WTP : how to assess differences in WTP values by subgroups using a t-test?

[Rotana Radwan]

Hi everyone,

I have results from a discrete choice experiment.
My attributes are: progression-free survival (PFS) coded as 6, 12, 24 months, neruropathy in hands (mild=1,moderate=2, severe=3),neuropathy in feet (mild=1, moderate=2, severe=3), and neuropathy persistence (short-term=1, long-term=2, permanent=3). I coded all the levels continuously and want to measure the maximum acceptable risk patients are willing to tolerate in exchange for 6 months improvement in PFS (again progression free survival) using the WTP formula.

Now, I am assessing differences by subgroup- the name of the variable is Q58_numeric and group= 1 are those without children, and group 2 are those with children. I got the WTP results per group, and I want to assess the differences between WTP values between the two groups using a t-test, but do not know how to code for it. I will show the code and result below. Can someone help me out please?


*Run model for group 1
foreach v in hands feet persistence {
clogit choice PFS hands feet persistence if Q58_numeric == 1, group(resptask)
wtp `v' PFS
matrix `v'_1 = r(wtp)
matrix list `v'_1
}
matrix append = persistence_1, hands_1, feet_1
matrix colnames append = "Persistence" "hands" "feet"
matrix list append


*Run model for group 2
foreach v in PFS hands feet persistence {
clogit choice PFS hands feet persistence if Q58_numeric == 2, group(resptask)
wtp `v' PFS
matrix `v'_1 = r(wtp)
matrix list `v'_1
}
matrix append = persistence_1, hands_1, feet_1
matrix colnames append = "Persistence" "hands" "feet"
matrix list append


MODEL 1 RESULTS (those with children):
Conditional logit results:

choice | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
PFS | .0568094 .0047743 11.90 0.000 .047452 .0661668
hands | -.3651211 .0430996 -8.47 0.000 -.4495948 -.2806474
feet | -.179239 .040492 -4.43 0.000 -.258602 -.0998761
persistence | -.4500053 .0430675 -10.45 0.000 -.534416 -.3655945

WTP results:
Persistence hands feet
wtp .12624174 .1555907 .31694796
ll .09833833 .1156495 .17409462
ul .15414516 .1955319 .4598013


MODEL 2 RESULTS (those without children):
Conditional logit results:

------------------------------------------------------------------------------
choice | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
PFS | .0245991 .005904 4.17 0.000 .0130275 .0361707
hands | -.19401 .0537993 -3.61 0.000 -.2994548 -.0885653
feet | -.0466953 .0527311 -0.89 0.376 -.1500462 .0566557
persistence | -.3721953 .0543844 -6.84 0.000 -.4787866 -.2656039
------------------------------------------------------------------------------
WTP results:
append[3,3]
Persistence hands feet
wtp .06609183 .12679275 .52680012
ll .03076077 .03796859 -.65304013
ul .10142289 .21561691 1.7066404

[Carlo Lazzaro]

Rotana:
you may want to take a look at -suest-:

. use https://www.stata-press.com/data/r17/clogitid

. clogit y x1, group(id)
note: multiple positive outcomes within groups encountered.

Iteration 0:   log likelihood = -124.50064  
Iteration 1:   log likelihood = -124.49672  
Iteration 2:   log likelihood = -124.49672  

Conditional (fixed-effects) logistic regression         Number of obs =    369
                                                        LR chi2(1)    =   6.91
                                                        Prob > chi2   = 0.0086
Log likelihood = -124.49672                             Pseudo R2     = 0.0270

------------------------------------------------------------------------------
           y | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
          x1 |   .7386672   .2811067     2.63   0.009     .1877082    1.289626
------------------------------------------------------------------------------

. estimates store A

. clogit y x2, group(id)
note: multiple positive outcomes within groups encountered.

Iteration 0:   log likelihood = -126.00197  
Iteration 1:   log likelihood =   -125.992  
Iteration 2:   log likelihood =   -125.992  

Conditional (fixed-effects) logistic regression         Number of obs =    369
                                                        LR chi2(1)    =   3.92
                                                        Prob > chi2   = 0.0478
Log likelihood = -125.992                               Pseudo R2     = 0.0153

------------------------------------------------------------------------------
           y | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
          x2 |   .0853067    .043447     1.96   0.050     .0001521    .1704613
------------------------------------------------------------------------------

. estimates store B

. suest A B

Simultaneous results for A, B                              Number of obs = 369

                                    (Std. err. adjusted for 66 clusters in id)
------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
A_y          |
          x1 |   .7386672   .2877388     2.57   0.010     .1747095    1.302625
-------------+----------------------------------------------------------------
B_y          |
          x2 |   .0853067   .0454059     1.88   0.060    -.0036873    .1743006
------------------------------------------------------------------------------


. test [A_y]x1=[B_y]x2

 ( 1)  [A_y]x1 - [B_y]x2 = 0

           chi2(  1) =    5.18
         Prob > chi2 =    0.0228

.

and in addition:

. lincom [A_y]x1-[B_y]x2

 ( 1)  [A_y]x1 - [B_y]x2 = 0

------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   .6533605   .2870692     2.28   0.023     .0907153    1.216006
------------------------------------------------------------------------------

.

[Rotana Radwan]

Thank you for your prompt response and help! I tried it and it was comparing the conditional logit model results , but not the WTP values....

[Carlo Lazzaro]

Rotana:
is -ttesti- an option?

[Rotana Radwan]

You know what! you are right I have all the info to conduct it except for delta standard errors... I read that I would probably need to use nlcom command to have it, just don't know where to add that on my WTP code...

[Carlo Lazzaro]

Rotana:
a proxy for the WTP standard error computation can be (1st mention of Persistence):

. di (.15414516 -.09833833)/(2*1.96)
.01423644

[Rotana Radwan]

Thank you so much! it worked like a charm