Derived Transition Probabilities Research Articles

Latent trajectory models for spatio-temporal dynamics in Alaskan ecosystems.

The Alaskan landscape has undergone substantial changes in recent decades, most notably the expansion of shrubs and trees across the Arctic. We developed a Bayesian hierarchical model to quantify the impact of climate change on the structural transformation of ecosystems using remotely sensed imagery. We used latent trajectory processes to model dynamic state probabilities that evolve annually, from which we derived transition probabilities between ecotypes. Our latent trajectory model accommodates temporal irregularity in survey intervals and uses spatio-temporally heterogeneous climate drivers to infer rates of land cover transitions. We characterized multi-scale spatial correlation induced by plot and subplot arrangements in our study system. We also developed a Pólya-Gamma sampling strategy to improve computation. Our model facilitates inference on the response of ecosystems to shifts in the climate and can be used to predict future land cover transitions under various climatescenarios.

Multistate Markov model application for blood pressure transition among the Chinese elderly population: a quantitative longitudinal study

ObjectiveTo explore the transitions of different blood pressure states based on a multistate Markov model among the Chinese elderly population.SettingA community health centre in Xiamen, China.Participants1833 elderly Chinese people.MethodsA multistate...

States Transitions Inference of Postpartum Depression Based on Multi-State Markov Model.

Background: Postpartum depression (PPD) has been recognized as a severe public health problem worldwide due to its high incidence and the detrimental consequences not only for the mother but for the infant and the family. However, the pattern of natural transition trajectories of PPD has rarely been explored. Methods: In this research, a quantitative longitudinal study was conducted to explore the PPD progression process, providing information on the transition probability, hazard ratio, and the mean sojourn time in the three postnatal mental states, namely normal state, mild PPD, and severe PPD. The multi-state Markov model was built based on 912 depression status assessments in 304 Chinese primiparous women over multiple time points of six weeks postpartum, three months postpartum, and six months postpartum. Results: Among the 608 PPD status transitions from one visit to the next visit, 6.2% (38/608) showed deterioration of mental status from the level at the previous visit; while 40.0% (243/608) showed improvement at the next visit. A subject in normal state who does transition then has a probability of 49.8% of worsening to mild PPD, and 50.2% to severe PPD. A subject with mild PPD who does transition has a 20.0% chance of worsening to severe PPD. A subject with severe PPD is more likely to improve to mild PPD than developing to the normal state. On average, the sojourn time in the normal state, mild PPD, and severe PPD was 64.12, 6.29, and 9.37 weeks, respectively. Women in normal state had 6.0%, 8.5%, 8.7%, and 8.8% chances of progress to severe PPD within three months, nine months, one year, and three years, respectively. Increased all kinds of supports were associated with decreased risk of deterioration from normal state to severe PPD (hazard ratio, HR: 0.42–0.65); and increased informational supports, evaluation of support, and maternal age were associated with alleviation from severe PPD to normal state (HR: 1.46–2.27). Conclusions: The PPD state transition probabilities caused more attention and awareness about the regular PPD screening for postnatal women and the timely intervention for women with mild or severe PPD. The preventive actions on PPD should be conducted at the early stages, and three yearly; at least one yearly screening is strongly recommended. Emotional support, material support, informational support, and evaluation of support had significant positive associations with the prevention of PPD progression transitions. The derived transition probabilities and sojourn time can serve as an importance reference for health professionals to make proactive plans and target interventions for PPD.

Cost-Effectiveness of Once-Weekly Selinexor, Bortezomib, and Dexamethasone (SVd) Versus Twice-Weekly Bortezomib and Dexamethasone (Vd) in Relapsed or Refractory Multiple Myeloma

Introduction: The phase III BOSTON trial reported that once-weekly therapy with selinexor, bortezomib, and dexamethasone (SVd) significantly prolonged progression-free survival for patients with relapsed or refractory (R/R) multiple myeloma compared to twice-weekly treatment with bortezomib and dexamethasone alone (Vd). Although once-weekly SVd reduces the risk of disease progression as well as the cumulative exposure of patients to bortezomib and dexamethasone, selinexor is a costly drug-priced at nearly $22,000 per month-and is associated with significant toxicity. As a result, it is unclear whether SVd provides sufficient value in this clinical setting. In this study, we assess the cost-effectiveness of once-weekly SVd versus twice-weekly Vd in patients with R/R multiple myeloma. Methods: Our cost-effectiveness analysis was based on a Markov model. Simulated patients mirrored the cohort studied in the BOSTON trial; the median age of the population was 66 years, 57% were male and all had received 1-3 prior lines of therapy. Patients entered the model with R/R myeloma and received treatment with SVd or Vd; upon disease progression, all patients subsequently received identical lines of post-progression therapy. Our base-case model (Figure 1) followed SVd/Vd progression sequentially with daratumumab, carfilzomib, and dexamethasone (DKd), pomalidomide and dexamethasone (Pd), and best supportive care. We derived transition probabilities from large randomized trials using parametric survival modeling. The utility of each health state and the costs of treatment, adverse events, and terminal care were derived from literature and Medicare fee schedules. As data evaluating the quality of life with SVd vs Vd is not yet available, we assumed identical utility values for both treatment regimens. We calculated the incremental cost effectiveness ratio (ICER) from a US payer perspective, using a lifetime horizon, an annual discount rate of 3%, and a willingness-to-pay threshold of $150,000/quality-adjusted life year (QALY). One-way and probabilistic sensitivity analyses were conducted to evaluate uncertainty in our model. Results: In our base-case model, SVd was associated with an improvement of 0.37 QALYs compared to Vd alone (3.43 vs 3.06 QALYs, respectively). However, the incremental lifetime cost of SVd was $177,126 ($1,013,851 vs $836,725, respectively), leading to an ICER of $479,572/QALY. The monthly cost of selinexor would need to be decreased by approximately 51%, from $21,424 to $10,415, in order for SVd to be cost-effective compared to Vd alone in R/R patients. Our model was most sensitive to the hazard ratio of SVd relative to Vd; decreasing the HR from 0.70 to 0.53 decreased the ICER to $285,251/QALY, while increasing the HR to 0.93 increased the ICER to $1,738,546/QALY. Of note, all ICERs during one-way sensitivity analysis and >99% of ICERs during probabilistic sensitivity analysis remained above the willingness-to-pay threshold of $150,000 QALY. We also incorporated two scenario analyses; in the first, patients in the Vd arm received therapy with selinexor and dexamethasone (Sd) after progression from Pd, before receiving best supportive care. In this scenario, SVd was associated with an incremental cost of $112,445 ($1,013,851 vs $901,406), an incremental effectiveness of 0.24 QALYs (3.43 vs 3.19 QALYs), and an ICER of $464,557/QALY. In the second scenario analysis, we assumed that patients had received DKd prior to SVd/Vd; as a result, patients that progressed on SVd or Vd subsequently received Pd followed by best supportive care. Here, SVd was associated with an incremental cost of $222,864 ($418,526 vs $195,662), an incremental effectiveness of 0.49 QALYs (1.90 vs 1.41 QALYs), and an ICER of $456,080/QALY. Conclusions: Use of once-weekly SVd for patients with relapsed or refractory multiple myeloma is unlikely to be cost-effective under current pricing, compared to twice-weekly Vd. The price of selinexor would need to be decreased substantially in order to reduce the ICER of SVd to widely acceptable values. Disclosures Huntington: DTRM: Research Funding; Pharmacyclics: Honoraria; TG Therapeutics: Research Funding; Genentech: Consultancy; Celgene: Consultancy, Research Funding; Bayer: Consultancy, Honoraria; Astrazeneca: Honoraria; AbbVie: Consultancy; Novartis: Consultancy. Giri:Carevive Systems: Research Funding; Carevive Systems: Honoraria; Pack Health: Research Funding.

Cost-Effectiveness Analysis of Stereotactic Ablative Radiation Therapy in Patients With Oligometastatic Cancer

The Stereotactic Ablative Radiation therapy for Comprehensive Treatment of Oligometastatic Tumors phase 2 randomized clinical trial found that stereotactic ablative radiation therapy (SABR) improved outcomes among cancer patients with oligometastatic disease. Yet, the cost of SABR along with the large number of patients with oligometastatic disease raises the important question of value. This study sought to evaluate the cost-effectiveness of the addition of SABR compared with standard therapy alone among cancer patients with oligometastatic disease. We constructed a Markov model to simulate treatment with stereotactic ablative radiation therapy or standard therapy among patients with oligometastatic cancers. The model derived transition probabilities from Stereotactic Ablative Radiation therapy for Comprehensive Treatment of Oligometastatic Tumors clinical trial data to estimate risks of toxicity, disease progression and survival. Health care costs and health utilities were estimated from the literature. Probabilistic and one-way sensitivity analyses evaluate model uncertainty. Cost-effectiveness was estimated from both the health care sector and societal perspectives with an incremental cost-effectiveness ratio (ICER) defined as dollars per quality-adjusted life year (QALY). An ICER less than $100,000/QALY was considered cost-effective. One-way and probabilistic sensitivity analyses were used to examine model uncertainty. The addition of SABR increased total costs by $54,260 (health care sector perspective) or $72,799 (societal perspective) and improved effectiveness by 1.88 QALYs compared with standard therapy, leading to an ICER of $28,906/QALY (health care sector perspective) or $38,783/QALY (societal perspective). The model was modestly sensitive to assumptions about tumor progression, although the model was not sensitive to assumptions about survival or cost of treatment. Probabilistic sensitivity analyses demonstrated that SABR was the cost-effective treatment option 99.8% (health care sector perspective) or 98.7% (societal perspective) of the time. The addition of SABR increased costs and improved quality adjusted survival, overall leading to a cost-effective treatment strategy for patients with oligometastatic cancer.

Identification of the Most Effective Position for Ustekinumab in Treatment Algorithms for Crohn’s Disease

Ustekinumab is a monoclonal antibody against interleukin 12 and interleukin 23 that has been approved by the Food and Drug Administration for treatment of Crohn's disease (CD). We sought to identify the ideal position for ustekinumab in treatment algorithms for CD. We constructed a Markov model to identify an optimal treatment sequence for CD that included ustekinumab for 1 year or more. The base case was a 35-year old male with moderate to severe CD who had not previously received biologic or immunomodulator therapy. The standard of care treatment algorithm was defined as initial therapy with infliximab and azathioprine, followed by adalimumab and azathioprine, vedolizumab, and lastly surgical resection. The model assessed positions for ustekinumab before standard of care, ustekinumab after infliximab and azathioprine but before the remaining treatments, after infliximab, azathioprine, and adalimumab but before vedolizumab and surgery, or after the other biologics but before surgery. We derived transition probabilities and quality adjusted life years (QALYs) from relevant trials, observational studies, and time trade-off analyses. Primary analyses consisted of first order Monte Carlo simulation of 100 trials of cohorts of 100,000 individuals. Ustekinumab as first-line therapy yielded the greatest QALYs (incremental effectiveness, 0.016-0.020 QALYs), resulting in 10% more patients in remission or response, and 2% fewer surgeries at 1 year, compared with other algorithms. The model was not sensitive to 25% variation in transition probabilities. In a simulation based on a 35-year old male patient with moderate to severe CD, we found that ustekinumab as the first-line biologic therapy yields greater QALYs at the end of 1 year than compared with use later in the CD treatment algorithm.

Cost-effectiveness analysis of stereotactic ablative radiotherapy in patients with oligometastatic cancer.

7085 Background: The SABR-COMET randomized clinical trial found that stereotactic ablative radiotherapy (SABR) improved outcomes among cancer patients with oligometastatic disease. Yet, the cost of SABR along with the large number of patients with oligometastatic disease raises the important question of value. This study sought to evaluate the cost-effectiveness of SABR compared to standard therapy among cancer patients with oligometastatic disease. Methods: We constructed a Markov model to simulate treatment with stereotactic ablative radiotherapy or standard therapy among patients with oligometastatic cancers. The model derived transition probabilities from clinical trial data to estimate risks of toxicity, disease progression and survival. Healthcare costs and health utilities were estimated from the literature. Cost-effectiveness was estimated with an incremental cost-effectiveness ratio (ICER) defined as dollars per quality-adjusted life year (QALY), with an ICER less than $100,000/QALY considered cost-effective. One-way and probabilistic sensitivity analyses were used to examine model uncertainty. Results: The addition of SABR increased total costs by $54,279 and improved effectiveness by 1.20 QALYs compared with standard therapy, leading to an ICER of $45,162/QALY. The model was sensitive to assumptions about tumor progression, though the model was not sensitive to assumptions about survival or cost of treatment. The cost of SABR would need to increase approximately six-fold from $12,241 to $78,151 before SABR becomes cost-ineffective. Probabilistic sensitivity analyses demonstrated that SABR was the cost-effective treatment option 97.2% of the time. Conclusions: The addition of SABR increased costs and improved quality adjusted survival, overall leading to a cost-effective treatment strategy for patients with oligometastatic cancer.

