A multistate model incorporating estimation of excess hazards and multiple time scales

A Multistate Model Incorporating Relative Survival Extrapolation and Mixed Time Scales for Health Technology Assessment

BACKGROUND

Multistate models have been widely applied in health technology assessment. However, extrapolating survival in a multistate model setting presents challenges in terms of precision and bias. In this article, we develop an individual-level continuous-time multistate model that integrates relative survival extrapolation and mixed time scales.

METHODS

We illustrate our proposed model using an illness-death model. We model the transition rates using flexible parametric models. We update the hesim package and the microsimulation package in R to simulate event times from models with mixed time scales. This feature allows us to incorporate relative survival extrapolation in a multistate setting. We compare several multistate settings with different parametric models (standard vs. flexible parametric models), and survival frameworks (all-cause vs. relative survival framework) using a previous clinical trial as an illustrative example.

RESULTS

Our proposed approach allows relative survival extrapolation to be carried out in a multistate model. In the example case study, the results agreed better with the observed data than did the commonly applied approach using standard parametric models within an all-cause survival framework.

CONCLUSIONS

We introduce a multistate model that uses flexible parametric models and integrates relative survival extrapolation with mixed time scales. It provides an alternative to combine short-term trial data with long-term external data within a multistate model context in health technology assessment.

Effect of early administration of tetracosactide on mortality and host response in critically ill patients requiring rescue surgery: a sensitivity analysis of the STOPSHOCK phase 3 randomized controlled trial

BACKGROUND

Undifferentiated shock is recognized as a criticality state that is transitional in immune-mediated topology for casual risk of lethal microcirculatory dysfunction. This was a sensitivity analysis of a drug (tetracosactide; TCS10) targeting melanocortin receptors (MCRs) in a phase 3 randomized controlled trial to improve cardiovascular surgical rescue outcome by reversing mortality and hemostatic disorders.

METHODS

Sensitivity analysis was based on a randomized, two-arm, multicenter, double-blind, controlled trial. The Naïve Bayes classifier was performed by density-based sensitivity index for principal strata as proportional hazard model of 30-day surgical risk mortality according to European System for Cardiac Operative Risk Evaluation inputs-outputs in 100 consecutive cases (from August to September 2013 from Emilia Romagna region, Italy). Patients included an agent-based TCS10 group (10 mg, single intravenous bolus before surgery; n = 56) and control group (n = 44) and the association with cytokines, lactate, and bleeding-blood transfusion episodes with the prior-risk log-odds for mortality rate in time-to-event was analyzed.

RESULTS

Thirty-day mortality was significantly improved in the TCS10 group vs. control group (0 vs. 8 deaths, P < 0.0001). Baseline levels of interleukin (IL)-6, IL-10, and lactate were associated with bleeding episodes, independent of TCS10 treatment [odds ratio (OR) = 1.90, 95% confidence interval (CI) 1.39-2.79; OR = 1.53, 95%CI 1.17-2.12; and OR = 2.92, 95%CI 1.40-6.66, respectively], while baseline level of Fms-like tyrosine kinase 3 ligand (Flt3L) was associated with lower bleeding rates in TCS10-treated patients (OR = 0.31, 95%CI 0.11-0.90, P = 0.03). For every 8 TCS10-treated patients, 1 bleeding case was avoided. Blood transfusion episodes were significantly reduced in the TCS10 group compared to the control group (OR = 0.32, 95%CI 0.14-0.73, P = 0.01). For every 4 TCS10-treated patients, 1 transfusion case was avoided.

CONCLUSIONS

Sensitivity index underlines the quality target product profile of TCS10 in the runway of emergency casualty care. To introduce the technology readiness level in real-life critically ill patients, further large-scale studies are required.

TRIAL REGISTRATION

European Union Drug Regulating Authorities Clinical Trials Database (EudraCT Number: 2007-006445-41 ).

Walking pace and the time between the onset of noncommunicable diseases and mortality: a UK Biobank prospective cohort study

PURPOSE

To estimate time spent in various cardiovascular disease (CVD) and cancer states, according to self-reported walking pace.

