Flexible parametric proportional‐hazards and proportional‐odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects

Royston, Patrick; Parmar, Mahesh

doi:10.1002/sim.1203

Cited by 1,206 publications

(1,217 citation statements)

References 32 publications

(43 reference statements)

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“…For participants without a history of stroke, the time until stroke was observed until the end of the first extension period (2010). Adjusted hazard ratios were estimated through the Cox regression model framework accounting for left and right censoring that allowed a flexible spline fit to the baseline hazard 65. Models used age as the time scale and accounted for left censoring of participants who reported stroke before WHI enrollment and right censoring for those who did not have a stroke event.…”

Section: Methodsmentioning

confidence: 99%

Breastfeeding History and Risk of Stroke Among Parous Postmenopausal Women in the Women's Health Initiative

Jacobson

Hade

Collins

et al. 2018

JAHA

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BackgroundStroke is the third leading cause of death among US Hispanic and non‐Hispanic black women aged 65 and older. One factor that may protect against stroke is breastfeeding. Few studies have assessed the association between breastfeeding and stroke and whether this association differs by race and ethnicity.Methods and ResultsData were taken from the Women's Health Initiative Observational Study with follow‐up through 2010; adjusted hazard ratios for stroke subsequent to childbirth were estimated with Cox regression models accounting for left and right censoring, overall and stratified by race/ethnicity. Of the 80 191 parous women in the Women's Health Initiative Observational Study, 2699 (3.4%) had experienced a stroke within a follow‐up period of 12.6 years. The average age was 63.7 years at baseline. Fifty‐eight percent (n=46 699) reported ever breastfeeding; 83% were non‐Hispanic white, 8% were non‐Hispanic black, 4% were Hispanic, and 5% were of other race/ethnicity. After adjustment for nonmodifiable potential confounders, compared with women who had never breastfed, women who reported ever breastfeeding had a 23% lower risk of stroke (adjusted hazard ratio=0.77; 95% confidence interval 0.70‐0.83). This association was strongest for non‐Hispanic black women (adjusted hazard ratio=0.52; 95% confidence interval 0.37‐0.71). Further, breastfeeding for a relatively short duration (1‐6 months) was associated with a 19% lower risk of stroke (adjusted hazard ratios=0.81; 95% confidence interval 0.74‐0.89). This association appeared stronger with longer breastfeeding duration and among non‐Hispanic white and non‐Hispanic black women (test for trend P<0.01).ConclusionsStudy results show an association and dose‐response relationship between breastfeeding and lower risk of stroke among postmenopausal women after adjustment for multiple stroke risk factors and lifestyle variables. Further investigation is warranted.

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Section: Methodsmentioning

confidence: 99%

Breastfeeding History and Risk of Stroke Among Parous Postmenopausal Women in the Women's Health Initiative

Jacobson

Hade

Collins

et al. 2018

JAHA

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“…The cubic spline models were based on those developed by Royston and Parmar. 192 Cubic spline models expressed on the proportional odds scale were used as they appeared to converge to an optimised solution more frequently than the proportional hazards or probit variants of the cubic spline model. A series of one-, two-, three-and four-knot spline models was considered.…”

Section: Input Assumptionmentioning

confidence: 99%

The assessment and appraisal of regenerative medicines and cell therapy products: an exploration of methods for review, economic evaluation and appraisal

Hettle

Corbett

Hinde

et al. 2017

Health Technol Assess

106

143

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BackgroundThe National Institute for Health and Care Excellence (NICE) commissioned a ‘mock technology appraisal’ to assess whether changes to its methods and processes are needed. This report presents the findings of independent research commissioned to inform this appraisal and the deliberations of a panel convened by NICE to evaluate the mock appraisal.MethodsOur research included reviews to identify issues, analysis methods and conceptual differences and the relevance of alternative decision frameworks, alongside the development of an exemplar case study of chimeric antigen receptor (CAR) T-cell therapy for treating acute lymphoblastic leukaemia.ResultsAn assessment of previous evaluations of regenerative medicines found that, although there were a number of evidential challenges, none was unique to regenerative medicines or was beyond the scope of existing methods used to conceptualise decision uncertainty. Regarding the clinical evidence for regenerative medicines, the issues were those associated with a limited evidence base but were not unique to regenerative medicines: small non-randomised studies, high variation in response and the intervention subject to continuing development. The relative treatment effects generated from single-arm trials are likely to be optimistic unless it is certain that the historical data have accurately estimated the efficacy of the control agent. Pivotal trials may use surrogate end points, which, on average, overestimate treatment effects. To reduce overall uncertainty, multivariate meta-analysis of all available data should be considered. Incorporating indirectly relevant but more reliable (more mature) data into the analysis can also be considered; such data may become available as a result of the evolving regulatory pathways being developed by the European Medicines Agency. For the exemplar case of CAR T-cell therapy, target product profiles (TPPs) were developed, which considered the ‘curative’ and ‘bridging to stem-cell transplantation’ treatment approaches separately. Within each TPP, three ‘hypothetical’ evidence sets (minimum, intermediate and mature) were generated to simulate the impact of alternative levels of precision and maturity in the clinical evidence. Subsequent assessments of cost-effectiveness were undertaken, employing the existing NICE reference case alongside additional analyses suggested within alternative frameworks. The additional exploratory analyses were undertaken to demonstrate how assessments of cost-effectiveness and uncertainty could be impacted by alternative managed entry agreements (MEAs), including price discounts, performance-related schemes and technology leasing. The panel deliberated on the range of TPPs, evidence sets and MEAs, commenting on the likely recommendations for each scenario. The panel discussed the challenges associated with the exemplar and regenerative medicines more broadly, focusing on the need for a robust quantification of the level of uncertainty in the cost-effective estimates and the potential value of MEAs in limiting the exposure of the NHS to high upfront costs and loss associated with a wrong decision.ConclusionsIt is to be expected that there will be a significant level of uncertainty in determining the clinical effectiveness of regenerative medicines and their long-term costs and benefits, but the existing methods available to estimate the implications of this uncertainty are sufficient. The use of risk sharing and MEAs between the NHS and manufacturers of regenerative medicines should be investigated further.FundingThe National Institute for Health Research Health Technology Assessment programme.

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“…However, it has recently been suggested that RSRs should be estimated using a modelling approach that enables flexible modelling of the baseline excess hazard [7], and one such model is the flexible parametric survival model [22,23].…”

Section: Relative Survivalmentioning

confidence: 99%

“…The flexible parametric survival model [22,23] uses restricted cubic splines to model the baseline cumulative hazard. The use of splines enables the model to capture complex baseline cumulative hazard functions, and gives a parametric model without the need of strong distributional assumptions.…”

Section: Flexible Parametric Survival Modelmentioning

confidence: 99%

Assessment of lead-time bias in estimates of relative survival for breast cancer

Andersson

Rutherford

Humphreys

2017

Cancer Epidemiology

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Relative survival ratios (RSRs) can be useful for evaluating the impact of changes in cancer care on the prognosis of cancer patients or for comparing the prognosis for different subgroups of patients, but their use is problematic for cancer sites where screening has been introduced due to the potential of lead-time bias. Lead-time is survival time that is added to a patient's survival time because of an earlier diagnosis irrespective of a possibly postponed time of death. In the presence of screening it is difficult to disentangle how much of an observed improvement in survival is real and how much is due to lead-time bias. Even so, RSRs are often presented for breast cancer, a site where screening has led to early diagnosis, with the assumption that the lead-time bias is small. We describe a simulation-based framework for studying the lead-time bias due to mammography screening on RSRs of breast cancer based on a natural history model developed in a Swedish setting. We have performed simulations, using this framework, under different assumptions for screening sensitivity and breast cancer survival with the aim of estimating the lead-time bias. Screening every second year among ages 40-75 was introduced assuming that screening had no effect on survival, except for lead-time bias. Relative survival was estimated both with and without screening to enable quantification of the lead-time bias. Scenarios with low, moderate and high breast cancer survival, and low, moderate and high screening sensitivity were simulated, and the lead-time bias assessed in all scenarios.

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Flexible parametric proportional‐hazards and proportional‐odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects

Cited by 1,206 publications

References 32 publications

Breastfeeding History and Risk of Stroke Among Parous Postmenopausal Women in the Women's Health Initiative

Breastfeeding History and Risk of Stroke Among Parous Postmenopausal Women in the Women's Health Initiative

The assessment and appraisal of regenerative medicines and cell therapy products: an exploration of methods for review, economic evaluation and appraisal

Assessment of lead-time bias in estimates of relative survival for breast cancer

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