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Introduction Time-to-event data from clinical trials are routinely extrapolated using parametric models to estimate the cost effectiveness of novel therapies, but how this approach performs in the presence of heterogeneous populations remains unknown. Methods We performed a simulation study of seven scenarios with varying exponential distributions modelling treatment and prognostic effects across subgroup and complement populations, with follow-up typical of clinical trials used to appraise the cost effectiveness of therapies by agencies such as the UK National Institute for Health and Care Excellence (NICE). We compared established and emerging methods of estimating population life-years (LYs) using parametric models. We also proved analytically that an exponential model fitted to censored heterogeneous survival times sampled from two distinct exponential distributions will produce a biased estimate of the hazard rate and LYs. Results LYs are underestimated by the methods in the presence of heterogeneity, resulting in either under- or overestimation of the incremental benefit. In scenarios where the overestimation of benefit is likely, which is of interest to the healthcare provider, the method of taking the average LYs from all plausible models has the least bias. LY estimates from complete Kaplan–Meier curves have high variation, suggesting mature data may not be a reliable solution. We explore the effect of increasing trial sample size and accounting for detected treatment–subgroup interactions. Conclusions The bias associated with heterogeneous populations suggests that NICE may need to be more cautious when appraising therapies and to consider model averaging or the separate modelling of subgroups when heterogeneity is suspected or detected. Supplementary Information The online version contains supplementary material available at 10.1007/s40273-021-01082-x.

Objective: To evaluate the efficacy and safety of opioids for analgesic therapy for people with osteoarthritis.\ud \ud Study design: Systematic review and meta‐analysis of randomised, placebo‐controlled trials of opioid therapies for treating the pain of osteoarthritis. The primary outcome was medium term pain relief (six weeks to less than 12 months). Quality of evidence was assessed with GRADE criteria.\ud \ud Data sources: MEDLINE, EMBASE, the Cochrane Database of Systematic Reviews and Central Register of Controlled Trials, CINAHL, PsycINFO, AMED, and the WHO International Clinical Trials Registry; trials published to 31 October 2020.\ud \ud Data synthesis: We extracted pain, disability, health‐related quality of life, and adverse events data for 36 eligible trials (overall dose range: 10‒210 oral morphine milligram equivalents [MME] per day). Continuous pain and disability outcomes were converted to common 0–100‐point scales; changes of less than ten points were deemed to be very small effects. Differences in dichotomous outcomes were expressed as risk ratios. Data were pooled for meta‐analysis in random effects models. The evidence from 19 trials (8965 participants; dose range, 10–126 MME/day) for very small medium term pain relief (mean difference [MD], –4.59 points; 95% CI, –7.17 to –2.02 points) was low quality, as was that from 16 trials (6882 participants; dose range, 10–126 MME/day) for a very small effect on disability (MD, –4.15 points; 95% CI, –6.94 to –1.35 points). Opioid dose was not statistically significantly associated with either degree of pain relief or incidence of adverse events in a meta‐regression analysis. Evidence that opioid therapy increased the risk of adverse events (risk ratio, 1.43; 95% CI, 1.29‒1.59) was of very low quality.\ud \ud Conclusions: Opioid medications may provide very small pain and disability benefits for people with osteoarthritis, but may also increase the risk of adverse events.

Advances in medical technology have led to a better understanding of heterogeneity of diseases and patients, and to the development of targeted medicines. This development is beneficial to society but can come at an increased cost to pharmaceutical manufacturers due to the costs associated with developing and manufacturing a diagnostic test. For such medicines, the conventional pricing structure, where a therapy is approved if it is deemed cost-effective, may not appropriately incentivise targeted drug development. We model the decision-making processes for both the healthcare provider and the pharmaceutical manufacturer, capturing their main priorities, and populate it with information from a recent appraisal by the National Institute of Health and Care Excellence. Healthcare providers prefer a stratified drug to be developed for a subgroup of the population when the drug is on average effective in the subgroup but with a detrimental effect in the complement. Whilst pharmaceutical manufacturers’ preferences are similar, regions of disagreement exist. We show how preferences can be aligned by either penalising the development of a non-stratified drug or rewarding the development of a stratified drug. The cost and position of alignment depends on the true value of health to the healthcare provider, among other parameters.

