EffTox - Nuts and Bolts

This notebook demonstrates the nuts and bolts of EffTox, the technical details rather than the general user interface. For example, I use it to check calculations in implementations in other languages. For a general EffTox usage tutorial, use EffTox.ipynb.



In [1]:

    
import numpy as np



In [2]:

    
from clintrials.dosefinding.efftox import _pi_E, _pi_T, _pi_ab, _L_n, scale_doses

In the Matchpoint trial, the daily doses of Ponatinib under investigation were:

7.5mg
15mg
30mg
45mg



In [3]:

    
real_doses = [7.5, 15, 30, 45]



In [4]:

    
scaled_doses = scale_doses(real_doses)



In [5]:

    
scaled_doses









    Out[5]:





array([-0.96780025, -0.27465307,  0.41849411,  0.82395922])

Create some notional values for the two coefficients in the toxicity logit:



In [6]:

    
alpha0 = np.array([0.0, 1.0, 0.2])
alpha1 = np.array([1.0, -0.5, -1.0])



In [7]:

    
_pi_T(scaled_doses[1], alpha0, alpha1)









    Out[7]:





array([ 0.43176513,  0.75718845,  0.61648448])



In [8]:

    
_pi_T(scaled_doses[3], alpha0, alpha1)









    Out[8]:





array([ 0.69507612,  0.6429108 ,  0.34888153])

Create some notional values for the three coefficients in the efficacy logit:



In [9]:

    
beta0 = np.array([-0.5, -1.0, 0.2])
beta1 = np.array([-1.0, -2.0, 1.0])
beta2 = np.array([0.1, 0.2, -0.1])



In [10]:

    
_pi_E(scaled_doses[0], beta0, beta1, beta2)









    Out[10]:





array([ 0.63679121,  0.75453142,  0.29703357])



In [11]:

    
_pi_E(scaled_doses[2], beta0, beta1, beta2)









    Out[11]:





array([ 0.28884907,  0.14161255,  0.64588057])

Create some notional values for psi



In [12]:

    
psi = np.array([-5.0, 0.7, 5.0])

Join it all up



In [13]:

    
_pi_ab(scaled_doses[0], 0, 1, alpha0, alpha1, beta0, beta1, beta2, psi)









    Out[13]:





array([ 0.50699895,  0.1300797 ,  0.03319174])



In [14]:

    
_pi_ab(scaled_doses[2], 1, 1, alpha0, alpha1, beta0, beta1, beta2, psi)









    Out[14]:





array([ 0.22272268,  0.0886512 ,  0.23205335])

Now create some notional cases: 1N 2E 3T, using the nomenclature of Implementing the EffTox dose-finding design in the Matrchpoint trial, by Brock et al.



In [15]:

    
X = [(scaled_doses[0], 0, 0), (scaled_doses[1], 0, 1), (scaled_doses[2], 1, 0)]

Calculate the compound likelihood under the parameter combinations



In [16]:

    
_L_n(X, alpha0, alpha1, beta0, beta1, beta2, psi)









    Out[16]:





array([ 0.0461508 ,  0.0016879 ,  0.00166065])

What do these "nuts and bolts" contribute to?



In [17]:

    
from clintrials.dosefinding.efftox import efftox_get_posterior_probs, efftox_get_posterior_params



In [18]:

    
cases = [(1, 0, 0), (2, 0, 1), (3, 1, 0)]



In [19]:

    
from scipy.stats import norm



In [20]:

    
mu_t_mean, mu_t_sd = -5.4317, 2.7643
beta_t_mean, beta_t_sd = 3.1761, 2.7703
mu_e_mean, mu_e_sd = -0.8442, 1.9786
beta_e_1_mean, beta_e_1_sd = 1.9857, 1.9820
beta_e_2_mean, beta_e_2_sd = 0, 0.2
psi_mean, psi_sd = 0, 1
priors = [
    norm(loc=mu_t_mean, scale=mu_t_sd),
    norm(loc=beta_t_mean, scale=beta_t_sd),
    norm(loc=mu_e_mean, scale=mu_e_sd),
    norm(loc=beta_e_1_mean, scale=beta_e_1_sd),
    norm(loc=beta_e_2_mean, scale=beta_e_2_sd),
    norm(loc=psi_mean, scale=psi_sd),
    ]



In [21]:

    
np.random.seed(123)
probs, thing = efftox_get_posterior_probs(cases, priors, scaled_doses, tox_cutoff=0.4, eff_cutoff=0.45, n=10**6)



In [22]:

    
prob_tox, prob_eff, prob_acc_tox, prob_acc_eff = zip(*probs)



In [23]:

    
prob_tox









    Out[23]:





(0.018196222456040894,
 0.077553494319095986,
 0.46887905231555532,
 0.7362166520914275)



In [24]:

    
prob_acc_tox









    Out[24]:





(0.99320475928614682,
 0.96901298353152288,
 0.47169110764562977,
 0.15821473148281351)



In [25]:

    
prob_eff









    Out[25]:





(0.22013447186187166,
 0.30243690338867141,
 0.4600635818911748,
 0.54455913160027725)



In [26]:

    
prob_acc_eff









    Out[26]:





(0.17175012210796936,
 0.23131955018761038,
 0.47183893926980514,
 0.61438570166558037)

Higher precision

Warning: this takes a while and peaks memory usage (on my machine) at roughly 1Gb



In [46]:

    
np.random.seed(123)
probs, thing = efftox_get_posterior_probs(cases, priors, scaled_doses, tox_cutoff=0.4, eff_cutoff=0.45, n=10**7)



In [48]:

    
prob_tox, prob_eff, prob_acc_tox, prob_acc_eff = zip(*probs)



In [49]:

    
prob_tox









    Out[49]:





(0.017721596042804065,
 0.077300802973282567,
 0.47664283361147941,
 0.74481378531497666)



In [50]:

    
prob_acc_tox









    Out[50]:





(0.99364311416251194,
 0.96463287117519392,
 0.43994562896133421,
 0.156595042211854)



In [51]:

    
prob_eff









    Out[51]:





(0.21301090872543804,
 0.2985971523841035,
 0.45994786342568222,
 0.54434065144599786)



In [52]:

    
prob_acc_eff









    Out[52]:





(0.15485703706407367,
 0.2318339137152034,
 0.48924984978095742,
 0.60206723461811928)



In [54]:

    
efftox_get_posterior_params(cases, priors, scaled_doses, n=10**7)









    Out[54]:





([(-2.2703011519429555,
   5.1516424515286898,
   -0.75467247679595473,
   1.2708491348927389,
   -0.0091021824701728229,
   -0.10086623116956173)],
 <clintrials.stats.ProbabilityDensitySample instance at 0x10da183b0>)



In [ ]: