Evaluation of Flexible Parametric Relative Survival Approaches for Enforcing Long-Term Constraints When Extrapolating All-Cause Survival.

OBJECTIVES: Parametric models are used to estimate the lifetime benefit of an intervention beyond the range of trial follow-up. Recent recommendations have suggested more flexible survival approaches and the use of external data when extrapolating. Both of these can be realized by using flexible parametric relative survival modeling. The overall aim of this article is to introduce and contrast various approaches for applying constraints on the long-term disease-related (excess) mortality including cure models and evaluate the consequent implications for extrapolation. METHODS: We describe flexible parametric relative survival modeling approaches. We then introduce various options for constraining the long-term excess mortality and compare the performance of each method in simulated data. These methods include fitting a standard flexible parametric relative survival model, enforcing statistical cure, and forcing the long-term excess mortality to converge to a constant. We simulate various scenarios, including where statistical cure is reasonable and where the long-term excess mortality persists. RESULTS: The compared approaches showed similar survival fits within the follow-up period. However, when extrapolating the all-cause survival beyond trial follow-up, there is variation depending on the assumption made about the long-term excess mortality. Altering the time point from which the excess mortality is constrained enables further flexibility. CONCLUSIONS: The various constraints can lead to applying explicit assumptions when extrapolating, which could lead to more plausible survival extrapolations. The inclusion of general population mortality directly into the model-building process, which is possible for all considered approaches, should be adopted more widely in survival extrapolation in health technology assessment.

Modeling the multi-state natural history of rare diseases with heterogeneous individual patient data: A simulation study.

Multi-state survival models are used to represent the natural history of a disease, forming the basis of a health technology assessment comparing a novel treatment to current practice. Constructing such models for rare diseases is problematic, since evidence sources are typically much sparser and more heterogeneous. This simulation study investigated different one-stage and two-stage approaches to meta-analyzing individual patient data (IPD) in a multi-state survival setting when the number and size of studies being meta-analyzed are small. The objective was to assess methods of different complexity to see when they are accurate, when they are inaccurate and when they struggle to converge due to the sparsity of data. Biologically plausible multi-state IPD were simulated from study- and transition-specific hazard functions. One-stage frailty and two-stage stratified models were estimated, and compared to a base case model that did not account for study heterogeneity. Convergence and the bias/coverage of population-level transition probabilities to, and lengths of stay in, each state were used to assess model performance. A real-world application to Duchenne Muscular Dystrophy, a neuromuscular rare disease, was conducted, and a software demonstration is provided. Models not accounting for study heterogeneity were consistently out-performed by two-stage models. Frailty models struggled to converge, particularly in scenarios of low heterogeneity, and predictions from models that did converge were also subject to bias. Stratified models may be better suited to meta-analyzing disparate sources of IPD in rare disease natural history/economic modeling, as they converge more consistently and produce less biased predictions of lengths of stay.

Perils of Randomized Controlled Trial Survival Extrapolation Assuming Treatment Effect Waning: Why the Distinction Between Marginal and Conditional Estimates Matters.

OBJECTIVES: A long-term, constant, protective treatment effect is a strong assumption when extrapolating survival beyond clinical trial follow-up; hence, sensitivity to treatment effect waning is commonly assessed for economic evaluations. Forcing a hazard ratio (HR) to 1 does not necessarily estimate loss of individual-level treatment effect accurately because of HR selection bias. A simulation study was designed to explore the behavior of marginal HRs under a waning conditional (individual-level) treatment effect and demonstrate bias in forcing a marginal HR to 1 when the estimand is "survival difference with individual-level waning". METHODS: Data were simulated under 4 parameter combinations (varying prognostic strength of heterogeneity and treatment effect). Time-varying marginal HRs were estimated in scenarios where the true conditional HR attenuated to 1. Restricted mean survival time differences, estimated having constrained the marginal HR to 1, were compared with true values to assess bias induced by marginal constraints. RESULTS: Under loss of conditional treatment effect, the marginal HR took a value >1 because of covariate imbalances. Constraining this value to 1 lead to restricted mean survival time difference bias of up to 0.8 years (57% increase). Inflation of effect size estimates also increased with the magnitude of initial protective treatment effect. CONCLUSIONS: Important differences exist between survival extrapolations assuming marginal versus conditional treatment effect waning. When a marginal HR is constrained to 1 to assess efficacy under individual-level treatment effect waning, the survival benefits associated with the new treatment will be overestimated, and incremental cost-effectiveness ratios will be underestimated.

Survival Extrapolation Incorporating General Population Mortality Using Excess Hazard and Cure Models: A Tutorial.

BACKGROUND: Different parametric survival models can lead to widely discordant extrapolations and decision uncertainty in cost-effectiveness analyses. The use of excess hazard (EH) methods, which incorporate general population mortality data, has the potential to reduce model uncertainty. This review highlights key practical considerations of EH methods for estimating long-term survival. METHODS: Demonstration of methods used a case study of 686 patients from the German Breast Cancer Study Group, followed for a maximum of 7.3 y and divided into low (1/2) and high (3) grade cancers. Seven standard parametric survival models were fit to each group separately. The same 7 distributions were then used in an EH framework, which incorporated general population mortality rates, and fitted both with and without a cure parameter. Survival extrapolations, restricted mean survival time (RMST), and difference in RMST between high and low grades were compared up to 30 years along with Akaike information criterion goodness-of-fit and cure fraction estimates. The sensitivity of the EH models to lifetable misspecification was investigated. RESULTS: In our case study, variability in survival extrapolations was extensive across the standard models, with 30-y RMST ranging from 7.5 to 14.3 y. Incorporation of general population mortality rates using EH cure methods substantially reduced model uncertainty, whereas EH models without cure had less of an effect. Long-term treatment effects approached the null for most models but at varying rates. Lifetable misspecification had minimal effect on RMST differences. CONCLUSIONS: EH methods may be useful for survival extrapolation, and in cancer, EHs may decrease over time and be easier to extrapolate than all-cause hazards. EH cure models may be helpful when cure is plausible and likely to result in less extrapolation variability. HIGHLIGHTS: In health economic modeling, to help anchor long-term survival extrapolation, it has been recommended that survival models incorporate background mortality rates using excess hazard (EH) methods.We present a thorough description of EH methods with and without the assumption of cure and demonstrate user-friendly software to aid researchers wishing to use these methods.EH models are applied to a case study, and we demonstrate that EHs are easier to extrapolate and that the use of the EH cure model, when cure is plausible, can reduce extrapolation variability.EH methods are relatively robust to lifetable misspecification.

Comparing the number and length of primary care consultations in people with and without intellectual disabilities and health needs: observational cohort study using electronic health records.

BACKGROUND: In the United Kingdom, 15-min appointments with the general practitioner (GP) are recommended for people with complex health conditions, including intellectual disabilities and health needs, but we do not know whether this happens. AIMS: We compared number and length of primary care consultations (GP, nurse, other allied health, other) for people with and without intellectual disabilities and health needs. METHODS: Linked primary care data from the Clinical Practice Research Datalink (CPRD) in England were used to investigate face-to-face and telephone primary care consultations in 2017-2019. Health needs investigated were: epilepsy; incontinence; severe visual/hearing impairments; severe mobility difficulties; cerebral palsy; and percutaneous endoscopic gastrostomy feeding. Age and gender-standardized consultation rates per year (Poisson), duration of consultations, and the proportion of "long consultations" (≥15 min) were reported. RESULTS: People with intellectual disabilities (n = 7,794) had 1.9 times as many GP consultations per year as those without (n = 176,807; consultation rate ratio = 1.87 [95% confidence interval 1.86-1.89]). Consultation rates with nurses and allied healthcare professionals were also twice as high. Mean GP consultation time was 9-10 min regardless of intellectual disability/health need status. Long GP consultations were less common in people with intellectual disabilities (18.2% [17.8-18.7] vs. 20.9% [20.8-21.0]). Long consultations with practice nurses were more common in people with health needs, particularly severe visual loss. CONCLUSIONS: People with intellectual disabilities and/or health needs tend to have more, rather than longer, GP consultations compared with the rest of the population. We recommend further investigation into the role of practice nurses to support people with intellectual disabilities and health needs.

Health Needs and Their Relationship with Life Expectancy in People with and without Intellectual Disabilities in England.

Health needs are common in people living with intellectual disabilities, but we do not know how they contribute to life expectancy. We used the Clinical Practice Research Datalink (CPRD) linked with hospital/mortality data in England (2017-2019) to explore life expectancy among people with or without intellectual disabilities, indicated by the presence or absence, respectively, of: epilepsy; incontinence; severe visual loss; severe visual impairment; severe mobility difficulties; cerebral palsy and PEG feeding. Life expectancy and 95% confidence intervals were compared using flexible parametric methods. At baseline, 46.4% (total n = 7794) of individuals with intellectual disabilities compared with 9.7% (total n = 176,807) in the comparison group had ≥1 health need. Epilepsy was the most common health need (18.7% vs. 1.1%). All health needs except hearing impairment were associated with shorter life expectancy: PEG feeding and mobility difficulties were associated with the greatest loss in life years (65-68% and 41-44%, respectively). Differential life expectancy attenuated but remained (≈12% life years lost) even after restricting the population to those without health needs (additional years expected to live at 10 years: 65.5 [60.3, 71.1] vs. 74.3 [73.8, 74.7]). We conclude that health needs play a significant role but do not explain all of the differential life expectancy experienced by people with intellectual disabilities.

Understanding the impact of socioeconomic differences in colorectal cancer survival: potential gain in life-years.

BACKGROUND: Colorectal cancer prognosis varies substantially with socioeconomic status. We investigated differences in life expectancy between socioeconomic groups and estimated the potential gain in life-years if cancer-related survival differences could be eliminated. METHODS: This population-based study included 470,000 individuals diagnosed with colon and rectal cancers between 1998 and 2013 in England. Using flexible parametric survival models, we obtained a range of life expectancy measures by deprivation status. The number of life-years that could be gained if differences in cancer-related survival between the least and most deprived groups were removed was also estimated. RESULTS: We observed up to 10% points differences in 5-year relative survival between the least and most deprived. If these differences had been eliminated for colon and rectal cancers diagnosed in 2013 then almost 8231 and 7295 life-years would have been gained respectively. This results for instance in more than 1-year gain for each colon cancer male patient in the most deprived group on average. Cancer-related differences are more profound earlier on, as conditioning on 1-year survival the main reason for socioeconomic differences were factors other than cancer. CONCLUSION: This study highlights the importance of policies to eliminate socioeconomic differences in cancer survival as in this way many life-years could be gained.

Potential gain in life years for Swedish women with breast cancer if stage and survival differences between education groups could be eliminated - Three what-if scenarios.

Many studies have found evidence of socioeconomic differences in breast cancer survival. This study aimed to quantify the impact of removing differences in stage distribution and stage-specific relative survival between education groups in Swedish women with breast cancer. Using information from a breast cancer research database, the study population contained 62 121 women diagnosed with breast cancer in three healthcare regions of Sweden from 1992 to 2012. The loss in expectation of life and life years lost due to breast cancer were estimated using flexible parametric relative survival models by education group and age at diagnosis. The potential gain in life years and postponable deaths were calculated by applying the 1) stage distribution, 2) stage-specific relative survival, and 3) both stage distribution and stage-specific relative survival of the high education group to the low and medium education groups. For a cohort of around 3500 women diagnosed with breast cancer residing in three Swedish healthcare regions in a typical calendar year, we estimated that removing stage differences would postpone an additional 25 deaths at five years after diagnosis, and result in a gain of approximately 573 life years. Alternatively, if stage-specific breast cancer survival could be equated, approximately 692 life years could be saved and an additional 26 deaths could be postponed five years after diagnosis. Results such as these can help guide decisions on interventions intended to minimise socioeconomic differences in breast cancer outcomes.

Estimating the impact of a cancer diagnosis on life expectancy by socio-economic group for a range of cancer types in England.

BACKGROUND: Differences in cancer survival exist across socio-economic groups for many cancer types. Standard metrics fail to show the overall impact for patients and the population. METHODS: The available data consist of a population of ∼2.5 million patients and include all patients recorded as being diagnosed with melanoma, prostate, bladder, breast, colon, rectum, lung, ovarian and stomach cancers in England between 1998 and 2013. We estimated the average loss in expectation of life per patient in years and the proportion of life lost for a range of cancer types, separately by deprivation group. In addition, estimates for the total number of years lost due to each cancer were also obtained. RESULTS: Lung and stomach cancers result in the highest overall loss for males and females in all deprivation groups in terms of both absolute life years lost and loss as a proportion of expected life remaining. Female lung cancer patients in the least- and most-deprived group lose 14.4 and 13.8 years on average, respectively, that is translated as 86.1% and 87.3% of their average expected life years remaining. Melanoma, prostate and breast cancers have the lowest overall loss. On the basis of the number of patients diagnosed in 2013, lung cancer results in the most life years lost in total followed by breast cancer. Melanoma and bladder cancer account for the lowest total life years lost. CONCLUSIONS: There are wide differences in the impact of cancer on life expectancy across deprivation groups, and for most cancers the most affluent lose less years.

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

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.