evaluate_power: Power of a design to estimate a parameter.

In PopED: Population (and Individual) Optimal Experimental Design

Description

Evaluate the power of a design to estimate a parameter value different than some assumed value (often the assumed value is zero). The power is calculated using the linear Wald test and the the design is defined in a poped database.

Usage

evaluate_power(
  poped.db,
  bpop_idx,
  h0 = 0,
  alpha = 0.05,
  power = 0.8,
  twoSided = TRUE,
  find_min_n = TRUE,
  fim = NULL,
  out = NULL,
  ...
)

Arguments

poped.db	A poped database
bpop_idx	Index for an unfixed population parameter (bpop) for which the power should be evaluated for being different than the null hypothesis (h0).
h0	The null hypothesized value for the parameter.
alpha	Type 1 error.
power	Targeted power.
twoSided	Is this a two-sided test.
find_min_n	Should the function compute the minimum n needed (given the current design) to achieve the desired power?
fim	Provide the FIM from a previous calculation
out	provide output from a previous calculation (e.g., calc_ofv_and_fim, ...)
...	Extra parameters passed to calc_ofv_and_fim and get_rse

Value

A list of elements evaluating the current design including the power.

References

1. Retout, S., Comets, E., Samson, A., and Mentre, F. (2007). Design in nonlinear mixed effects models: Optimization using the Fedorov-Wynn algorithm and power of the Wald test for binary covariates. Statistics in Medicine, 26(28), 5162-5179. doi: 10.1002/sim.2910.

2. Ueckert, S., Hennig, S., Nyberg, J., Karlsson, M. O., and Hooker, A. C. (2013). Optimizing disease progression study designs for drug effect discrimination. Journal of Pharmacokinetics and Pharmacodynamics, 40(5), 587-596. doi: 10.1007/s10928-013-9331-3.

See Also

Other evaluate_design: evaluate.fim(), evaluate_design(), get_rse(), model_prediction(), plot_efficiency_of_windows(), plot_model_prediction()

Examples

# Folowing the examples presented in Retout, 2007

ff <- function(model_switch,xt,parameters,poped.db){
  with(as.list(parameters),{
    
    lambda1 <- lam1a
    if(TREAT==2) lambda1 <- lam1b
    
    y=log10(P1*exp(-lambda1*xt)+P2*exp(-lam2*xt))
    
    return(list(y=y,poped.db=poped.db))
  })
}

sfg <- function(x,a,bpop,b,bocc){
  parameters=c(P1=exp(bpop[1]+b[1]),
               P2=exp(bpop[2]+b[2]),
               lam1a=exp(bpop[3]+b[3]),
               lam1b=exp(bpop[3]+bpop[4]+b[3]),
               lam2=exp(bpop[5]+b[4]),
               TREAT=a[1])
  return(parameters) 
}
  

poped.db <- create.poped.database(ff_fun = ff,
                                  fg_fun = sfg,
                                  fError_fun = feps.add,
                                  bpop=c(P1=12, P2=8,
                                         lam1=-0.7,beta=0,lam2=-3.0),
                                  d=c(P1=0.3, P2=0.3,
                                      lam1=0.3,lam2=0.3), 
                                  sigma=c(0.065^2),
                                  groupsize=100,
                                  m=2,
                                  xt=c(1, 3, 7, 14, 28, 56),
                                  minxt=0,
                                  maxxt=100,
                                  a=list(c(TREAT=1),c(TREAT=2)))

plot_model_prediction(poped.db)
evaluate_design(poped.db)

poped.db_2 <- create.poped.database(poped.db,bpop=c(P1=12, P2=8,
                                      lam1=-0.7,beta=0.262,lam2=-3.0))

plot_model_prediction(poped.db_2)
evaluate_design(poped.db_2)

evaluate_power(poped.db_2,bpop_idx = 4)

Example output

$ofv
[1] 74.52441

$fim
                   P1         P2       lam1       beta       lam2         d_P1
P1         611.712173 -12.723468 -24.210864 -12.105432  -5.109809 0.000000e+00
P2         -12.723468 580.838635 -16.202945  -8.101473 -39.342222 0.000000e+00
lam1       -24.210864 -16.202945 648.887538 324.443769  -6.742703 0.000000e+00
beta       -12.105432  -8.101473 324.443769 324.443769  -3.371351 0.000000e+00
lam2        -5.109809 -39.342222  -6.742703  -3.371351 643.716238 0.000000e+00
d_P1         0.000000   0.000000   0.000000   0.000000   0.000000 9.354418e+02
d_P2         0.000000   0.000000   0.000000   0.000000   0.000000 4.051226e-01
d_lam1       0.000000   0.000000   0.000000   0.000000   0.000000 1.465796e+00
d_lam2       0.000000   0.000000   0.000000   0.000000   0.000000 6.533664e-02
SIGMA[1,1]   0.000000   0.000000   0.000000   0.000000   0.000000 5.831126e+03
                   d_P2       d_lam1       d_lam2   SIGMA[1,1]
P1            0.0000000    0.0000000 0.000000e+00        0.000
P2            0.0000000    0.0000000 0.000000e+00        0.000
lam1          0.0000000    0.0000000 0.000000e+00        0.000
beta          0.0000000    0.0000000 0.000000e+00        0.000
lam2          0.0000000    0.0000000 0.000000e+00        0.000
d_P1          0.4051226    1.4657963 6.533664e-02     5831.126
d_P2        843.4338997    0.6563403 3.869526e+00     8499.377
d_lam1        0.6563403 1052.6375905 1.136601e-01     1889.172
d_lam2        3.8695261    0.1136601 1.035926e+03     2335.057
SIGMA[1,1] 8499.3770636 1889.1721996 2.335057e+03 11411954.974

