Multistate Model Approach Research Articles

PCN224 TREATMENT BENEFIT DISCONTINUATION: COMPARISON OF A PARTITIONED SURVIVAL ANALYSIS AND A SEMI-MARKOV MULTI-STATE MODEL APPROACH USING AN ONCOLOGY CASE STUDY

To compare three scenarios modelling treatment benefit discontinuation (TBD), also known as treatment waning, within a partitioned survival analysis (PartSA) or semi-Markov multi-state model (MSM) framework. The PartSA was developed using data from a cohort of patients with late-stage cancer (N>700) enrolled within a randomised, controlled trial. Health states were pre-progression, progressed disease and death. Patients were treated until progression. Clinician feedback indicated that treatment effect would be unlikely to extend beyond treatment discontinuation. To incorporate TBD, the PartSA considered two scenarios: (1) survival rates in the TX1 arm equal to TX2 after the median follow-up (15-months) and (2) survival rates in the TX1 arm equal to TX2 after the maximum follow-up (24-months). The MSM was constructed using the same data and inputs, but no TBD inputs were required as the long-term extrapolation for the transition from progressed disease to death was based on empirical data collected beyond progression. The PartSA estimated an incremental cost-effectiveness ratio (ICER) of £342,474 without adjustment for TBD. When considering TBD, the ICER increased by 135% (£803,992) and 91% (£653,301) for scenarios (1) and (2), respectively. The MSM estimated an ICER of £483,097. Despite adjusting for TBD, the PartSA framework resulted in more optimistic long-term survival for patients in the progressed disease health state compared with the MSM framework. An increasingly common theme in UK health technology appraisals is exploring the discontinuation of the treatment effect when extrapolating survival data. However, there are no guidelines as to how this should be approached within the PartSA framework. It is important to note that attempting to incorporate dependency of endpoints within a PartSA – as is attempted within the TBD scenarios – invalidates the assumptions underpinning a PartSA. Alternative model structures, such as the MSM approach, may provide a more robust estimate.

Cost-effectiveness of pembrolizumab for the adjuvant treatment of resected high-risk stage III melanoma in the United States

Aims: To evaluate the cost-effectiveness of adjuvant pembrolizumab relative to observation alone following complete resection of high-risk stage III melanoma with lymph node involvement, from a US health system perspective.Materials and methods: A Markov cohort model with four health states (recurrence-free, locoregional recurrence, distant metastases, and death) was developed to estimate costs, life-years, and quality-adjusted life-years (QALYs) associated with pembrolizumab vs observation over a lifetime (46-year) horizon. Using a parametric multi-state modeling approach, transition probabilities starting from recurrence-free were estimated based on patient-level data from KEYNOTE-054 (NCT02362594), a direct head-to-head phase 3 trial. Post-recurrence transition probabilities were informed by real-world retrospective data and clinical trials in advanced melanoma. Health state utilities and adverse event-related disutility were derived from KEYNOTE-054 trial data and published literature. Costs of drug acquisition and administration, adverse events, disease management, and terminal care were estimated in 2018 US dollars. Deterministic and probabilistic sensitivity analyses were conducted to assess robustness.Results: Over a lifetime horizon, adjuvant pembrolizumab and observation were associated with total QALYs of 9.24 and 5.95, total life-years of 10.54 and 7.15, and total costs of $489,820 and $440,431, respectively. The resulting incremental cost-effectiveness ratios (ICERs) for pembrolizumab vs observation were $15,009/QALY and $14,550/life-year. Across the range of input values and assumptions tested in deterministic sensitivity analyses, pembrolizumab ranged from being a dominant strategy to having an ICER of $57,449/QALY vs observation. The ICER was below a willingness-to-pay threshold of $100,000/QALY in 90.2% of probabilistic simulations.Limitations: Long-term extrapolation of outcomes was based on interim results from KEYNOTE-054, with a median follow-up of 15 months.Conclusions: Based on common willingness-to-pay benchmarks, pembrolizumab is highly cost-effective compared with observation alone for the adjuvant treatment of completely resected stage III melanoma in the US.

MS4 A COMPARISON OF THE PARTITIONED SURVIVAL AND MULTISTATE EXTRAPOLATION METHODS: A CASE STUDY BASED ON THE GASTRIC CANCER TRIAL ATTRACTION-2

Partitioned survival modelling (PartSA) is frequently used in cost-effectiveness analysis in oncology and is characterized by separate modelling of time to event (TTE) outcomes. The multistate modelling (MSM) approach is defined by its ability to jointly estimate TTEs. The aim of this study was to compare PartSA and MSM-obtained survival extrapolations using data from the ATTRACTION-2 (NCT02267343) trial, which compared nivolumab with best supportive care (BSC) in advanced or metastatic gastric cancer. Two data cutoffs were available for ATTRACTION-2, from August 2016 and February 2018, with median follow-up periods of 9 and 24 months, respectively. Standard parametric models were fitted to the 2016 data using the PartSA and MSM approaches. The MSM approach included a covariate to account for patients’ history of time on treatment. Extrapolations for overall survival (OS) based on 2016 data were compared with the more mature 2018 data. The observed restricted mean survival (RMS) at 3 years in ATTRACTION-2 was 0.50 years (95% CI: 0.42-0.58 years) and 0.78 years (95% CI: 0.70-0.87 years) for BSC and nivolumab, respectively (2018 data). Both modelling approaches using the 2016 data successfully predicted the observed OS in the 2018 data, as the 3-year RMS estimates were within the observed 95% CIs. OS estimates for BSC were similar for both approaches (3-year RMS, PartSA: 0.51 years; MSM: 0.52 years). OS estimates for nivolumab were lower using PartSA than MSM (PartSA: 0.77 years; MSM: 0.85 years). Both PartSA and MSM, based on the 2016 data, provided accurate predictions up to three years as estimates were within the observed 95% CI of the 2018 data. MSM predicted a higher mean survival for nivolumab compared to PartSA, as MSM predicted a long-term survival plateau whereas PartSA did not. Clinical insight could provide additional guidance on the preferred extrapolation approach.

Impact of Checkpoint Inhibitor Pneumonitis on Survival in NSCLC Patients Receiving Immune Checkpoint Immunotherapy

With increasing use of immune checkpoint inhibitors (ICIs) for advanced NSCLC, there is increasing recognition of immune-related adverse events associated with ICI use. We recently reported increased incidence of checkpoint inhibitor pneumonitis (CIP) in ICI-treated NSCLC patients. Since development of immune-related adverse events in other organ systems has been associated with either no change or even improvement in tumor response/cancer outcomes, we sought to better understand the impact of CIP development on overall survival in ICI-treated NSCLC patients. Using baseline and follow-up data collected on a cohort of 205 ICI-treated NSCLC patients, we used a multi-state modeling approach to understand the effect of developing CIP on the risk of death. We observed time-dependent changes in risk of developing and recovery from CIP, with an increased risk of both developing and recovering from CIP in the first year after initiating ICI. We found that developing CIP independently increased the risk of transitioning to death in both adjusted and unadjusted models. In the multivariate model, we found that the increase in mortality associated with CIP was only seen in patients with adenocarcinoma tumor histology. Collectively, these findings suggest that in NSCLC, development of CIP worsens survival in patients receiving immunotherapy.

Economic Evaluation of Lupus Nephritis in the Systemic Lupus International Collaborating Clinics Inception Cohort Using a Multistate Model Approach.

Little is known about the long-term costs of lupus nephritis (LN). The costs were compared between patients with and without LN using multistate modeling. Patients from 32 centers in 11 countries were enrolled in the Systemic Lupus International Collaborating Clinics inception cohort within 15 months of diagnosis and provided annual data on renal function, hospitalizations, medications, dialysis, and selected procedures. LN was diagnosed by renal biopsy or the American College of Rheumatology classification criteria. Renal function was assessed annually using the estimated glomerular filtration rate (GFR) or estimated proteinuria. A multistate model was used to predict 10-year cumulative costs by multiplying annual costs associated with each renal state by the expected state duration. A total of 1,545 patients participated; 89.3% were women, the mean ± age at diagnosis was 35.2 ± 13.4 years, 49% were white, and the mean followup duration was 6.3 ± 3.3 years. LN developed in 39.4% of these patients by the end of followup. Ten-year cumulative costs were greater in those with LN and an estimated glomerular filtration rate (GFR) <30 ml/minute ($310,579 2015 Canadian dollars versus $19,987 if no LN and estimated GFR >60 ml/minute) or with LN and estimated proteinuria >3 gm/day ($84,040 versus $20,499 if no LN and estimated proteinuria <0.25 gm/day). Patients with estimated GFR <30 ml/minute incurred 10-year costs 15-fold higher than those with normal estimated GFR. By estimating the expected duration in each renal state and incorporating associated annual costs, disease severity at presentation can be used to anticipate future health care costs. This is critical knowledge for cost-effectiveness evaluations of novel therapies.

Intraspecific temporal resource partitioning at white-tailed deer feeding sites.

Individuals may reduce competition by temporally partitioning their use of a shared resource. Behavioral differences between sexes in ungulates may encourage segregation as individuals attempt to avoid antagonistic interactions. However, dominant sex and age groups may reduce subordinates’ access to food resources, regardless of the subordinate’s sex. We hypothesized that white-tailed deer Odocoileus virginianus temporally segregated at supplemental feeding sites based on social rank (subordinate: yearling males and adult females; dominant: adult males) and that segregation was affected by phase of the breeding season and diel cycle. If deer temporally segregate according to social rank, we predicted that the resulting activity patterns would manifest in one social class being relatively more susceptible to hunter-induced mortality. We used a multi-state modeling approach to quantify temporal segregation and calculated the probability that a feeding site was in a particular state during diurnal and nocturnal hours for each of the 3 phases of the breeding season. We determined that transition probabilities differed by season and diel cycle and dominant and subordinate social classes clearly avoided each other, with <1% co-occurrence at feeding sites. During the pre-breeding season, the probability of a subordinate being present during diurnal hours was 3.0× more likely than a dominant being present, but did not differ during nocturnal hours. There was no difference for dominants and subordinates during diurnal or nocturnal hours during the breeding season. In the post-breeding season, subordinates were 1.7× more likely to occur at the feeding site than a dominant during diurnal hours but they did not differ during nocturnal hours. Our results indicate that dominance status influences temporal segregation at feeding sites and is affected by the phase of the breeding season. Therefore, the resulting activity patterns may increase subordinates’ risk to human predation during the pre-breeding and post-breeding seasons.

Comorbid conditions and the transition among states of hip osteoarthritis and symptoms in a community-based longitudinal study: a multi-state model approach

Purpose: Conditions such as obesity, diabetes mellitus (DM), and cardiovascular disease (CVD) are associated with osteoarthritis (OA). However, it is unknown how these associations translate to progression among states of OA. We sought to examine the association of obesity, DM, and CVD, overall, with characteristics of hip OA. Methods: A longitudinal analysis of 3857 individuals with complete data was performed using data from baseline and up to three follow-up periods in the Johnston County Osteoarthritis Project (JoCoOA), a longitudinal community-based study of African American and Caucasian men aged 45 years or older and women over 50 with approximately 18 years of follow-up. Radiographic hip OA (rHOA) was defined by radiographic hip evidence of OA in at least one hip (Kellgren-Lawrence grade ≥ 2. Hip symptoms were defined by self-reported pain, aching, or stiffness on most days, and symptomatic rHOA (sxHOA) was defined by rHOA and hip symptoms in the same hip. rHOA progression states of interest included: 1) no rHOA or hip symptoms, 2) asymptomatic rHOA, 3) hip symptoms only, 4) sxHOA, and 5) death—with transitions of interest indicated by arrows in Fig. 1. Vital status was ascertained through National Death Index records to determine death date and allow for modeling of death as an absorbing state. Person-years of follow-up were accrued from baseline to death or censored at loss to follow-up or December 31, 2015. A Markov multistate model (MSM), based on the theory of stochastic processes, was conducted to model the progression of rHOA states over time and allow for the analysis of states observed at arbitrary times (i.e., interval censored events or panel data). These models rely on piecewise-constant hazard approximation and were fit using the msm R package. Obesity (body mass index ≥ 30 kg/m2), self-reported DM, and self-reported CVD were included as time-dependent comorbid conditions of interest. This Markov MSM was used to estimate hazard ratios (HR) and 95% confidence intervals (CI) to determine associations between each comorbid condition and rHOA state transitions. Additionally, the model adjusted for baseline demographics including age, sex, race, education, enrollment cohort, birth year, as well as time-dependent hip injury history. Results: At baseline, the sample consisted of 33% African Americans, 39% men, with a mean (SD) age of 62.2 (9.8) years, and 37% with less than a 12 year education level. Forty percent were obese at baseline increasing up to 50% during follow-up; 14% had DM at baseline increasing up to 28% during follow-up; and 22% had CVD at baseline increasing up to 48% during follow-up. At baseline, 45% had no rHOA or hip symptoms, 25% had hip symptoms only, 19% had asymptomatic rHOA, and 11% had sxHOA. Table 1 shows frequencies for observed transitions among these four rHOA states as well as death. Table 2 shows HR and 95% CI, with significant associations indicated in bold. CVD decreased the chance of improving from a state of hip symptoms only to a state of neither rHOA nor symptoms (3–>1) and, although not significantly, increased the risk of worsening from a state of neither rHOA nor symptoms to a state of asymptomatic rHOA (1–>2). Obesity increased the risk of worsening from a state of neither rHOA nor symptoms to a state of hip symptoms only (1–>3). DM was not associated overall with any modeled transitions. Conclusions: Results suggest that there are a few single impacts between conditions of obesity and CVD, in particular, with specific hip OA and symptom state transitions, independent of relevant demographic and clinical factors. Further analysis should consider whether these conditions in combination are associated similarly or additionally with transitions of hip OA and symptoms.

Comorbid conditions and the transition among states of knee osteoarthritis and symptoms in a community-based longitudinal study: a multi-state model approach

Comorbid conditions and the transition among states of knee osteoarthritis and symptoms in a community-based longitudinal study: a multi-state model approach

Refractory Graft-Versus-Host Disease–Free, Relapse-Free Survival as an Accurate and Easy-to-Calculate Endpoint to Assess the Long-Term Transplant Success

The aim of this study was to develop a new composite endpoint that accurately reflects the long-term success of allogeneic hematopoietic stem cell transplantation (allo-HSCT), as the conventional graft-versus-host disease (GVHD)–free, relapse-free survival (GRFS) overestimates the impact of GVHD. First, we validated current GRFS (cGRFS), which recently was proposed as a more accurate endpoint of long-term transplant success. cGRFS was defined as survival without disease relapse/progression or active chronic GVHD at a given time after allo-HSCT, calculated using 2 distinct methods: a linear combination of a Kaplan-Meier estimates approach and a multistate modelling approach. Next, we developed a new composite endpoint, refractory GRFS (rGRFS). rGRFS was calculated similarly to conventional GRFS treating grade III to IV acute GVHD, chronic GVHD requiring systemic treatment, and disease relapse/progression as events, except that GVHD that resolved and did not require systemic treatment at the last evaluation was excluded as an event in rGRFS. The 2 cGRFS curves obtained using 2 different approaches were superimposed and both were superior to that of conventional GRFS, reflecting the proportion of patients with resolved chronic GVHD. Finally, the curves of cGRFS and rGRFS overlapped after the first 2 years of post-transplant follow-up. These results suggest that cGRFS and rGRFS more accurately reflect transplant success than conventional GRFS. Especially, rGRFS can be more easily calculated than cGRFS and analyzed with widely used statistical approaches, whereas cGRFS more accurately represents the burden of GVHD-related morbidity in the first 2 years after transplantation.

The association between asthma and type 1 diabetes: a paediatric case-cohort study in Finland, years 1981-2009.

The association between asthma and type 1 diabetes, two chronic, immune-mediated diseases, has been of longstanding interest, but the evidence is still conflicting. We examined this association in a large, nationwide case-cohort study among Finnish children, using a novel statistical approach. Among the initial cohort of all children born between 1 January 1981 and 31 December 2008, those who were diagnosed with asthma (n = 81 473) or type 1 diabetes (n = 9541) up to age 16 years by the end of 2009 were identified from the Central Drug Register maintained by the Social Insurance Institution of Finland. A 10% random sample from each initial birth year cohort was selected as a reference cohort (n = 171 138). The association between asthma and type 1 diabetes was studied using a multistate modelling approach to estimate transition rates between healthy and disease states since birth. Hazard ratios (HRs) with 95% confidence intervals (CIs) were calculated to represent the change in the transition rate between the disease states. After adjusting for sex and birth decade, previous diagnosis of asthma increased the risk of subsequent type 1 diabetes by 41% (95% CI: 1.28, 1.54), whereas previous diagnosis of type 1 diabetes decreased the risk of subsequent asthma by 18% (95% CI: 0.69, 0.98). The findings of the present study imply that the association between the diseases is more complex than previously thought, and its direction depends on the sequential appearance of the diseases.

Worklife expectancy in a cohort of Danish employees aged 55\u201365\xa0years - comparing a multi-state Cox proportional hazard approach with conventional multi-state life tables

BackgroundWork life expectancy (WLE) expresses the expected time a person will remain in the labor market until he or she retires. This paper compares a life table approach to estimating WLE to an approach based on multi-state proportional hazards models. The two methods are used to estimate WLE in Danish members and non-members of an early retirement pensioning (ERP) scheme according to levels of health.MethodsIn 2008, data on self-rated health (SRH) was collected from 5212 employees 55–65 years of age. Data on previous and subsequent long-term sickness absence, unemployment, returning to work, and disability pension was collected from national registers. WLE was estimated from multi-state life tables and through multi-state models.ResultsResults from the multi-state model approach agreed with the life table approach but provided narrower confidence intervals for small groups. The shortest WLE was seen for employees with poor SRH and ERP membership while the longest WLE was seen for those with good SRH and no ERP membership. Employees aged 55–56 years with poor SRH but no ERP membership had shorter WLE than employees with good SRH and ERP membership. Relative WLE reversed for the two groups after age 57.At age 55, employees with poor SRH could be expected to spend approximately 12 months on long-term sick leave and 9–10 months unemployed before they retired – regardless of ERP membership. ERP members with poor SRH could be expected to spend 4.6 years working, while non-members could be expected to spend 7.1 years working.ConclusionWLE estimated through multi-state models provided an effective way to summarize complex data on labor market affiliation. WLE differed noticeably between members and non-members of the ERP scheme. It has been hypothesized that while ERP membership would prompt some employees to retire earlier than they would have done otherwise, this effect would be partly offset by reduced time spent on long-term sick leave or unemployment. Our data showed no indication of such an effect, but this could be due to residual confounding and self-selection of people with poor health into the ERP scheme.