METHODS

In total, 391,744 UK Biobank participants were included (median age = 57 years; 54.7% women). Data were collected 2006-2010, with follow-up collected in 2021. Usual walking pace was self-defined as slow, steady, average, or brisk. Multistate modeling determined the transition rate and mean sojourn time in and across three different states (healthy, CVD or cancer, and death) upon a time horizon of 10 years.

RESULTS

The mean sojourn time in the healthy state was longer, while that in the CVD or cancer state was shorter in individuals reporting an average or brisk walking pace (vs. slow). A 75-year-old woman reporting a brisk walking pace spent, on average, 8.4 years of the next 10 years in a healthy state; an additional 8.0 (95% CI: 7.3, 8.7) months longer than a 75-year-old woman reporting a slow walking pace. This corresponded to 4.3 (3.7, 4.9) fewer months living with CVD or cancer. Similar results were seen in men.

CONCLUSIONS

Adults reporting an average or brisk walking pace at baseline displayed a lower transition to disease development and a greater proportion of life lived without CVD or cancer.

AVAILABILITY OF DATA AND MATERIALS

Research was conducted using the UK Biobank resource under Application #33266. The UK Biobank resource can be accessed by researchers on application. Variables derived for this study have been returned to the UK Biobank for future applicants to request. No additional data are available.

Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched population comparison group

BACKGROUND

Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices.

METHODS

We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions.

RESULTS

Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable.

CONCLUSIONS

Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.

The Lung Allocation Score Remains Inequitable for Patients with Pulmonary Arterial Hypertension, Even after the 2015 Revision

Rationale: The lung allocation score (LAS) was revised in 2015 to improve waiting list mortality and rate of transplant for patients with pulmonary arterial hypertension (PAH). Objectives: We sought to determine if the 2015 revision achieved its intended goals. Methods: Using the Standard Transplant Analysis and Research file, we assessed the impact of the 2015 LAS revision by comparing the pre- and postrevision eras. Registrants were divided into the LAS diagnostic categories: group A-chronic obstructive pulmonary disease; group B-pulmonary arterial hypertension; group C-cystic fibrosis; and group D-interstitial lung disease. Competing risk regressions were used to assess the two mutually exclusive competing risks of waiting list death and transplant. Cumulative incidence plots were created to visually inspect risks. Measurements and Main Results: The LAS at organ matching increased by 14.2 points for registrants with PAH after the 2015 LAS revision, the greatest increase among diagnostic categories (other LAS categories: Δ, -0.9 to +2.8 points). Before the revision, registrants with PAH had the highest risk of death and lowest likelihood of transplant. After the 2015 revision, registrants with PAH still had the highest risk of death, now similar to those with interstitial lung disease, and the lowest rate of transplant, now similar to those with chronic obstructive pulmonary disease. Conclusions: Although the 2015 LAS revision improved access to transplant and reduced the risk of waitlist death for patients with PAH, it did not go far enough. Significant differences in waitlist mortality and likelihood of transplant persist.

Modelling multiple time-scales with flexible parametric survival models

BACKGROUND

There are situations when we need to model multiple time-scales in survival analysis. A usual approach in this setting would involve fitting Cox or Poisson models to a time-split dataset. However, this leads to large datasets and can be computationally intensive when model fitting, especially if interest lies in displaying how the estimated hazard rate or survival change along multiple time-scales continuously.

METHODS

We propose to use flexible parametric survival models on the log hazard scale as an alternative method when modelling data with multiple time-scales. By choosing one of the time-scales as reference, and rewriting other time-scales as a function of this reference time-scale, users can avoid time-splitting of the data.

RESULT

Through case-studies we demonstrate the usefulness of this method and provide examples of graphical representations of estimated hazard rates and survival proportions. The model gives nearly identical results to using a Poisson model, without requiring time-splitting.

CONCLUSION

Flexible parametric survival models are a powerful tool for modelling multiple time-scales. This method does not require splitting the data into small time-intervals, and therefore saves time, helps avoid technological limitations and reduces room for error.

Integrating relative survival in multi-state models—a non-parametric approach

Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate.