Incorporating patient preferences and burden-of-disease in evaluating ALS drug candidate AMX0035: a Bayesian decision analysis perspective

Figures & data

Table 1 Assumed values of parameters in the Bayesian clinical trial model.

Parameter	Value(s)	Description	Sources
N	16,583	Prevalence of ALS in the US in 2015.	(2(2) $$C(n,\lambda )=p_0\mathrm{ }(\alpha {\cdot C}_{10}+(1-\alpha )\cdot C_{00})+p_1\mathrm{ }(\beta \cdot C_{01}+(1-\beta )\cdot C_{11})$$(2) )
$c_1$	0.07 (0.16)	Severity of adverse effects of ALS treatment calibrated by YLD (DALY).	(10)
$c_2$	0.29 (2.75)	Disease severity of ALS calibrated by YLD (DALY).	(10,24)
$p_0$	[0.1, 0.3, 0.5, 0.7, 0.95]	Probability that ALS treatment is ineffective or has adverse effects. Adjusted to model different scenarios with baseline value $p_0=0.5\text{.}$	(7)
$\rho$	[0.25, 0.33, 0.5]	Signal-to-noise ratio of treatment effect. Adjusted to model different scenarios with baseline value $\rho =0.33\text{.}$	(7)
${\beta }_{\min }$	0.2	Minimum type II error of Bayesian decision analysis.	(7,10)
$\eta$	100 patients per year	The rate at which patients enroll in the trial. We assume a uniform accrual rate over time.	(20)
$s$	6 months	The time before the trial starts needed for paperwork, etc.	(20)
$f$	1 year	After the last patient is enrolled, patients are followed up for this amount of time before any data analysis is conducted.	(20)
$\tau$	9 months	The time required for the FDA to review an application and make an approval decision.	(20)
$r$	[0.1, 0.2, 0.5, 0.75, 1.0]	Annual discount rate.	(20)
$h_0$	0.037 (AMX0035) 0.059 (Riluzole)	Expected hazard rate in the control group.	(8) (27)
$hr=\frac{h_1}{h_0}$	0.560 (AMX0035) 0.660 (Riluzole)	Expected hazard ratio between the control and treatment groups.	(8) (27)
$t_{\mathit{obs}}$	36 (AMX0035) 21 (Riluzole)	Observation period used in the AMX0035 and Riluzole clinical trials.	(8) (27)

The bold values indicate the parameter values used in the baseline assumption of Bayesian decision analysis.

Table 2 Assumed cost matrix $C_{ij}\text{ for Bayesian decision analysis}.\text{ Here }N$ denotes the prevalence of ALS in the US, ${DF}_t\text{ the time discount factor},\text{ and }{c}_1\text{ and}\mathrm{ }{c}_2$ the costs of type I and II errors, respectively.

	Post-trial Loss
	$\widehat{\mathit{H}}=0 (\text{do not approve})$	$\widehat{\mathit{H}}=1 (\mathrm{approve})$
$\mathit{H}=0$ (not effective)	$C_{00}=0$	$C_{10}={DF}_t·N·c_1$ (Type I Error)
$\mathit{H}=1$ (effective)	$C_{01}=N\cdot c_2$ (Type II Error)	$C_{11}=\left(1-{DF}_t\right)\cdot N·c_2$

Table 3 Optimal type I error rate for phase 2 trial of AMX0035 with 89 patients in the treatment arm and 48 in the control arm.

${\mathit{p}}_0$ (%)	$\mathit{\rho }$	${\mathit{\alpha }}^{\mathrm{*}}$ (%)	Power (%)
Burden of Disease Measure: YLD
10	0.25	29.0	80.0
10	0.33	15.4	80.0
10	0.50	2.6	80.0
30	0.25	29.0	80.0
30	0.33	15.4	80.0
30	0.50	2.6	80.0
50	0.25	26.3	77.7
50	0.33	15.4	80.0
50	0.50	2.6	80.0
70	0.25	10.7	56.1
70	0.33	11.8	75.1
70	0.50	2.6	80.0
95	0.25	0.3	8.9
95	0.33	1.0	32.7
95	0.50	1.5	73.3
Burden of Disease Measure: DALY
10	0.25	29.0	80.0
10	0.33	15.4	80.0
10	0.50	2.6	80.0
30	0.25	29.0	80.0
30	0.33	15.4	80.0
30	0.50	2.6	80.0
50	0.25	29.0	80.0
50	0.33	15.4	80.0
50	0.50	2.6	80.0
70	0.25	29.0	80.0
70	0.33	15.4	80.0
70	0.50	2.6	80.0
95	0.25	3.8	35.1
95	0.33	5.6	60.8
95	0.50	2.6	80.0

The disease severity measures,  c₁ and c₂, are calibrated using YLD and DALY. p₀ denotes the probability that the ALS treatment is ineffective or has adverse effects; ρ denotes the signal-to-noise ratio of treatment effect; and  α* denotes the type I error rate. The baseline models (highlighted with $p_0=50\mathrm{\%}$ and $\rho =0.33$) have ${\alpha }^{\mathrm{*}}=15.4\mathrm{\%}$ for both burden-of-disease measures.

Table 4 Optimal type I error rate for a hypothetical ALS therapy under a phase 2 trial of AMX0035 with 89 patients in the treatment arm and 48 in the control arm.

${\mathit{p}}_0$ (%)	$\mathit{hr}$	${\mathit{T}}_{\mathit{obs}} (\mathit{months})$	${\mathit{\alpha }}^{\mathbf{*}}$ (%)	Power (%)
AMX0035
30	0.56	36	3.7	80.0
50	0.56	36	3.7	80.0
95	0.56	36	3.1	77.5
Riluzole
30	0.66	21	14.4	80.0
50	0.66	21	14.4	80.0
95	0.66	21	14.4	80.0

The disease severity measures, $c_1\text{ and }{c}_2$, are calibrated using YLD. $p_0$ denotes the probability that the ALS treatment is ineffective or has adverse effects; $hr$ denotes the hazard ratio of ALS treatment versus placebo; t_obs denotes the observation time of the trial; and α* denotes the type I error rate. The baseline models (highlighted with $p_0=50\%)\text{ have }{\alpha }^{\mathrm{*}}=3.7\%\text{ under AMX}0035$ survival data and α* = 14.4% under Riluzole survival data.

Table 5a Optimal sample size and type I error rate for a hypothetical ALS therapy with randomization ratio 2:1 and $h_0$ calibrated with AMX0035 survival data. The disease severity measures, c₁ and c₂, are calibrated using YLD and DALY. hr denotes the hazard ratio of ALS treatment versus placebo; t_obs denotes the observation time of the trial; and n* and α* denote the Bayesian optimal sample size and type I error rate, respectively.

$hr$	$t_{\mathit{obs}}\mathrm{ }$(Months)	$n^{\mathrm{*}}$	${\alpha }^{\mathrm{*}}$ (%)	Power (%)
Burden of Disease Measure: YLD
0.4	24	54	10.1	80.0
0.4	36	48	7.4	80.0
0.4	48	42	6.8	80.0
0.5	24	66	15.5	80.0
0.5	36	57	12.9	80.0
0.5	48	57	9.7	80.0
0.6	24	75	24.9	80.0
0.6	36	72	19.7	80.0
0.6	48	66	18.1	80.0
0.7	24	66	42.5	80.0
0.7	36	72	35.3	80.0
0.7	48	75	31.0	80.0
0.8	24	108	49.7	80.0
0.8	36	84	49.9	80.0
0.8	48	75	49.5	80.0
Burden of Disease Measure: DALY
0.4	24	21	31.6	80.0
0.4	36	18	28.7	80.0
0.4	48	18	24.7	80.0
0.5	24	15	48.2	80.0
0.5	36	12	47.4	80.0
0.5	48	21	32.4	80.0
0.6	24	24	49.3	80.0
0.6	36	18	49.7	80.0
0.6	48	18	47.1	80.0
0.7	24	45	49.7	80.0
0.7	36	36	49.2	80.0
0.7	48	30	49.8	80.0
0.8	24	105	50.0	79.9
0.8	36	84	49.9	80.0
0.8	48	72	50.0	79.9

Table 5b Optimal sample size and type I error rate for a hypothetical ALS therapy with randomization ratio 2:1 and $h_0$ calibrated with Riluzole survival data. The disease severity measures, c₁ and $c_2$, are calibrated using YLD and DALY. hr denotes the hazard ratio of ALS treatment versus placebo; $t_{\mathit{obs}}$ denotes the observation time of the trial; and n* and α* denote the Bayesian optimal sample size and type I error rate, respectively.

$hr$	$t_{\mathit{obs}}\mathrm{ }$(Months)	$n^{\mathrm{*}}$	${\alpha }^{\mathrm{*}}$ (%)	Power (%)
Burden of Disease Measure: YLD
0.4	24	33	13.7	80.0
0.4	36	30	11.1	80.0
0.4	48	27	10.7	80.0
0.5	24	36	22.5	80.0
0.5	36	36	17.5	80.0
0.5	48	33	16.8	80.0
0.6	24	36	35.2	80.0
0.6	36	36	30.6	80.0
0.6	48	36	28.2	80.0
0.7	24	33	50.0	79.9
0.7	36	30	48.5	80.0
0.7	48	33	45.1	80.0
0.8	24	81	50.0	80.0
0.8	36	66	50.0	79.7
0.8	48	63	49.9	80.0
Burden of Disease Measure: DALY
0.4	24	9	43.3	80.0
0.4	36	9	38.7	80.0
0.4	48	9	35.8	80.0
0.5	24	12	46.8	80.0
0.5	36	9	48.1	80.0
0.5	48	9	46.1	80.0
0.6	24	18	49.1	80.0
0.6	36	15	48.9	80.0
0.6	48	15	47.0	80.0
0.7	24	33	50.0	79.9
0.7	36	27	50.0	79.8
0.7	48	27	48.7	80.0
0.8	24	75	50.0	79.1
0.8	36	66	50.0	79.7
0.8	48	63	49.9	80.0

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Data availability statement

The data supporting the results reported in the article can be found in the cited references. The software for Bayesian decision analysis is available upon reasonable request to the corresponding author.