Signature
R = sum_(j=1)^J [pi_j * p_est_j]
| Inputs | Definition | Unit |
|---|---|---|
pi_j | Share of the population expected to be treated in practice whose tumour type corresponds to basket j; the shares sum to 1 | proportion |
p_est_j | Response estimate for basket j, either the observed proportion p_hat_j or the partially pooled p_tilde_j from HE-FM-BSKT-001 | probability |
R | Expected response probability in a population with tumour-type shares pi_j | probability |
|---|
JNumber of baskets, each a tumour type (count)
Function
Partial pooling of response rates across basket trial baskets
Maps the responders and evaluable patients in each basket of a basket trial, together with a common mean response and a between-basket variance, to a response estimate for each basket that borrows information from the other baskets. The result lies between analysing each basket separately and pooling every patient. The basket estimates can then be reweighted to the mix of tumour types expected in practice before they enter a response-based economic model. A full hierarchical model does the same jointly on the log-odds scale.
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Implementations
Excel
Tumour-type mix response in one cell
With the shares in a range named PopulationShares and the basket estimates in a range of the same size named BasketResponse, the formula returns R.
=SUMPRODUCT(PopulationShares,BasketResponse)
Assumptions
Tumour-type shares describe the treated population
The shares pi_j describe the tumour-type mix in the population that will be treated, for example NHS practice, and sum to 1 across the J baskets. Trial enrolment shares are not a substitute: in TA630 patients were recruited by convenience sampling, with no systematic attempt to represent the distribution of tumour types in NHS practice.
Basket estimates transfer to the same tumour types in practice
Each basket estimate is taken to apply to patients with that tumour type in practice. Tumour types covered by the licence but absent from the trial have no basket estimate and need a separate assumption, such as a predictive estimate from a hierarchical model.
Worked examples
NHS tumour-type mix with separate basket estimates
With an illustrative mix of 10% A, 10% B, 60% C and 20% D and the separate basket proportions, the expected response is 0.30, as in the article.
J = 4; pi_j = [0.1,0.1,0.6,0.2]; p_est_j = [0.60,0.60,0.10,0.60]; R = 0.30
NHS tumour-type mix with partially pooled basket estimates
The same mix applied to the partially pooled estimates as rounded in the article, 0.56, 0.56, 0.31 and 0.53, gives 0.404, as in the article. With unrounded estimates the result is about 0.4047, as in the computational function.
J = 4; pi_j = [0.1,0.1,0.6,0.2]; p_est_j = [0.56,0.56,0.31,0.53]; R = 0.404
Trial enrolment mix reproduces the pooled basket trial response
Weighting the observed proportions by trial enrolment, 20, 15, 10 and 5 of the 50 patients, returns 0.50, the complete pooling figure of 25 responders among 50. The pooled trial response is therefore a weighted average whose weights are set by recruitment.
J = 4; pi_j = [0.4,0.3,0.2,0.1]; p_est_j = [0.60,0.60,0.10,0.60]; R = 0.50
Common errors
Using the pooled basket trial response as the population estimate
The pooled trial figure implies 50 responders per 100 patients treated, against 30 with the separate basket estimates weighted to the illustrative NHS mix. A response-based economic model fed the pooled figure overstates benefit when the trial over-represents tumour types that respond well.
Dropping unrepresented tumour types from the basket mix
Rescaling the shares of the represented baskets to sum to 1 assumes that tumour types absent from the trial respond like the weighted average of those present. In TA630 the committee noted that it would need to accept that unrepresented solid tumours, for which there were no data, would respond to larotrectinib. Murphy and colleagues instead used the hierarchical model's predictive distribution, a mean response of 56.9% with a 95% credible interval of 0.2% to 99.9% for an unrepresented histology.
Sources
Murphy and colleagues on weighting histology results by the eligible population
Murphy P, Claxton L, Hodgson R, Glynn D, Beresford L, Walton M, Llewellyn A, Palmer S, Dias S. Exploring heterogeneity in histology-independent technologies and the implications for cost-effectiveness. Medical Decision Making. 2021;41(2):165-178. Methods section on decision options (decision 2 weights histology-specific results by the distribution of patients in each histology making up the eligible population) and the predictive distribution of response for an unrepresented histology, reported in the abstract as 56.9% (0.2% to 99.9%).
TA630 on trial tumour mix and unrepresented tumour types
National Institute for Health and Care Excellence. Larotrectinib for treating NTRK fusion-positive solid tumours (TA630). London: NICE; 2020. Section 3.10, on convenience sampling with no systematic attempt to represent the distribution of tumour types in NHS clinical practice and on tumour types not represented at all, and section 3.16, where comparator survival was weighted by the distribution of the efficacy population.
Canonical Identity
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