Computational Model of Progression to Multiple Myeloma Identifies Optimum Screening Strategies

Abstract

Purpose: Recent advances have uncovered therapeutic interventions that might reduce the risk of progression of premalignant diagnoses, such as monoclonal gammopathy of undetermined significance (MGUS) to multiple myeloma (MM). It remains unclear how to best screen populations at risk and how to evaluate the ability of these interventions to reduce disease prevalence and mortality at the population level. To address these questions, we developed a computational modeling framework.

Materials and methods: We used individual-based computational modeling of MGUS incidence and progression across a population of diverse individuals to determine best screening strategies in terms of screening start, intervals, and risk-group specificity. Inputs were life tables, MGUS incidence, and baseline MM survival. We measured MM-specific mortality and MM prevalence after MGUS detection from simulations and mathematic modeling predictions.

Results: Our framework is applicable to a wide spectrum of screening and intervention scenarios, including variation of the baseline MGUS to MM progression rate and evolving MGUS, in which progression increases over time. Given the currently available point estimate of progression risk reduction to 61% risk, starting screening at age 55 years and performing follow-up screening every 6 years reduced total MM prevalence by 19%. The same reduction could be achieved with starting screening at age 65 years and performing follow-up screening every 2 years. A 40% progression risk reduction per patient with MGUS per year would reduce MM-specific mortality by 40%. Specifically, screening onset age and screening frequency can change disease prevalence, and progression risk reduction changes both prevalence and disease-specific mortality. Screening would generally be favorable in high-risk individuals.

Conclusion: Screening efforts should focus on specifically identified groups with high lifetime risk of MGUS, for which screening benefits can be significant. Screening low-risk individuals with MGUS would require improved preventions.

Fig 1.

Population dynamics of unscreened and screened individuals with monoclonal gammopathy of undetermined significance (MGUS) as well as those with multiple myeloma (MM). (A) Possible individual transitions from healthy to MGUS to MM can be modeled as a Markov chain. The transitions describe incidence and screening of MGUS and progression to MM. The four possible states are healthy (blue), undetected MGUS (pink), detected MGUS (pink with dashed outline), and MM (red). (B) Example time evolution of a cohort at risk for MGUS and subsequent MM without screening. Undetected MGUS cases accumulate and can lead to a baseline number of MM cases. (C) Time evolution of a cohort with screening and intervention that reduces MGUS to MM progression. MGUS cases accumulate; individuals are screened and receive preventive treatment if positive for MGUS, leading to a lower number of MM cases (red indicates a few screened individuals who may develop MM nonetheless).

Fig 2.

Number of patients with multiple myeloma (MM), age at MM diagnosis, and variability of screening strategy. (A) When monoclonal gammopathy of undetermined significance (MGUS) screening was applied, we measured the number of patients diagnosed with MGUS (dashed line, open circles) and MM (solid line, filled circles) relative to the r = 1 values, with respect to changing the risk reduction factor r (circles, simulations; lines, analytic model; Data Supplement), with a₀ = 50 years and Δa = 1 year. At r = 0.61, the MM fraction dropped to < 70% of its value at r = 1 (where screening had no effect on progression). (B) Variability in MM fraction at r = 0.61, with respect to changes in a₀ and Δa (analytic approach, point estimates; Table S4, Data Supplement). (C, D) Distributions of age at MM diagnosis (Δa = 1 year), with varying a₀ and fixed r of (C) 0.61 or (D) 0.1. Width in these violin plots is equal to probability of MM diagnosis at that age. All point estimates were calculated from a simulation of approximately 10⁸ individuals.

Fig 3.

Lead-time bias, cumulative multiple myeloma (MM) –specific mortality, and monoclonal gammopathy of undetermined significance (MGUS) to MM progression variability. All simulations were performed with populations of 10⁸ healthy individuals (20% high risk). (A) Potential lead-time bias, comparing median survival after MM diagnosis without screening (blue: median survival, 4 years) and with screening (gold: median survival, 15 years; gray: median survival, 17 years after MGUS screen, respectively). Without screening, disease detection was the event of MM diagnosis. With screening, disease detection was diagnosis of asymptomatic MGUS. (B) Cumulative MM-specific mortality in years after MGUS detection was measured for the groups of 50, 60, and 70 years of age at MGUS detection (a₀ = 50 years, Δa = 1, and r = 1). In older patients, death resulting from other cause becomes more dominant. (C) MM-specific mortality changed dramatically with r (a₀ = 50 years, Δa = 1), here shown for individuals diagnosed with MGUS at age 60 years, sampled from simulations. (D) MM-specific mortality is influenced by variability in MGUS to MM progression rate (inset, truncated normal distribution\; mean, 0.01; standard deviation, 0.03), for different r, using the analytic model (Δa = 1; Data Supplement). (E) Simple evolving MGUS progression rates [β × (1 − β)^t], fitted to data from Rosiñol et al (filled circles; nonevolving: 10% at 10 years, 13% at 20 years follow-up; evolving: 55% at 10 years, 80% at 20 years follow-up), for which we show 95% CIs. Nonevolving MGUS confirms the low value of β (here 0.007; R² = 0.996), corresponding to constant progression risk p (Table 1). Evolving MGUS led to a progression rate of p = .071 (R² = 0.975). (F, G) Impacts of age at MGUS detection and progression risk reduction r on MM-specific mortality as a function of evolving progression rate calculated as described in Data Supplement: (F) r = 0.61 and (G) age at MGUS detection 60 years.

Fig 4.

Equal disease fractions as a criterion for optimal screening distribution. (A, B) Comparing multiple myeloma (MM) fractions in the high-risk and low-risk populations (men and women, respectively), with a₀ = 50 years and Δa = 1 year, for different r. (A) For r = 0.61, equality could not be observed for any percentage of high-risk screens. (B) For r = 0.1, equality was observed at approximately 81% high-risk screens. Thus, an optimal fraction of screens was defined as the point where the fractions of patients with MM in both subpopulations were the same. (C) Location of the optimal fraction (scale) under variation of r and Δa (Table S5, Data Supplement), with a₀ = 50 years. Changing r from 0 to 0.3 would lead to up to 20% change in the optimal high-risk fraction of screens. Changing Δa from 1 to 4 would lead to 1% to 3% change in the optimal high-risk fraction of screens. (D) For fixed r = 0.1, changes in a₀ had more drastic effects than changes in Δa (Table S6, Data Supplement). (E) For risk groups with a lifetime risk higher than two-fold, we examined the effect of risk reduction and screening interval (a₀ = 50 years) on the number of patients with MM (Data Supplement). (F) MM-specific deaths per 100,00 were calculated as the product of screened individuals with monoclonal gammopathy of undetermined significance (MGUS) at age 60 years and the 10-year follow-up MM-specific mortality (a₀ = 50 years and Δa = 1; age at MGUS detection, 60 years). Both risk reduction and spacing of screens have more pronounced effects in higher-risk groups.