Multi-state models for the analysis of time-to-treatment modification among HIV patients under highly active antiretroviral therapy in Southwest Ethiopia

BackgroundHighly active antiretroviral therapy (HAART) has shown a dramatic change in controlling the burden of HIV/AIDS. However, the new challenge of HAART is to allow long-term sustainability. Toxicities, comorbidity, pregnancy, and treatment failure, among others, would result in frequent initial HAART regimen change. The aim of this study was to evaluate the durability of first line antiretroviral therapy and to assess the causes of initial highly active antiretroviral therapeutic regimen changes among patients on HAART.MethodsA Hospital based retrospective study was conducted from January 2007 to August 2013 at Jimma University Hospital, Southwest Ethiopia. Data on the prescribed ARV along with start date, switching date, and reason for change was collected. The primary outcome was defined as the time-to-treatment change. We adopted a multi-state survival modeling approach assuming each treatment regimen as state. We estimate the transition probability of patients to move from one regimen to another.ResultA total of 1284 ART naive patients were included in the study. Almost half of the patients (41.2%) changed their treatment during follow up for various reasons; 442 (34.4%) changed once and 86 (6.69%) changed more than once. Toxicity was the most common reason for treatment changes accounting for 48.94% of the changes, followed by comorbidity (New TB) 14.31%. The HAART combinations that were robust to treatment changes were tenofovir (TDF) + lamivudine (3TC)+ efavirenz (EFV), tenofovir + lamivudine (3TC) + nevirapine (NVP) and zidovudine (AZT) + lamivudine (3TC) + nevirapine (NVP) with 3.6%, 4.5% and 11% treatment changes, respectively.ConclusionMoving away from drugs with poor safety profiles, such as stavudine(d4T), could reduce modification rates and this would improve regimen tolerability, while preserving future treatment options.

Factors influencing territorial occupancy and reproductive success in a Eurasian Eagle-owl (Bubo bubo) population

Modelling territorial occupancy and reproductive success is a key issue for better understanding the population dynamics of territorial species. This study aimed to investigate these ecological processes in a Eurasian Eagle-owl (Bubo bubo) population in south-eastern Spain during a seven-year period. A multi-season, multi-state modelling approach was followed to estimate the probabilities of occupancy and reproductive success in relation to previous state, time and habitat covariates, and accounting for imperfect detection. The best estimated models showed past breeding success in the territories to be the most important factor determining a high probability of reoccupation and reproductive success in the following year. In addition, alternative occupancy models suggested the positive influence of crops on the probability of territory occupation. By contrast, the best reproductive model revealed strong interannual variations in the rates of breeding success, which may be related to changes in the abundance of the European Rabbit, the main prey of the Eurasian Eagle-owl. Our models also estimated the probabilities of detecting the presence of owls in a given territory and the probability of detecting evidence of successful reproduction. Estimated detection probabilities were high throughout the breeding season, decreasing in time for unsuccessful breeders but increasing for successful breeders. The probability of detecting reproductive success increased with time, being close to one in the last survey. These results suggest that reproduction failure in the early stages of the breeding season is a determinant factor in the probability of detecting occupancy and reproductive success.

Inferential biases linked to unobservable states in complex occupancy models

Modeling of species distributions has undergone a shift from relying on equilibrium assumptions to recognizing transient system dynamics explicitly. This shift has necessitated more complex modeling techniques, but the performance of these dynamic models has not yet been assessed for systems where unobservable states exist. Our work is motivated by the impacts of the emerging infectious disease chytridiomycosis, a disease of amphibians that is associated with declines of many species worldwide. Using this host‐pathogen system as a general example, we first illustrate how misleading inferences can result from failing to incorporate pathogen dynamics into the modeling process, especially when the pathogen is difficult or impossible to survey in the absence of a host species. We found that traditional modeling techniques can underestimate the effect of a pathogen on host species occurrence and dynamics when the pathogen can only be detected in the host, and pathogen information is treated as a covariate. We propose a dynamic multistate modeling approach that is flexible enough to account for the detection structures that may be present in complex multistate systems, especially when the sampling design is limited by a species’ natural history or sampling technology. When multistate occupancy models are used and an unobservable state is present, parameter estimation can be influenced by model complexity, data sparseness, and the underlying dynamics of the system. We show that, even with large sample sizes, many models incorporating seasonal variation in vital rates may not generate reasonable estimates, indicating parameter redundancy. We found that certain types of missing data can greatly hinder inference, and we make study design recommendations to avoid these issues. Additionally, we advocate the use of time‐varying covariates to explain temporal trends in the data, and the development of sampling techniques that match the biology of the system to eliminate unobservable states when possible.

