1 is the rho of the Peto-Prentice statistic. On line
33, we input the taus of the statistics, and the inputs are 0 0. Another important input
parameter is the number of simulations used in each iteration. This parameter is located
on line 37, where we input 5000 simulations per iterations. On line 40, we
specify the Type I error probability, which is 0.05. On line 43, we use 2 to indicate that
our tests are 2-sided. Since we have specified 2 on line 11, we can ignore the inputs on
lines 49, 54 and 61. On line 70, we use 1 to indicate that we are going to use the
O'Brien-Fleming use function. On lines 74, 78 and 83, we specify the baseline survival
function. On line 74, we use 5 to indicate to the program that the baseline survival
function will be specified by 5 intervals. On line 78, five right endpoints, 1, 2, 3, 4
and 5 , of the intervals are specified. On line 83, the survival probabilities at 1 2 3 4
and 5 are specified, they are .9 .8 .7 .6 and .5, which give the failure rate of 10 % per
year. The survival probabilities between the endpoints are interpolated by using the
exponential function. Since our final interim analysis is at 5 (years), the probabilities
are arbitrary at points larger then 5. Another important input is at line 88, where
we specify the accrual length and the accrual rate. We use 3 300, indicating an accrual
length of 3 years and an accrual rate of 300 per year. At lines 93, 96, 101 and 106
we specify the alternative distribution function. At line 93, we use 5 to indicate that
five intervals will be used to specify the alternative distribution function. At line 96,
the five right endpoints of the intervals are specified. They are 1 2 3 4 5. The input on
line 101 indicates whether the numbers on line 106 are the survival probabilities at the
points used in line 96 or they are the hazard ratios on the five intervals. The number 1
indicates to the program that they are the survival probabilities. We input the five
survival probabilities in line 106 as .96, .88, .80, .70, .60, according to our
alternative failure rates specified in the preceding paragraph. The inputs starting at
line 111 are for the baseline and alternative survival probabilities for the censoring
distribution and the drop-in and drop-out rates. The logic of these inputs is the same as
that of the survival probabilities for the baseline distribution.
Once we finish editing the input file, we can run the program with the input file. It took
a PC with Pentium II 300 processor about 25 minutes to get the result. The results are
contained in the file 'exam5.log', which is also available at this Web page. Since the
Lan-DeMets approach requires the program to calculate the boundary at every interim
analysis of every simulation, it takes longer for the simulation to finish than the
Haybittle-type boundary. It only took only about 4 minutes for the simulation to finish
with the same input file but with input on line 11 changed to 3.
After becoming familiar with the program, the user can use the program to exploit many other aspects of the design of a trial. For example, an investigator may not be sure what the cross-over rates are and may try the program to find the power with different sets of the cross-over rates.