Disentangling age, gender, and racial/ethnic disparities in multiple myeloma burden: a modeling study

Multiple myeloma (MM) is a hematological malignancy that is consistently preceded by an asymptomatic condition, monoclonal gammopathy of undetermined significance (MGUS). Disparities by age, gender, and race/ethnicity in both MGUS and MM are well-established. However, it remains unclear whether these disparities can be explained by increased incidence of MGUS and/or accelerated progression from MGUS to MM. Here, we fit a mathematical model to nationally representative data from the United States and showed that the difference in MM incidence can be explained by an increased incidence of MGUS among male and non-Hispanic Black populations. We did not find evidence showing differences in the rate of progression from MGUS to MM by either gender or race/ethnicity. Our results suggest that screening for MGUS among high-risk groups (e.g., non-Hispanic Black men) may hold promise as a strategy to reduce the burden and MM health disparities.

2. The authors state the pre-clinical dwell time is shorter for black individuals e.g."Furthermore, independent of sex, black race was associated with a shorter preclinical dwell time.For instance, at age 70, the expected dwell times were 6.6 (95% CI: 6.1 -7.1) years for non-Hispanic white males compared to 6.1 (95% CI: 5.6 -6.5) years for non Hispanic black males".They also state that the rate of MM development (for a given time period) in MGUS individuals were not affected by race.Unless I have misunderstood is there not a contradiction in these statements?
3. The NHANES and SEER have biases including non-responder biases (e.g.https://www.cdc.gov/nchs/data/bsc/bscpres_fakhouri_january_2018.pdf).The authors should discuss this, how this might impact on their model and how it would affect their assertion that their model can address inconsistencies in the literature.4. Whilst simulation studies were used to assess the validity of their model.Independent validation of their model would bring strength to this manuscript.
5. There are a number of important references missing -discussion would benefit the manuscript: 1) https://www.nature.com/articles/leu2014342) https://www.nature.com/articles/s41467-020-15740-9 3) https://ashpublications.org/bloodadvances/article/6/12/3746/484453/Prevalence-of-heavychain-MGUS-by-race-and-family Reviewer #2 (Remarks to the Author): Huber et al. conducted an important study which found that the increased incidence of MGUS can explain disparities in MM.Therefore, screening and prevention of MGUS among high-risk groups hold promise as strategies to reduce the burden of MM.The paper is well written with robust statistical analysis conducted.I have a few comments for further improvement of the paper.1) Data used were relatively old: 1999-2004 for NHANES and 2010 for SEER.It would be better if updated data (2020) can be used for the modelling.
2) The authors should include a Table explaining the different characteristics between NHANES and SEER.
3) The assumptions made should be highlighted in the abstract and discussion of the paper.4) Asian population should also be included in the analysis.5) Is it possible to adjust for drug use in the analysis?6) Obesity is another risk factor to be considered in the analysis.7) Socioeconomic status should also be considered to explain the disparities observed.8) Any explanations for the progression rate from MGUS to MM peaked at 71 years of age?
Reviewer #3 (Remarks to the Author): This study describes a mathematical model of multiple myeloma natural history, particularly the transition from MGUS to MM.The authors use data from NHANES on the age-specific prevalence of MGUS and from SEER on the age-specific incidence of MM.They define a multi-state model and formulate the dynamics of the various transitions as a set of differential equations parameterized by the transition rates.They then estimate the transition rates by formulating a likelihood function for the incidence and prevalence data and applying a Bayesian MCMC algorithm.The model is fit separately to population subgroups defined by sex and race to infer whether the data are consistent with similar rates of MGUS onset or transition from MGUS to MM across age-and race groups.This is very informative and could offer direction for interventions to prevent MM in the different subgroups.I have some key concerns however about the methods and results.
First, regarding the likelihood development, the use of a normal distribution for the incidence piece does not really comport with the count data nature of incidence figures for which the mean and variance should be related e.g.via a Poisson or other count data type model and also informed by the sample size.
Second, the incidence information is on a different scale than the prevalence information, and it is unclear, when the two parts of the likelihood are multiplied, how this is weighted relative to the prevalence?In other words, in the model fitting, is the fit prioritizing prevalence or incidence?One thing that strikes me is that the prevalence of MGUS by age actually contains information on both the incidence of MGUS and the transition rate to MM if the rate of other-cause death among people with MGUS is known (indeed it is assumed known and provided as an input to the model).So, the model could in principle be fit just to the prevalence data and then validated against the incidence data.I wonder if the investigators have considered this?At any rate, some discussion of the validity and implications of the product formulation of the likelihood seems important including some insight into the relative contributions of the incidence and prevalence data.
Finally, I understand the explanation for the pattern of MGUS duration by age in Figure 4, but I don't understand why the authors could not produce a version of this figure in the absence of other-cause death, which would be a much cleaner comparison of natural history across ages.Can this be added alongside or as an additional figure?
The Discussion does not address the limitation of the model structure in that it is essentially agegroup-specific and does not lend itself to aging from one age group into another (MM incidence in a given age group depends not only on MGUS prevalence in that group but on MGUS prevalence in prior groups).It would be of value to understand this and to see some discussion of alternative modeling approaches that have been used for cancer natural history modeling e.g.continuoustime multi-state models.We thank the reviewer for identifying studies relevant to our work.We agree with the reviewer that racial disparities in MGUS and multiple myeloma is an area of intense focus.However, we believe that our study fills a gap in the literature not addressed by the referenced studies above.Specifically, we adopted a mechanistic modeling approach to link two nationally representative databases on MGUS prevalence and MM incidence to better understand the contribution to age, sex, and race to observed disparities in MM incidence.We agree with the reviewer that Landgren et al. (2014) and subsequent studies established that MGUS is more prevalent among non-Hispanic black populations.However, our study answers three unique questions, which have not been able to be answered in the past studies -1) whether this increased MGUS prevalence and/or the increased transformation of MGUS to MM was contributing to racial difference in MM incidence; 2) how long the preclinical dwell time is as a function of age, sex, and race; and3) factors contributing to the preclinical dwell time.
Finally, we agree with the reviewer that Therneau et al. (2012) demonstrated that the rate of MGUS development increased monotonically with age in a predominately white cohort.Nonetheless, our study further demonstrates that that this result holds true for non-Hispanic black populations.Additionally, we show that the rate of MM progression has a nonlinear relationship with age and importantly peaks around age 70 and that individuals greater than 70 years of age have a lower rate of MM progression, even when adjusting for all-cause mortality, which fills the gap in the literature and warrants further investigation.
We appreciate the reviewer raising all of these points as we believe that it has helped to better communicate the gap in the literature that our study addresses.We reference these studies now throughout the manuscript to better highlight the prior literature in this area.

Comment 1.3
The authors state the pre-clinical dwell time is shorter for black individuals e.g."Furthermore, independent of sex, black race was associated with a shorter preclinical dwell time.For instance, at age 70, the expected dwell times were 6.6 (95% CI: 6.1 -7.1) years for non-Hispanic white males compared to 6.1 (95% CI: 5.6 -6.5) years for non Hispanic black males".They also state that the rate of MM development (for a given time period) in MGUS individuals were not affected by race.Unless I have misunderstood is there not a contradiction in these statements?

Response 1.3
We apologize for the confusion.This appears to be a contradiction, because pre-clinical dwell time is determined by both 1) the rate of MM development; and 2) the mortality rate.Although we identified no statistically significant difference in the rate of MM development across race, non-Hispanic blacks are subject to a higher mortality rate, thereby shortening the pre-clinical dwell time.We clarify this in the Discussion on Lines 417-421: "This explains apparent differences in the preclinical dwell time between non-Hispanic blacks and whites.Although we identified no statistically significant difference in the rate of progression from MGUS to MM across race/ethnicity, non-Hispanic blacks are subject to a higher mortality, resulting in shorter preclinical dwell times as compared to non-Hispanic whites."

Comment 1.4
The NHANES and SEER have biases including non-responder biases (e.g.https://www.cdc.gov/nchs/data/bsc/bscpres_fakhouri_january_2018.pdf).The authors should discuss this, how this might impact on their model and how it would affect their assertion that their model can address inconsistencies in the literature.

Response 1.4
We thank the reviewer for raising this.Ultimately, this bias in the NHANES is known, and we are unable to comment on the direction it would have on our conclusions, given that we do not know the prevalence of MGUS and among non-respondents as compared to respondents.We do not believe that SEER data is subject to the same bias, because SEER data are submitted by cancer registries.We have acknowledged this limitation in the Discussion on Lines 429-431: "However, the NHANES database is subject to non-response bias, which could affect our conclusions if the prevalence of MGUS was significantly different among those that responded as compared to those that did not respond."

Comment 1.5
Whilst simulation studies were used to assess the validity of their model.Independent validation of their model would bring strength to this manuscript.

Response 1.5
We thank the reviewer for this suggestion.We compared model predictions for MGUS prevalence to those reported by Kyle et al. (2006) in Olmsted County, Minnesota.Additionally, we compared our model predictions for the lifetime risk of developing MM to estimates published by the American Cancer Society.A description of the methods taken be found in the supplement on lines 534-544:

Independent Validation
We performed an independent validation of our fitted model by comparing our model predictions to data sources that were not used to fit the model.Specifically, we compared predicted MGUS prevalence by age and sex from our model to predicted MGUS prevalence by age and sex in Olmsted County, Minnesota between 1995 and 2001 3 .Because 97.3% of the Olmsted County cohort identified as white, we made use of model predictions for non-Hispanic white males and females.Next, we compared our model's prediction for lifetime risk of developing MM to estimates reported by the American Cancer Society's Cancer Statistics from 2023 30 .Estimates were only available by sex, so we compared our model predictions for non-Hispanic whites, non-Hispanic blacks, and a composite of non-Hispanic whites and non-Hispanic blacks weighted by population size.
The results of this independent validation can be found in the supplement on lines 665-693:

Independent Validation
We compared model estimates of MGUS prevalence for non-Hispanic white males and females to estimates from Olmsted County, Minnesota between 1995-2001 3 .Although the data used for validation reflects a single cohort from a separate time period in one geographical location, there is reasonably good agreement between the model predictions and the validation data with respect to the magnitude of MGUS prevalence and its relationship with age (Fig. S6).A previous study comparing NHANES 1999NHANES -2003 to the Olmsted County cohort noted higher MGUS prevalence in Olmsted County, suggesting that the higher MGUS prevalence in Olmsted County may reflect geographical variation 9 .We additionally compared our model estimates of lifetime risk of developing MM to estimates published by the American Cancer Society 34 .Reported lifetime risk of developing MM for males is 0.9%.Our model predictions for the lifetime risk of developing MM were 0.77% (95% CI: 0.68 -0.87%) for non-Hispanic white males and 1.42% (95% CI: 1.25 -1.59%) for non-Hispanic black males.Weighting each race/ethnicity by population size, we obtained a lifetime risk of developing MM for males of 0.88% (95% CI: 0.77 -0.99%), comparable to the estimate reported by the American Cancer Society.For females, reported lifetime risk of developing MM is 0.7%.Our model predictions for the lifetime risk of developing MM were 0.66% (95% CI: 0.57 -0.75%) for non-Hispanic white females and 1.33% (95% CI: 1.18 -1.48%) for non-Hispanic black females.Weighting each race/ethnicity by population size, we obtained a lifetime risk of developing MM for females of 0.77% (95% CI: 0.68 -0.87%), comparable to the estimate reported by the American Cancer Society.

Response 1.6
We thank the reviewer for these references.We have cited them in the discussion.

