tradeoff ratio {EurosarcBayes}

Functions for integration for Bayesian loss methodology

Description

An integral and graph for an acceptable region for the bayesian loss function approach (see bayes_binom_two_loss). tradeoff_ratio_intercepts computes the intercepts of the odd ratio curve with the limits.

Usage

tradeoff_ratio_intercepts(R_min,R_max,T_min,T_max,theta=0)

tradeoff_ratio_integrate(ar, br, at, bt, efficacy_region_min, 
	toxicity_region_max, efficacy_region_max, toxicity_region_min, 
	theta, intercepts)

tradeoff_ratio_graph(input)

Arguments

R_min, R_max, T_min, T_max

Limis for tradeoff region

theta

odd ratio for efficacy-toxicity tradeoff

intercepts

The values returned from tradeoff_ratio_intercepts

ar, br

Parameters for the posterior distribution for response

at, bt

Parameters for the posterior distribution for toxicity

efficacy_region_min

Smallest acceptable efficacy

toxicity_region_max

Largest acceptable toxicity

efficacy_region_max

Point where no more tradeoff occurs for efficacy

toxicity_region_min

Point where no more tradeoff occurs for toxicity

input

A list values needed for the graph. It is expecting max.patients, efficacy_region_min, toxicity_region_max and will error without

Value

Returns value of the integration.

References

Chen Y, Smith BJ. Adaptive group sequential design for phase II clinical trials: a Bayesian decision theoretic approach. Stat Med 2009; 28: 3347-3362.

See Also

bayes_binom_two_loss

Integration functions and corresponding graphs: tradeoff_square_integrate,tradeoff_ellipse_integrate,tradeoff_linear_integrate,tradeoff_ratio_integrate

Examples

# modelled toxicity probability
t=c(0.1,0.1,0.3,0.3)
# modelled response probability
r=c(0.35,0.2,0.2,0.35)

reviews=c(10,15,20,25,30,35,40)
stage_after_trial=40

# uniform prior
pra=1;prb=1;pta=1;ptb=1

efficacy_critical_value=0.2
futility_critical_value=0.35
toxicity_critical_value=0.1
no_toxicity_critical_value=0.3

# alpha/beta ratio
l_alpha_beta=3
# cost of continuing compared to cost of alpha
l_alpha_c=750

efficacy_region_min=0.2
toxicity_region_max=0.3

########################################
# odds ratio region
efficacy_region_min=0.2
efficacy_region_max=0.35
toxicity_region_min=0.1
toxicity_region_max=0.3

theta= 0.275/0.725 * 0.8/0.2

intercepts=tradeoff_ratio_intercepts(efficacy_region_min,
efficacy_region_max,toxicity_region_min,toxicity_region_max,theta)

s=bayes_binom_two_loss(t,r,reviews,pra,prb,pta,ptb,l_alpha_beta,
l_alpha_c,stage_after_trial,fun.integrate=tradeoff_ratio_integrate,
fun.graph=tradeoff_ratio_graph,efficacy_critical_value,
toxicity_critical_value,futility_critical_value,
no_toxicity_critical_value,efficacy_region_min=efficacy_region_min,
toxicity_region_max=toxicity_region_max,
efficacy_region_max=efficacy_region_max,
toxicity_region_min=toxicity_region_min,
theta=theta,intercepts=intercepts)

plot(s)