Table 1.
Glossary for important terms related to platform trials, taken partly from ICH E9 [25], partly EU-PEARL D2.1 [12].
Fig 1.
Phase 2b platform trial design in non-alcoholic steatohepatitis (NASH).
After an initial inclusion of two cohorts consisting of control (usually the standard-of-care, “SOC”) and “regimen” arm (which could be a monotherapy or a combination therapy), more cohorts of the same structure are entering the trial over time. Within each cohort, several interim and a final analysis are conducted using the co-primary binary endpoints “NASH resolution without worsening of fibrosis” and “Fibrosis improvement without worsening of NASH”. The platform trial ends when all cohorts have been evaluated.
Fig 2.
Schematic overview of decision rules used.
On the x-axis, the difference in response rates between the control and treatment group (i.e. treatment effect) in percentage points is shown. At the two interim analyses, cohorts can be stopped early for futility, if there is very little evidence (interim analysis 1: less than 20%, interim analysis 2: less than 30%) that the treatment is better than control by 25 percentage points or more (red box). At all analysis time points, the same efficacy decision rules are used (blue boxes). Depending on the aim of the study, all or only certain levels of evidence could be required (see also Table 2). The treatment effects (δs) presented in this figure correspond to the decision rules used for endpoint 1—for endpoint 2, we used δ1 = 0, δ2 = 0.175, δ3 = 0.25, as well as a futility margin of 10 percentage points.
Table 2.
Different levels of evidence required to graduate treatment for efficacy.
The ordering is hierarchical in nature, i.e. requiring two levels of evidence means level 1 and level 2 need to be simultaneously fulfilled. E1 and E2 refer to endpoint 1 (resolution of NASH without worsening of fibrosis) and endpoint 2 (1-stage fibrosis improvement without worsening of NASH) respectively.
Fig 3.
Impact of different levels of correlation between endpoints 1 and 2 on the expected number of responders.
Assuming a response rate of 30% for endpoint 1 and 40% for endpoint 2, we expect 30/100 patients to reach endpoint 1 (in red) and 40/100 patients to reach endpoint 2 (in yellow), regardless of the correlation. Depending on different levels of the correlation, the number of responders that reach both endpoints simultaneously (in orange) varies; it increases with increasing correlation. In contrast, the expected number of trial participants that reach at least on of the two endpoints decreases with increasing correlation (in this example, this number is 69 when the correlation is -0.3 and 53 when the correlation is 0.7).
Table 3.
Specification of important simulation parameters.
Values are either fixed or varied in different simulation scenarios. For different simulation parameters, we differentiate between parameters that are considered a design choice (“D”) and parameters that are considered an assumption (“A”) regarding the future course of the platform trial or treatment effects (see second column “Type”).
Fig 4.
Success probabilities for the treatment arm with respect to the response rate for endpoint 1 (E1_Suc_Rate; columns), the response rate for endpoint 2 (E2_Suc_Rate; rows), the correlation between the two endpoints (x-axis), the type of data sharing used (point shape) and the planned cohort sample size per arm (colour).
The blue horizontal line marks 80% as a common target for the power and the red horizontal line marks 10% as a common target for type 1 error in early phase clinical trials. When the drug is truly effective, success probabilities correspond to power; when the drug is not effective, success probabilities correspond to type 1 error.
Fig 5.
Average platform trial duration in weeks with respect to the response rate for endpoint 1 (E1_Suc_Rate; columns), the response rate for endpoint 2 (E2_Suc_Rate; rows), the correlation between the two endpoints (x-axis), the type of data sharing used (point shape) and the planned cohort sample size per arm (colour).
Fig 6.
Cumulative probabilities to make a decision early (i.e. making an early efficacy or futility decision either at the first or second interim analysis) with respect to the response rate for endpoint 1 (E1_Suc_Rate; columns), the response rate for endpoint 2 (E2_Suc_Rate; rows), the correlation between the two endpoints (x-axis), the type of data sharing used (point shape) and the planned sample size per cohort (left panel 150 and right panel 250).
Fig 7.
Success probabilities for the treatment arm with respect to the response rate for endpoint 1 (E1_Suc_Rate; columns), the response rate for endpoint 2 (E2_Suc_Rate; rows), the correlation between the two endpoints (x-axis), the type of data sharing used (point shape), the level of evidence required (colour) and the planned sample size per cohort (left panel 150 and right panel 250).
The blue horizontal line marks 80% as a common target for the power and the red horizontal line marks 10% as a common target for type 1 error in early phase clinical trials. Level of evidence required refers to how many of the Bayesian efficacy rules specified in section 2.2 need to simultaneously hold for a treatment to be declared efficacious.
Fig 8.
Beta distributions corresponding to the posterior we would observe if a Beta(1,1) prior and a sample size of 75 was used and the observed response rate would equal 0.5.
Panel a: The posterior probability for a success rate greater or equal to 0.5 is 50%. If in our Bayesian decision rules we set a target of 0.5 and require a confidence of 50%, for large sample sizes we will graduate compounds with true responder rate of 0.5 in 50% of the cases, i.e. achieve a power of 50%. Panel b: The posterior probability for a success rate greater or equal to 0.45 is 81%. If in our Bayesian decision rules we set a target of 0.45 and require a confidence of 81%, for large sample sizes we will graduate compounds with true responder rate of 0.5 in 50% of the cases, i.e. achieve a power of 50%. Panel c: The posterior probability for a success rate greater or equal to 0.40 is 96%. If in our Bayesian decision rules we set a target of 0.40 and require a confidence of 96%, for large sample sizes we will graduate compounds with true responder rate of 0.5 in 50% of the cases, i.e. achieve a power of 50%. In order to achieve larger power values, required confidences and target success rates need to be adapted.
Table 4.
2x2 crosstable of possible short-term (S) and long-term (L) outcomes and their respective probabilities, as well as the marginal probabilities, with respect to treatment (denoted by superscript k).
Fig 9.
sensSL and specSL with respect to (columns),
(rows) and ρ (shade of color).
For scenarios , there is an upper uspec < 1 bound for specSL. For scenarios
, there is an upper usens < 1 bound for sensSL. For scenarios
either sensSL (
) or specSL (
) can take any values between 0 and 1. If the matrix of figures was transposed, we would see sensLS and specLS instead of sensSL and specSL. Please note that in the Figure the label “rho” is used for ρ.
Fig 10.
Relationship between specified correlation of the two continuous endpoints ρk prior to dichotomization and achieved correlation ϕk of the two binary endpoints after dichotomization.
Only when can ϕk ∈ [0, 1] be achieved, otherwise it is bounded above and/or below (see paragraph “Correlation” in section “Implicit specification” for more details on the bounds). The more
and
differ, the closer either the upper or lower bound of ϕk is to 0. Please note that in the Figure the labels “phi” and “rho” are used for ϕ and ρ.