Response 2.1
We thank the reviewer for this summary and assessment of our work.We hope that the revised manuscript addresses the concerns raised by the reviewer.

Comment 2.2
Data used were relatively old: 1999-2004 for NHANES and 2010 for SEER.It would be better if updated data ( 2020) can be used for the modelling.

Response 2.2
We agree with the reviewer that we would prefer to have more updated data.The MGUS prevalence survey from 1999-2004 is the most recent nationally representative MGUS survey.We choose the SEER data from 2010 to be approximately comparable in the age groups considered in the NHANES data from 1999-2004.We clarify that the NHANES data is the most current nationally representative data source available on Lines 164-165: "This data is the most current nationally representative survey on MGUS prevalence within the United States."

Response 2.3
We thank the reviewer for this suggestion.We have included a table in the Methods on Lines 191-192:

Comment 2.4
The assumptions made should be highlighted in the abstract and discussion of the paper.

Response 2.4
We thank the reviewer for this suggestion.Due to the word limit of the abstract, we are limited in the assumptions that we can list there.However, we have specified the model structure on Line 20:

"We constructed a discrete time, multi-state compartmental model of the natural history of MM."
Additionally, we specify the model structure in the Discussion on Lines 372-376: By leveraging nationally representative data on MGUS prevalence 14-16 , our study calibrated a discrete time, multi-state compartmental model of the natural history of MM that was able to uncover whether the higher incidence of MGUS, the progression rate of MGUS to MM, or both contributed to MM health disparities across age, sex, and race/ethnicity.
Finally, we expanded in the Discussion on Lines 380-384 on the supplementary analyses that were performed to clarify some of the assumptions that were made and how robust our analyses were to these assumptions: "Importantly, we found no statistically significant difference in the rate of progression from MGUS to MM, and these results were robust to multiple supplementary analyses that considered alternative models, including one in which there was no effect of MGUS on mortality, as well as alternative years of SEER MM incidence data."

Comment 2.5
Asian population should also be included in the analysis.

Response 2.5
The NHANES MGUS prevalence survey did not identify Asian as a demographic population.There was a category for "other non-Hispanic white," but this was not specific to the Asian population alone.As such, we limited our analysis to non-Hispanic white and non-Hispanic black populations.

Comment 2.6
Is it possible to adjust for drug use in the analysis?

Response 2.6
The reviewer raises an interesting point regarding drug use and treatment for multiple myeloma.
In our analysis, we made use of all-cause survival data for individuals diagnosed with multiple myeloma from SEER.Because this considers a cohort of MM patients, irrespective of treatment modality or lack thereof, we obtained a mean all-cause mortality rate for the subset of the population diagnosed with multiple myeloma.We felt that this was appropriate given that our analysis was not focused on estimating the effects of various treatment regimens and was considered at a population scale.We clarify this in the text on Lines 185-189: "Finally, for individuals with MM, we estimated sex-and race/ethnicity-stratified all-cause mortality rates by fitting an exponential survival distribution to MM all-cause survival data provided by SEER (Fig. S1).Because these survival curves are derived from the cohort of all MM individuals within SEER, they provide an estimate of the mean all-cause mortality rate among MM individuals, irrespective of treatment characteristics."

Comment 2.7
Obesity is another risk factor to be considered in the analysis.

Response 2.7
We thank the reviewer for this suggestion.Obesity is a known risk factor for progression to MM and likely promotes development of MGUS as well, as also demonstrated by a previous study conducted by our team.Because the distributions of BMI, race/ethnicity, and sex are highly correlated, it is likely that some of the estimated effects of sex and race/ethnicity on MGUS development can be explained by obesity.We comment on this in the Discussion on Lines 391-395: "Alternatively, differences by race/ethnicity may be explained by socio-contextual factors 7 and differences in the distribution of known risk factors, such as obesity 13 .Future investigation that accounts for these and other hypotheses may eliminate the practice of essentializing race/ethnicity in cancer risk prediction models 28 ." BMI was available for NHANES data, but not SEER incidence.Accordingly, we chose to not estimate the effect of BMI in this study, but instead comment on its possible effect in the Discussion.Incorporating the effect of BMI on MGUS development and MM progression is an active area of work for this group.

Comment 2.8
Socioeconomic status should also be considered to explain the disparities observed.

Response 2.8
We thank the reviewer for this suggestion.We include this as a possible explanation for the patterns by race/ethnicity and sex on Lines 391-395: "Alternatively, differences by race/ethnicity may be explained by socio-contextual factors 7 and differences in the distribution of known risk factors, such as obesity 13 .Future investigation that accounts for these and other hypotheses may eliminate the practice of essentializing race/ethnicity in cancer risk prediction models 28 ." Comment 2.9 Any explanations for the progression rate from MGUS to MM peaked at 71 years of age?
Response 2.9 The peak in the progression rate from MGUS to MM at 71 years of age reflects the decline in MM incidence seen in later age groups.Given that we accounted for the competing risk of mortality through age-, race-and sex-stratified all-cause mortality rates, it is possible that the decline in the estimated progression rate at higher age groups may be capturing MGUS-positive individuals with characteristics of lower risk of transformation.That is to say, conditional on surviving up beyond age 71 without transforming to MM, you may have MGUS with features that are less likely to transform to MM.We comment on this possibility on Lines 402-405:

Response 3.3
We thank the reviewer for raising this point.We adopted a fully Bayesian approach, so we did not weight the prevalence and incidence data.We feel that this is the appropriate approach because we are not specifying beforehand which data that we feel are more "important," per se.We note that the data is not weighted in the likelihood on Lines 196-197: "Because we adopt a fully Bayesian approach, we do not specify a weight for each data type during model fitting." As the reviewer notes, depending upon the likelihood, the model could be fit more to one data type at the expense of the other data type.However, as can be observed in Figure 2, the fitted model is able to capture the patterns in both data types with appropriate uncertainty, suggesting that this is not an issue in this study.Had the model preferentially fit to MGUS prevalence or MM incidence at the expense of the other data type, we agree that a greater exploration of the weighting of the data types would be warranted.
Fitting to MGUS prevalence and validating against MM incidence is an interesting suggestion.Ultimately, we chose to fit to both data types because, fitting only to MGUS prevalence would likely yield more uncertain parameter estimates that would limit the conclusions that we could reach about the contributions of age, sex, and race to MM disparities.Nevertheless, as recommended by Reviewer #1 as well, we have performed an independent validation of our model which can be found in Response 1.5 and in the Supplement on Lines 665-693.

Comment 3.4
Finally, I understand the explanation for the pattern of MGUS duration by age in Figure 4, but I don't understand why the authors could not produce a version of this figure in the absence of other-cause death, which would be a much cleaner comparison of natural history across ages.Can this be added alongside or as an additional figure?
Response 3.4 We thank the reviewer for raising this point.The reviewer is correct that we could generate an expected duration of MGUS by age by taking one over the rate of MM progression.However, this quantity does not account for the competing risk of death.That is, it represents the expected duration of MGUS were an individual not to be subject to all-cause mortality.In practice, the pre-clinical dwell time shown in Fig. 4 is shaped not only by the rate of MM progression but also by all-cause mortality.We show that differences in all-cause mortality drive differences in the pre-clinical dwell time, because the rate of MM progression is not statistically different by race.We believe that this is a contribution of our study that has not been addressed by past studies.
We clarify that the pre-clinical dwell time depends on all-cause mortality in the Methods on Lines 273-274: To model the natural history of multiple myeloma 17 , we constructed a discrete time, multi-state compartmental model consisting of four health states: healthy (H), monoclonal gammopathy of undetermined significance (MGUS), multiple myeloma (MM), and death (D) (Fig. 1).
We agree with the reviewer that further discussion of the limitations of our approach is warranted.Specifically, we discuss on Lines 432-433 the limitation that we are in effect simulating a single cohort.Future more could build upon ours to account for period effects and time trends across cohorts: "Additionally, extensions to our modeling framework could simulate multiple cohorts to account for period effects that likely shape MGUS prevalence and MM incidence."

Figure S6 .
Figure S6.Independent validation of MGUS prevalence for non-Hispanic white males and females.Model predictions of MGUS prevalence for non-Hispanic white (A) males and (B) females are shown as a function of age and compared to estimates from Kyle et al. 3 in Olmsted County, Minnesota.The dashed black line is the estimate from Kyle et al. 3 .The solid line is median posterior model prediction, the darker shaded area is the 50% credible interval (CI), and the lighter shaded area is the 95% CI.

rate of MGUS development monotonically increased with increasing age as described here: https://linkinghub.elsevier.com/retrieve/pii/S0025-6196(12)00634-9 Response 1.2
We thank the reviewer for this summary of our work.We believe that the recommendations made by the reviewer have helped us to clarify how our work builds upon prior studies and have strengthened our manuscript.

Table 2 . Characteristics of the Data used for Modeling Fitting
"Furthermore, we estimated that the rate of progression from MGUS to MM peaked at approximately 71 years of age and subsequently declined, which mirrors the observed decline in MM incidence at higher age groups and may reflect a subset of older individuals with a more indolent presentation of MGUS and thus lower overall risk of progression to MM."This study describes a mathematical model of multiple myeloma natural history, particularly the transition from MGUS to MM.The authors use data from NHANES on the age-specific prevalence of MGUS and from SEER on the age-specific incidence of MM.They define a multistate model and formulate the dynamics of the various transitions as a set of differential equations parameterized by the transition rates.They then estimate the transition rates by formulating a likelihood function for the incidence and prevalence data and applying a Bayesian MCMC algorithm.The model is fit separately to population subgroups defined by sex and race to infer whether the data are consistent with similar rates of MGUS onset or transition from MGUS to MM across age-and race groups.This is very informative and could offer direction for interventions to prevent MM in the different subgroups.I have some key concerns however about the methods and results.We thank the reviewer for this summary and assessment of our work.We hope that the revised manuscript addresses the concerns raised by the reviewer.We apologize that this was not clear.The incidence estimates reported by SEER are rates, not count data.Since they are continuous, not discrete in nature, we did not feel that a count data type model was appropriate.We clarify that the data is a continuous rate on Lines 228-231: Second, the incidence information is on a different scale than the prevalence information, and it is unclear, when the two parts of the likelihood are multiplied, how this is weighted relative to the prevalence?In other words, in the model fitting, is the fit prioritizing prevalence or incidence?One thing that strikes me is that the prevalence of MGUS by age actually contains information on both the incidence of MGUS and the transition rate to MM if the rate of othercause death among people with MGUS is known (indeed it is assumed known and provided as an input to the model).So, the model could in principle be fit just to the prevalence data and then validated against the incidence data.I wonder if the investigators have considered this?At any rate, some discussion of the validity and implications of the product formulation of the likelihood seems important including some insight into the relative contributions of the incidence and prevalence data.
The preclinical dwell time depends upon the rate of progression from MGUS to MM and the competing baseline mortality rate, both of which depend upon age, sex, and race."The Discussion does not address the limitation of the model structure in that it is essentially agegroup-specific and does not lend itself to aging from one age group into another (MM incidence in a given age group depends not only on MGUS prevalence in that group but on MGUS prevalence in prior groups).It would be of value to understand this and to see some discussion of alternative modeling approaches that have been used for cancer natural history modeling e.g.continuous-time multi-state models.Our model simulates a discrete-time multi-state model to calculate MGUS prevalence and MM incidence.In this way, it does lend itself to aging from one age group into another.For instance, the prevalence of MGUS in age group a determines the MM incidence in age group a+1.We clarify this in the methods on Lines 92-94: