Borrowing information across patient subgroups in clinical trials, with application to a paediatric trial

Abstract

Background: Clinical trial investigators may need to evaluate treatment effects in a specific subgroup (or subgroups) of participants in addition to reporting results of the entire study population. Such subgroups lack power to detect a treatment effect, but there may be strong justification for borrowing information from a larger patient group within the same trial, while allowing for differences between populations. Our aim was to develop methods for eliciting expert opinions about differences in treatment effect between patient populations, and to incorporate these opinions into a Bayesian analysis.

Methods: We used an interaction parameter to model the relationship between underlying treatment effects in two subgroups. Elicitation was used to obtain clinical opinions on the likely values of the interaction parameter, since this parameter is poorly informed by the data. Feedback was provided to experts to communicate how uncertainty about the interaction parameter corresponds with relative weights allocated to subgroups in the Bayesian analysis. The impact on the planned analysis was then determined.

Results: The methods were applied to an ongoing non-inferiority trial designed to compare antiretroviral therapy regimens in 707 children living with HIV and weighing ≥ 14 kg, with an additional group of 85 younger children weighing < 14 kg in whom the treatment effect will be estimated separately. Expert clinical opinion was elicited and demonstrated that substantial borrowing is supported. Clinical experts chose on average to allocate a relative weight of 78% (reduced from 90% based on sample size) to data from children weighing ≥ 14 kg in a Bayesian analysis of the children weighing < 14 kg. The total effective sample size in the Bayesian analysis was 386 children, providing 84% predictive power to exclude a difference of more than 10% between arms, whereas the 85 younger children weighing < 14 kg provided only 20% power in a standalone frequentist analysis.

Conclusions: Borrowing information from a larger subgroup or subgroups can facilitate estimation of treatment effects in small subgroups within a clinical trial, leading to improved power and precision. Informative prior distributions for interaction parameters are required to inform the degree of borrowing and can be informed by expert opinion. We demonstrated accessible methods for obtaining opinions.

Keywords: Bayesian analysis; Borrowing information; Paediatric trials; Small samples; Subgroups.

Fig. 1

Experts’ opinions about the true treatment difference in 96-week failure rates in children weighing < 14 kg, assuming a 5% treatment difference in favour of DTG in children weighing ≥ 14 kg (stage 1): medians and inter-quartile ranges of fitted probability distributions

Fig. 2

Experts’ opinions about the true treatment difference in 96-week failure rates in children weighing < 14 kg, assuming a 0% treatment difference in children weighing ≥ 14 kg (stage 2): medians and inter-quartile ranges of fitted probability distributions

Fig. 3

Experts’ choices for relative weight to allocate to data from children weighing ≥ 14 kg in a Bayesian analysis of the children weighing < 14 kg (stage 3)

Fig. 4

Treatment difference estimates and 95% intervals in Example 1, obtained from a pooled analysis of all children and a Bayesian analysis for children weighing < 14 kg (incorporating evidence from children weighing ≥ 14 kg as a prior distribution), together with results from separate subgroups

Fig. 5

Treatment difference estimates and 95% intervals in Example 2, obtained from a pooled analysis of all children and a Bayesian analysis for children weighing < 14 kg (incorporating evidence from children weighing ≥ 14 kg as a prior distribution), together with results from separate subgroups