Simulation Scenarios

The first step in the simulation studies is usually to specify the simulation scenarios. This is done in visit by the function vtScenario:

tox       <-  c(0.07, 0.23, 0.66);
res       <-  c(0.50, 0.17, 0.59);
rho       <-  c(0.98, 0.40, 0.46);
scenario  <-  vtScenario(tox = tox, res = res, rho = rho);
summary(scenario);

##      No DLT, No Response No DLT, Response DLT, No Response DLT, Response
## [1,]                0.46             0.47             0.04          0.03
## [2,]                0.62             0.15             0.21          0.02
## [3,]                0.10             0.24             0.31          0.35
##      Toxicity Rate Response Rate  Rho
## [1,]          0.07          0.50 0.98
## [2,]          0.23          0.17 0.40
## [3,]          0.66          0.59 0.46

The simulation scenarios are constructed using the level-specific DLT risk rates (tox), immune response rates (res), and odds ratios (rho). The result is a class VTTRUEPS object which has S3 methods summary and “plot”.

summary(scenario);

##      No DLT, No Response No DLT, Response DLT, No Response DLT, Response
## [1,]                0.46             0.47             0.04          0.03
## [2,]                0.62             0.15             0.21          0.02
## [3,]                0.10             0.24             0.31          0.35
##      Toxicity Rate Response Rate  Rho
## [1,]          0.07          0.50 0.98
## [2,]          0.23          0.17 0.40
## [3,]          0.66          0.59 0.46

par(mfrow = c(1,2));
plot(scenario, draw.curves = 1:2, main = "Marginal DLT Risk and Response Rates");
plot(scenario, draw.curves = 3:6, main = "Joint DLT Risk and Response Rates");

Incorporate Prior Knowledge and Specify Priors

Prior knowledge about the DLT risk rates and the prior choices of the parametric model parameters should be encapsulate into a class VTPRIOR object by the function vtPriorPar. Details of the parameters can be found in Wang el. al. (2019).

tau   <- c(0.39, 0.87, 0.49);
prior <- vtPriorPar(tau = tau, sdalpha = 10, sdrho = 10);

Conduct Simulation

The main simulation function in the visit package is the vtSimu function. The function requires a class VTRUEPS object for simulation scenarios and a class “VTPRIOR” class object for priors and other design parameters including etas for the lower and upper boundary of DLT risks, size.cohort for cohort sizes, etc. Probability model needs to be specified by prob.mdl. The options are NONPARA for non-parametric model, NONPARA+ for non-parametric model with \(\rho=1\), PARA for partially parametric model, and PARA+ for partially parametric model with \(\rho=1\).

simu <- vtSimu(n.rep = 100, trueps = scenario,
               size.cohort = 5, size.level = 10,
               etas = c(0.3, 0.7), dec.cut = c(0.45, 0.55, 0.75),
               prob.mdl = "NONPARA+");

The result is a class VTSIMUT object with S3 methods summary and summary2.

sum.1 <- summary(simu);
print(sum.1);

## $dose
##            1 2 3
## Frequency 93 6 1
## %         93 6 1
## 
## $npat
##         stage 1 stage 2 total
## level 1    5.00     1.4  6.40
## level 2    5.00     0.4  5.40
## level 3    0.35     0.2  0.55
## 
## $samples
##                 No T, No R No T, R T, No R  T,R    T    R
## level 1 stage 1       2.32    2.38    0.13 0.17 0.30 2.55
## level 1 stage 2       0.66    0.63    0.06 0.05 0.11 0.68
## level 1 total         2.98    3.01    0.19 0.22 0.41 3.23
## level 2 stage 1       3.02    0.73    1.11 0.14 1.25 0.87
## level 2 stage 2       0.20    0.08    0.12 0.00 0.12 0.08
## level 2 total         3.22    0.81    1.23 0.14 1.37 0.95
## level 3 stage 1       0.03    0.09    0.11 0.12 0.23 0.21
## level 3 stage 2       0.00    0.04    0.05 0.11 0.16 0.15
## level 3 total         0.03    0.13    0.16 0.23 0.39 0.36
## 
## $decison
##                   N    Toxic Ineffective Safe,Effective
## level 1 stage 1 100  0.00000     0.00000       72.00000
## level 1 stage 2  28  0.00000     0.00000       67.85714
## level 2 stage 1 100  2.00000    87.00000        3.00000
## level 2 stage 2   8  0.00000    50.00000       12.50000
## level 3 stage 1   7 28.57143    14.28571        0.00000
## level 3 stage 2   4 75.00000     0.00000        0.00000
##                 Effective,Safety concern
## level 1 stage 1                 28.00000
## level 1 stage 2                 32.14286
## level 2 stage 1                  8.00000
## level 2 stage 2                 37.50000
## level 3 stage 1                 57.14286
## level 3 stage 2                 25.00000
## 
## $prob
##                        Toxic Ineffective Safe,Effective
## level 1 stage 1 0.0045375000   0.0000000     0.85938250
## level 1 stage 2 0.0004017857   0.0000000     0.83966964
## level 2 stage 1 0.0587200000   0.7712125     0.10558000
## level 2 stage 2 0.0203437500   0.4981562     0.27200000
## level 3 stage 1 0.4122857143   0.1745000     0.06960714
## level 3 stage 2 0.4241875000   0.0600000     0.00768750
##                 Effective,Safety concern
## level 1 stage 1                0.1360800
## level 1 stage 2                0.1599286
## level 2 stage 1                0.0644875
## level 2 stage 2                0.2095000
## level 3 stage 1                0.3436071
## level 3 stage 2                0.5081250
## 
## $ptox
##                      Mean         LB        UB
## level 1 stage 1 0.1336080 0.08041559 0.2569313
## level 1 stage 2 0.1783334 0.13390102 0.2578602
## level 2 stage 1 0.2915642 0.08075952 0.5860364
## level 2 stage 2 0.3399194 0.22383331 0.4847803
## level 3 stage 1 0.6316754 0.43865020 0.8943163
## level 3 stage 2 0.6598564 0.59730874 0.6845209
## 
## $pres
##                      Mean         LB        UB
## level 1 stage 1 0.5082704 0.16053040 0.7537984
## level 1 stage 2 0.5168683 0.31664741 0.7714243
## level 2 stage 1 0.2283458 0.08136799 0.4225707
## level 2 stage 2 0.2956403 0.13600664 0.4842143
## level 3 stage 1 0.5838975 0.41499903 0.7508539
## level 3 stage 2 0.7049501 0.59455436 0.7751161

sum.2 <- summary2(simu);
print(sum.2);

##       1       2       3         level 1 level 2 level 3               T       R 
##   93.00    6.00    1.00  100.00    6.40    5.40    0.55   12.35    0.41    3.23 
##       T       R       T       R       T       R 
##    1.37    0.95    0.39    0.36    2.17    4.54

Interim Analysis

To perform the interim analysis, the current level of observation and the previous level of observation is needed. Decision cuts, lower and upper bound of DLT risk, prob.mdl, and priors are all optional arguments. Please refer to the visit package PDF for details on the result decision map.

etas       <- c(0.1, 0.3)
dec.cut    <- c(0.6,0.6,0.6)
cur.obs.y  <- c(3, 2, 1, 1)
prev.obs.y <- c(5, 2, 0, 0)
rst.inter  <- vtInterim(cur.obs.y,  prev.obs.y = prev.obs.y,
                        prob.mdl = "NONPARA", etas = etas, dec.cut = dec.cut,
                        nsmp = 2000);

plot(rst.inter);

Track of Study History

A function vtTrack is provided to visualize the entire progress of the study, including the observed data and dose escalation decisions. The required data is a five column matrix, with the first column indicating the dose level, and the rest should indicate the observed number of patients with No DLT, No Response, No DLT, Response, DLT, No Response, and DLT, Response.

obs <- rbind(c(1, 6, 4, 3, 6), c(2, 4, 9, 3, 3), c(3, 2, 6, 6, 5));
vtTrack(obs, end.width = 0.8);