Evaluating Partitioned Survival and Markov Decision-Analytic Modeling Approaches for Use in Cost-Effectiveness Analysis: Estimating and Comparing Survival Outcomes.

ObjectiveThe objective of this study was to assess long-term survival outcomes for nivolumab and everolimus in renal cell carcinoma predicted by three model structures, a partitioned survival model (PSM) and two variations of a semi-Markov model (SMM), for use in cost-effectiveness analyses.MethodsThree economic model structures were developed and populated using parametric curves fitted to patient-level data from the CheckMate 025 trial. Models consisted of three health states: progression-free, progressed disease, and death. The PSM estimated state occupancy using an area under-the-curve approach from overall survival (OS) and progression-free survival (PFS) curves. The SMMs derived transition probabilities to calculate patient flow between health states. One SMM assumed that post-progression survival (PPS) was independent of PFS duration (PPS Markov); the second SMM assumed differences in PPS based on PFS duration (PPS–PFS Markov).ResultsAll models provide a reasonable fit to the observed OS data at 2 years. For estimating cost effectiveness, however, a more relevant comparison is between estimates of OS over the modeling horizon, because this will likely impact differences in costs and quality-adjusted life-years. Estimates of the incremental mean survival benefit of nivolumab versus everolimus over 20 years were 6.6 months (PSM), 7.6 months (PPS Markov), and 7.4 months (PPS–PFS Markov), reflecting non-trivial differences of + 14% and + 11%, respectively, compared with PSM.ConclusionsThe evidence from this study and previous work highlights the importance of the assumptions underlying any model structure, and the need to validate assumptions regarding survival and the application of treatment effects against what is known about the characteristics of the disease.

A method for calculating the implied no-recovery three-state transition matrix using observable population mortality incidence and disability prevalence rates among the elderly

The most accurate estimation of transition probabilities for a multi-state model of health status requires longitudinal data. However, for many countries such data are usually not available. Instead, population level mortality incidence and disability prevalence rates are often all that can be accessed. In this paper, for a three-state no-recovery model (with states healthy, disabled, dead), using simple mathematical derivations, we propose a framework to estimate the age- and gender-specific boundaries within which each of the transition probabilities should fall. We then provide two methods for estimating unique transition probabilities—a least squares procedure and a method based on the ‘extra mortality’ factor proposed by Rickayzen and Walsh (Br Actuarial J 8(2):341–393, 2002, https://doi.org/10.1017/s1357321700003755 ). We also show the acceptable range for the ‘extra mortality’ factor given the mortality and disability data. Furthermore, we provide a critique of the method proposed by Van der Gaag et al. (Demogr Res 32:75, 2015), as their estimates can fall outside the acceptable boundaries. Finally, we estimate life and health expectancies, as well as premium rates for a life care annuity and a disability annuity using our derived transition probabilities.

Cost-effectiveness of health coaching and financial incentives to promote physical activity after total knee replacement

We evaluated the cost-effectiveness of Telephonic Health Coaching and Financial Incentives (THC+FI) to promote physical activity in total knee replacement recipients. We used the Osteoarthritis Policy Model, a computer simulation of knee osteoarthritis, to evaluate the cost-effectiveness of THC+FI compared to usual care. We derived transition probabilities, utilities, and costs from trial data. We conducted lifetime analyses from the healthcare perspective and discounted all cost-effectiveness outcomes by 3% annually. The primary outcome was the Incremental Cost-Effectiveness Ratio (ICER), defined as the ratio of the differences in costs and Quality-Adjusted Life Years (QALYs) between strategies. We considered ICERs <$100,000/QALY to be cost-effective. We conducted one-way sensitivity analyses that varied parameters across their 95% confidence intervals (CI) and limited the efficacy of THC+FI to 1year or to 9months. We also conducted a probabilistic sensitivity analysis (PSA), simultaneously varying cost, utilities, and transition probabilities. THC+FI had an ICER of $57,200/QALY in the base case and an ICER below $100,000/QALY in most deterministic sensitivity analyses. THC+FI cost-effectiveness depended on assumptions about long-term efficacy; when efficacy was limited to 1year or to 9months, the ICER was $93,300/QALY or $121,800/QALY, respectively. In the PSA, THC+FI had an ICER below $100,000/QALY in 70% of iterations. Based on currently available information, THC+FI might be a cost-effective alternative to usual care. However, the uncertainty surrounding this choice is considerable, and further research to reduce this uncertainty may be economically justified.

Landscape‐scale regeneration dynamics of disturbed Mediterranean maquis

Abstract. Long‐term regeneration dynamics of Mediterranean maquis was investigated by analysing historical aerial photographs of Mt. Carmel, one of the largest protected areas in the Mediterranean region of Israel. Two sets of aerial photographs were processed, one from 1960 (before the area was protected), and the second from 1992 (21 yr after the area was declared a nature reserve). The photographs of each year were classified into three vegetation states based on the percentage cover of trees: open maquis with tree cover &lt; 33.3 %, moderately developed maquis (tree cover 33.3–66.6 %), and closed maquis (tree cover &gt; 66.6 %). Grid maps constructed from the classified images were used to determine probabilities of transition between vegetation states. Closed maquis showed zero probability of transition to either open or moderately developed maquis. Probabilities of ‘forward’ transitions (transitions from low‐cover to high‐cover classes) were higher on north‐facing than on south‐facing slopes. On north‐facing slopes, the area of open maquis decreased from 87 % to 46 % during the period studied, while that of closed maquis increased from 3 % to 29 %. On south‐facing slopes open maquis decreased from 87 % to 69 % while closed maquis increased from 1 % to 8 %. Within a particular aspect, tree cover in 1960 was a reliable predictor of tree cover in 1992. This indicates that micro‐scale patterns of tree distribution in 1960 were important in determining the structure of the maquis 32 yr later. Simulations based on the empirically derived transition probabilities suggest that, under current climatic conditions, the process of maquis regeneration on Mt. Carmel may take 500–1000 yr.

The near-infrared Fe II forbidden lines of MWC 922

Spectrophotometry from 0.8-1,6 μm of the peculiar emission-line object and strong [Fe II] source MWC 922 is presented. Detections or useful upper limits are given for nine [Fe II] features between 1.25 and 1.54 μm which are used to test the accuracy of theoretically derived transition probabilities. The measured intensity ratios of all the lines were found to agree with the values predicted from the transition probabilities of Nussbaumer and Storey to within 30%. The derived electron density and temperature for the gas producing the [Fe II] emission are 10 5 cm -3 and 5000 K

Experimental lifetimes of the 3p and 3d states of neutral fluorine

The radiative lifetimes of six 3p and 3d neutral fluorine states were measured using the High Frequency Deflection technique. The derived transition probabilities are compared to existing values obtained from shock tube and wall-stabilized arc measurements, theoretical calculations based on Coulomb approximation and semiempirical compilations.

Radiative decay processes of vanadium ions in III-V compound semiconductors

The infrared 3T2(F) to 3A2(F) emission transition of the substitutional V3+(d2) ion in Td symmetry is studied in GaAs, GaP, and InP host materials. The decay f this intracentre luminescence under pulsed Ar or YAG: Nd laser excitation is found to be exponential at low temperature. The derived transition probabilities are discussed in models comprising configuration interaction or covalency mixing. With GaAs:V, different decay time constants tau are measured for above band gap and intracentre excitation energies. The temperature dependence of tau is examined in the 4-300 K range and parameters are determined of a configurational coordinate model in which nonradiative transitions necessitate a thermal activation of the excited state.

Infrared Emission of OH in the Fundamental and First Overtone Bands

The infrared vibration–rotation spectrum of the hydroxyl radical produced by the reaction of hydrogen atoms and ozone has been recorded. The intensity of individual lines in the fundamental sequence was found to be considerably weaker than was previously predicted. The intensity of lines in the fundamental sequence is compared with the intensity of the first overtone lines to obtain ratios of the vibrational transition probabilities. These ratios are used to remove the ambiguity of the OH dipole moment function associated with previously unknown intensities of the fundamental bands. A complete set of relative transition probabilities is given. An equilibrium flux calculation using atmospheric data is performed using the derived transition probabilities to obtain the vibrational distribution of OH at formation.

Temperature of a copper arc

The temperature of a copper arc in air has been measured by comparing 31 sets of transition probabilities for spectra of 20 elements with spectral-line intensities from those elements separately added to the copper. The intensities are taken from the recently published NBS Tables of Spectral-line Intensities and the transition probabilities from the literature. The individual determinations are discussed. The set of determinations is shown to follow a Gaussian distribution about a mean of 5100 °K. The average deviation of the determinations is 470 °K and the standard deviation of the mean is 110 °K. This temperature may be used in the evaluation of thousands of atomic transition probabilities from the intensities in the new tables. The effect of the uncertainty in the temperature on derived transition probabilities is evaluated as a function of excitation potential.