$rse
         P1          P2        lam1        beta        lam2        d_P1 
 0.33728477  0.52006496  7.93579642  0.07851367  1.31669814 10.91610610 
       d_P2      d_lam1      d_lam2  SIGMA[1,1] 
11.52111962 10.27552547 10.35895352  7.04673895 

$ofv
[1] 74.54742

$fim
                   P1         P2       lam1       beta       lam2         d_P1
P1         606.085238 -12.699077 -26.355895 -14.250463  -5.275413 0.000000e+00
P2         -12.699077 590.575904 -15.713924  -7.612451 -35.363100 0.000000e+00
lam1       -26.355895 -15.713924 647.696264 323.252495  -6.706096 0.000000e+00
beta       -14.250463  -7.612451 323.252495 323.252495  -3.334744 0.000000e+00
lam2        -5.275413 -35.363100  -6.706096  -3.334744 645.343254 0.000000e+00
d_P1         0.000000   0.000000   0.000000   0.000000   0.000000 9.184094e+02
d_P2         0.000000   0.000000   0.000000   0.000000   0.000000 4.034200e-01
d_lam1       0.000000   0.000000   0.000000   0.000000   0.000000 1.748333e+00
d_lam2       0.000000   0.000000   0.000000   0.000000   0.000000 6.967869e-02
SIGMA[1,1]   0.000000   0.000000   0.000000   0.000000   0.000000 6.355130e+03
                   d_P2       d_lam1       d_lam2   SIGMA[1,1]
P1            0.0000000    0.0000000 0.000000e+00        0.000
P2            0.0000000    0.0000000 0.000000e+00        0.000
lam1          0.0000000    0.0000000 0.000000e+00        0.000
beta          0.0000000    0.0000000 0.000000e+00        0.000
lam2          0.0000000    0.0000000 0.000000e+00        0.000
d_P1          0.4034200    1.7483334 6.967869e-02     6355.130
d_P2        872.1867430    0.6179187 3.165957e+00     7662.896
d_lam1        0.6179187 1048.7796745 1.124326e-01     2004.881
d_lam2        3.1659566    0.1124326 1.041176e+03     2204.564
SIGMA[1,1] 7662.8956865 2004.8814928 2.204564e+03 11396938.075

$rse
        P1         P2       lam1       beta       lam2       d_P1       d_P2 
 0.3388987  0.5155216  7.9357907 29.9948370  1.3144681 11.0205831 11.3204962 
    d_lam1     d_lam2 SIGMA[1,1] 
10.2946096 10.3325268  7.0480557 

$ofv
[1] 74.54742

$fim
            [,1]       [,2]       [,3]       [,4]       [,5]         [,6]
 [1,] 606.085238 -12.699077 -26.355895 -14.250463  -5.275413 0.000000e+00
 [2,] -12.699077 590.575904 -15.713924  -7.612451 -35.363100 0.000000e+00
 [3,] -26.355895 -15.713924 647.696264 323.252495  -6.706096 0.000000e+00
 [4,] -14.250463  -7.612451 323.252495 323.252495  -3.334744 0.000000e+00
 [5,]  -5.275413 -35.363100  -6.706096  -3.334744 645.343254 0.000000e+00
 [6,]   0.000000   0.000000   0.000000   0.000000   0.000000 9.184094e+02
 [7,]   0.000000   0.000000   0.000000   0.000000   0.000000 4.034200e-01
 [8,]   0.000000   0.000000   0.000000   0.000000   0.000000 1.748333e+00
 [9,]   0.000000   0.000000   0.000000   0.000000   0.000000 6.967869e-02
[10,]   0.000000   0.000000   0.000000   0.000000   0.000000 6.355130e+03
              [,7]         [,8]         [,9]        [,10]
 [1,]    0.0000000    0.0000000 0.000000e+00        0.000
 [2,]    0.0000000    0.0000000 0.000000e+00        0.000
 [3,]    0.0000000    0.0000000 0.000000e+00        0.000
 [4,]    0.0000000    0.0000000 0.000000e+00        0.000
 [5,]    0.0000000    0.0000000 0.000000e+00        0.000
 [6,]    0.4034200    1.7483334 6.967869e-02     6355.130
 [7,]  872.1867430    0.6179187 3.165957e+00     7662.896
 [8,]    0.6179187 1048.7796745 1.124326e-01     2004.881
 [9,]    3.1659566    0.1124326 1.041176e+03     2204.564
[10,] 7662.8956865 2004.8814928 2.204564e+03 11396938.075

$rse
        P1         P2       lam1       beta       lam2       d_P1       d_P2 
 0.3388987  0.5155216  7.9357907 29.9948370  1.3144681 11.0205831 11.3204962 
    d_lam1     d_lam2 SIGMA[1,1] 
10.2946096 10.3325268  7.0480557 

$power
     Value      RSE power_pred power_want need_rse min_N_tot
beta 0.262 29.99484   91.52704         80 35.69408       142

PopED documentation built on May 21, 2021, 5:08 p.m.