Supplemental material, sj-docx-1-mdm-10.1177_0272989X211003880 for Multivariate Generalized Linear Mixed-Effects Models for the Analysis of Clinical Trial–Based Cost-Effectiveness Data by Felix Achana, Daniel Gallacher, Raymond Oppong, Sungwook Kim, Stavros Petrou, James Mason and Michael Crowther in Medical Decision Making

Supplemental material, sj-docx-1-mdm-10.1177_0272989X20973201 for Extrapolating Parametric Survival Models in Health Technology Assessment: A Simulation Study by Daniel Gallacher, Peter Kimani and Nigel Stallard in Medical Decision Making

Background A reliable biomarker signature for bipolar disorder sensitive to illness phase would be of considerable clinical benefit. Among circulating blood-derived markers there has been a significant amount of research into inflammatory markers, neurotrophins and oxidative stress markers. Aims To synthesise and interpret existing evidence of inflammatory markers, neurotrophins and oxidative stress markers in bipolar disorder focusing on the mood phase of illness. Method Following PRISMA (Preferred Reporting Items for Systematic reviews and Meta-analyses) guidelines, a systematic review was conducted for studies investigating peripheral biomarkers in bipolar disorder compared with healthy controls. We searched Medline, Embase, PsycINFO, SciELO and Web of Science, and separated studies by bipolar mood phase (mania, depression and euthymia). Extracted data on each biomarker in separate mood phases were synthesised using random-effects model meta-analyses. Results In total, 53 studies were included, comprising 2467 cases and 2360 controls. Fourteen biomarkers were identified from meta-analyses of three or more studies. No biomarker differentiated mood phase in bipolar disorder individually. Biomarker meta-analyses suggest a combination of high-sensitivity C-reactive protein/interleukin-6, brain derived neurotrophic factor/tumour necrosis factor (TNF)-α and soluble TNF-α receptor 1 can differentiate specific mood phase in bipolar disorder. Several other biomarkers of interest were identified. Conclusions Combining biomarker results could differentiate individuals with bipolar disorder from healthy controls and indicate a specific mood-phase signature. Future research should seek to test these combinations of biomarkers in longitudinal studies. Declaration of interest None.

Coal mining in nineteenth century British Columbia was confined almost exclusively to the tidewater coal measures of Vancouver Island where it was expanded rapidly from 1871 to 1891. This dissertation's purposes are to describe the coal industry's rise, account for its fast growth in the seventies and eighties, and assess the coal trade's general impact upon the region's economy. The approach is thematic, focusing in turn upon coal lands, capital, management, labour, technology, markets, production, and productivity. Standard research, organization, and interpretation methods for economic history are followed, including thorough descriptive use of statistical data. Comparisons are intensive and far-reaching, resulting in a close-knit framework upon which important conclusions are based. No effort has been made, however, to offer extensive biographical information on the coal trade's leading personalities. These studies confirm the coal industry's rapid expansion, and determine that all factors of production can explain that phenomenon with a high degree of certainty, though market demand and management technique do so more readily than other agents. It is shown that management methods and styles evolved quickly, the most effective being the owner-manager type as practiced by Robert Dunsmuir, the industry's most successful proprietor. Risk capital was drawn from various sources, including mainly British direct investments, local savings, partnerships (often involving foreign investors), and ploughed-back profits. Entrepreneurs and promoters were active in attempting to develop coal properties from 1864 on, though only those highly experienced in mining and management succeeded. Chronic worker shortages, coupled with the physical problems associated with coal mining in mountainous terrain, forced coal operators to opt early for labour saving technology imported almost exclusively from Britain. The introduction of large numbers of Oriental colliers by Dunsmuir after 1870, (who were willing to work at half the wages whites would), slowed the technological advance of the industry, but not annual rates of production increases. Considerable friction between white workers and management resulted from the latter's initiatives with Oriental labour, while the owners' policy of severely restricting wage-rates caused further serious labour problems, including a high number of work stoppages. Mine safety, job security, and general working conditions also were contentious issues. B.C.'s early collieries relied heavily upon the California market which often was unsteady, but which accounted for approximately seventy-five percent of all sales during the years 1849-91. Domestic users were mainly shipping companies, light industry, and households. Much of the local market was handled at the pithead. The major coal companies streamlined their channels of distribution by opening their own sales offices in Victoria and San Francisco, and. in the case of Dunsmuir, by also building a collier fleet and a railway of his own. The coal industry had a major influence upon southern Vancouver Island's economy, but not a large impact upon the remainder of the province. No determined "attempts were made by coal proprietors or other capitalists to create secondary industries linked to coal production, though colliery owners did invest in land, transport, and retail-wholesale ventures designed either to service their mining activities or to diversify their personal holdings. Such moves occurred later-on, however, as the main thrust of their initial efforts was to establish and maintain the coal trade with California.