Survival biases lead to flawed conclusions in observational treatment studies of influenza patients

Background and ObjectiveSeveral observational studies reported that Oseltamivir (Tamiflu) reduced mortality in infected and hospitalized patients. Because of the restriction of observation to hospital stay and time-dependent treatment assignment, such findings were prone to common types of survival bias (length, time-dependent and competing risk bias). MethodsBritish hospital data from the Influenza Clinical Information Network (FLU-CIN) study group were used which included 1,391 patients with confirmed pandemic influenza A/H1N1 2009 infection. We used a multistate model approach with following states: hospital admission, Oseltamivir treatment, discharge, and death. Time origin is influenza onset. We displayed individual data, risk sets, hazards, and probabilities from multistate models to study the impact of these three common survival biases. ResultsThe correct hazard ratio of Oseltamivir for death was 1.03 (95% confidence interval [CI]: 0.64–1.66) and for discharge 1.89 (95% CI: 1.65–2.16). Length bias increased both hazard ratios (HRs): HR (death) = 1.82 (95% CI: 1.12–2.98) and HR (discharge) = 4.44 (95% CI: 3.90–5.05), whereas the time-dependent bias reduced them: HR (death) = 0.62 (95% CI: 0.39–1.00) and HR (discharge) = 0.85 (95% CI: 0.75–0.97). Length and time-dependent bias were less pronounced in terms of probabilities. Ignoring discharge as a competing event for hospital death led to a remarkable overestimation of hospital mortality and failed to detect the reducing effect of Oseltamivir on hospital stay. ConclusionsThe impact of each of the three survival biases was remarkable, and it can make neuraminidase inhibitors appear more effective or even harmful. Incorrect and misclassified risk sets were the primary sources of biased hazard rates.

Estimation of Survival Probabilities for Use in Cost-effectiveness Analyses: A Comparison of a Multi-state Modeling Survival Analysis Approach with Partitioned Survival and Markov Decision-Analytic Modeling.

Modeling of clinical-effectiveness in a cost-effectiveness analysis typically involves some form of partitioned survival or Markov decision-analytic modeling. The health states progression-free, progression and death and the transitions between them are frequently of interest. With partitioned survival, progression is not modeled directly as a state; instead, time in that state is derived from the difference in area between the overall survival and the progression-free survival curves. With Markov decision-analytic modeling, a priori assumptions are often made with regard to the transitions rather than using the individual patient data directly to model them. This article compares a multi-state modeling survival regression approach to these two common methods. As a case study, we use a trial comparing rituximab in combination with fludarabine and cyclophosphamide v. fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia. We calculated mean Life Years and QALYs that involved extrapolation of survival outcomes in the trial. We adapted an existing multi-state modeling approach to incorporate parametric distributions for transition hazards, to allow extrapolation. The comparison showed that, due to the different assumptions used in the different approaches, a discrepancy in results was evident. The partitioned survival and Markov decision-analytic modeling deemed the treatment cost-effective with ICERs of just over £16,000 and £13,000, respectively. However, the results with the multi-state modeling were less conclusive, with an ICER of just over £29,000. This work has illustrated that it is imperative to check whether assumptions are realistic, as different model choices can influence clinical and cost-effectiveness results.

Multistate Model to Predict Heart Failure Hospitalizations and All-Cause Mortality in Outpatients With Heart Failure With Reduced Ejection Fraction: Model Derivation and External Validation.

Outpatients with heart failure (HF) who are at high risk for HF hospitalization and death may benefit from early identification. We sought to develop and externally validate a model to predict both HF hospitalization and mortality that accounts for the semicompeting nature of the 2 outcomes and captures the risk associated with the transition from the stable outpatient state to the post-HF hospitalization state. A multistate model to predict HF hospitalization and all-cause mortality was derived using data (n=3834) from the HEAAL study (Heart Failure Endpoint evaluation of Angiotensin II Antagonist Losartan), a multinational randomized trial in symptomatic patients with reduced left ventricular ejection fraction. Twelve easily and reliably obtainable demographic and clinical predictors were prespecified for model inclusion. Model performance was assessed in the SCD-HeFT cohort (Sudden Cardiac Death in Heart Failure Trial; n=2521). At 1 year, the probability of being alive without HF hospitalization was 94% for a typical patient in the lowest risk quintile and 77% for a typical patient in the highest risk quintile and this variability in risk continued through 7 years of follow-up. The model c-index was 0.72 in the derivation cohort, 0.66 in the validation cohort, and 0.69 in the implantable cardiac defibrillator arm of the validation cohort. There was excellent calibration across quintiles of predicted risk. Our findings illustrate the advantages of a multistate modeling approach, providing estimates of HF hospitalization and death in the same model, comparison of predictors for the different outcomes and demonstrating the different trajectories of patients based on baseline characteristics and intermediary events. URL: http://www.clinicaltrials.gov. Unique identifiers: NCT00000609 and NCT00090259.

Structured fusion lasso penalized multi-state models.

Multi-state models generalize survival or duration time analysis to the estimation of transition-specific hazard rate functions for multiple transitions. When each of the transition-specific risk functions is parametrized with several distinct covariate effect coefficients, this leads to a model of potentially high dimension. To decrease the parameter space dimensionality and to work out a clear image of the underlying multi-state model structure, one can either aim at setting some coefficients to zero or to make coefficients for the same covariate but two different transitions equal. The first issue can be approached by penalizing the absolute values of the covariate coefficients as in lasso regularization. If, instead, absolute differences between coefficients of the same covariate on different transitions are penalized, this leads to sparse competing risk relations within a multi-state model, that is, equality of covariate effect coefficients. In this paper, a new estimation approach providing sparse multi-state modelling by the aforementioned principles is established, based on the estimation of multi-state models and a simultaneous penalization of the L1 -norm of covariate coefficients and their differences in a structured way. The new multi-state modelling approach is illustrated on peritoneal dialysis study data and implemented in the R package penMSM. Copyright © 2016 John Wiley & Sons, Ltd.

Cost-effectiveness Analysis in R Using a Multi-state Modeling Survival Analysis Framework: A Tutorial.

This tutorial provides a step-by-step guide to performing cost-effectiveness analysis using a multi-state modeling approach. Alongside the tutorial, we provide easy-to-use functions in the statistics package R. We argue that this multi-state modeling approach using a package such as R has advantages over approaches where models are built in a spreadsheet package. In particular, using a syntax-based approach means there is a written record of what was done and the calculations are transparent. Reproducing the analysis is straightforward as the syntax just needs to be run again. The approach can be thought of as an alternative way to build a Markov decision-analytic model, which also has the option to use a state-arrival extended approach. In the state-arrival extended multi-state model, a covariate that represents patients’ history is included, allowing the Markov property to be tested. We illustrate the building of multi-state survival models, making predictions from the models and assessing fits. We then proceed to perform a cost-effectiveness analysis, including deterministic and probabilistic sensitivity analyses. Finally, we show how to create 2 common methods of visualizing the results—namely, cost-effectiveness planes and cost-effectiveness acceptability curves. The analysis is implemented entirely within R. It is based on adaptions to functions in the existing R package mstate to accommodate parametric multi-state modeling that facilitates extrapolation of survival curves.

Multimethod, multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves.

In many cases, the first step in large-carnivore management is to obtain objective, reliable, and cost-effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical-site-occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost-effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well-coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population-parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population parameters.