Clinical Management and Burden of Prostate Cancer: A Markov Monte Carlo Model

Background Prostate cancer (PCa) is the most common non-skin cancer among men in developed countries. Several novel treatments have been adopted by healthcare systems to manage PCa. Most of the observational studies and randomized trials on PCa have concurrently evaluated fewer treatments over short follow-up. Further, preceding decision analytic models on PCa management have not evaluated various contemporary management options. Therefore, a contemporary decision analytic model was necessary to address limitations to the literature by synthesizing the evidence on novel treatments thereby forecasting short and long-term clinical outcomes. Objectives To develop and validate a Markov Monte Carlo model for the contemporary clinical management of PCa, and to assess the clinical burden of the disease from diagnosis to end-of-life. Methods A Markov Monte Carlo model was developed to simulate the management of PCa in men 65 years and older from diagnosis to end-of-life. Health states modeled were: risk at diagnosis, active surveillance, active treatment, PCa recurrence, PCa recurrence free, metastatic castrate resistant prostate cancer, overall and PCa death. Treatment trajectories were based on state transition probabilities derived from the literature. Validation and sensitivity analyses assessed the accuracy and robustness of model predicted outcomes. Results Validation indicated model predicted rates were comparable to observed rates in the published literature. The simulated distribution of clinical outcomes for the base case was consistent with sensitivity analyses. Predicted rate of clinical outcomes and mortality varied across risk groups. Life expectancy and health adjusted life expectancy predicted for the simulated cohort was 20.9 years (95%CI 20.5–21.3) and 18.2 years (95% CI 17.9–18.5), respectively. Conclusion Study findings indicated contemporary management strategies improved survival and quality of life in patients with PCa. This model could be used to compare long-term outcomes and life expectancy conferred of PCa management paradigms.


Introduction
Prostate Cancer (PCa) is the most common non-skin cancer and among leading cause of cancer mortality in men in developed countries. [1] In 2013, the agestandardized incidence and mortality rates in Canada were estimated at 103.9 and 17.8 per 100,000, respectively. [2] Further, most men diagnosed with PCa was aged 65 years and older. [2] Various classification systems exist to stratify patients into low, intermediate, and high risks. [3] A range of curative treatment choices are used to manage the disease by risk groups at diagnosis, from diagnosis to endof-life. Beside active surveillance for low risk cancer, initial treatments with curative intent include radical prostatectomy and radiation therapy. Moreover, treatment options, such as hormonal manipulation, chemotherapy, and palliative radiation, are used to manage patients with advanced stages of the disease including metastatic castrate resistant prostate cancer (mCRPC). Treatment choices for the initial and advanced stages of the disease are aimed at prolonging survival and improve quality of life. However, these treatments entail uncertainty on risks and benefits that require complex clinical decision making to attain anticipated outcomes in patients [4][5][6][7][8].
Over the years, there has been growing use of decision analytic models or mathematical frameworks for evidence-informed decision making. Decision analytic models facilitate the quantitative synthesis of evidence on survival and other clinical outcomes of medical interventions over short and long term periods. The existing literature is limited on decision analytic models for the clinical management of PCa and outcomes in contemporary setting from diagnosis to end-of-life. [9][10][11] Moreover these models precede [9][10][11] the adoption of newer treatments or health technologies by healthcare systems, such as active surveillance and intensity modulated radiation therapy. [8,12] Systemic treatments for advanced stage of the disease were also not considered by preceding models. [5,6,[8][9][10][11] As a result, existing decision analytic models have not assessed the survival and other clinical outcomes attained by contemporary management options and its bearing on clinical burden of the disease. [9][10][11] To date, there is lack of randomized clinical trials that have concurrently evaluated the survival and other outcomes (e.g. recurrence or mCRPC) associated with active surveillance, radical prostatectomy, brachytherapy and intensity modulated radiation therapy. Further, concurrent assessment of all contemporary treatments by RCT's are challenged by ethical issues, expensive/resource intensive endeavour, highly selective subjects (inclusion/exclusion criteria) unrepresentative of clinical practice, and often conducted over short follow up. [13] In view of these limitations an up-to-date decision analytic model is needed to integrate the role of contemporary management strategies on the clinical burden of the disease. The objectives of this study were to develop and validate a Markov Monte Carlo model for the contemporary clinical management of PCa, and to assess the clinical burden of the disease from diagnosis to end-of-life.

Methods
A Markov model with Monte Carlo microsimulation was developed to simulate the evolution of the disease, its management and associated clinical outcomes in the contemporary context. [14] Figure 1 represents the proposed model with eight distinct health states from diagnosis to end-of-life. A hypothetical annual cohort of incident cases of men 65 years and older in Canada (n514,160) was simulated over a 5-, 10-, 15-year and lifetime period. [2] The sample size of the low, intermediate, and high risk groups were 7080, 4248, and 2832, respectively. [2] This state-transition model with microsimulation enabled flexible modeling of the evolution of the disease and treatment choices at an individual patient level.

Health states in the model
Hypothetical patients with PCa were simulated to receive active surveillance or active treatments as ascertained by level of risk at diagnosis. These patients based on disease evolution (or not), were transitioned to PCa recurrence free, or received treatments for recurrence, mCRPC, and finally die during the simulation from PCa or other causes. Figure 1 illustrates the eight distinct health states transit during the simulated period: (i) 'PCa diagnosis', incident cases stratified into low, intermediate, and high risk groups. (ii) 'Active surveillance', eligible low risk patients underwent surveillance.
During the simulation if the disease progressed they underwent radical prostatectomy or radiation therapy with (or without) androgen deprivation therapy. Otherwise, they were free of disease progression and died from other causes [8]. (iii) 'Active treatment', eligible patients in all risk groups received curative intent active (initial) treatment (i.e. radical prostatectomy or radiation therapy with/or without androgen deprivation therapy). [8] The clinical literature indicated similar clinical outcomes attained by open or robotic surgical approaches. [8,15,16] Internal radiation therapy (i.e. brachytherapy) and external beam radiation therapy (i.e. intensity modulated radiation therapy) were simulated by the model.
(iv) 'PCa recurrence', represents disease recurrence following failure of initial treatments that triggered initiation of subsequent treatment. [8] Patients who transited to PCa recurrence remained in this state till they progressed to mCRPC or died from other causes. (v) 'PCa recurrence free', represents disease recurrence free following initial treatments. (vi) 'mCRPC', represents the metastatic castrate resistant state of the disease following failure of subsequent therapy. Patients were simulated to receive systemic treatments to improve survival [5,8]. (vii) 'PCa death', represents death from PCa. Patients who transited to mCRPC state remained in that state till they progressed to PCa death [7]. (viii) 'Overall death', represents death from other competing causes. Patients on active surveillance, PCa recurrence, and PCa recurrence-free progressed to overall death during the simulation based on state transition probability.

Treatment options simulated by risk groups
Evolution of the disease was simulated based on level of risk at diagnosis. Hence, following treatment options were simulated based on level of risk at diagnosis: (i) Low risk -eligible patients were simulated to receive either active surveillance followed by delayed treatment (i.e. radical prostatectomy or radiation therapy) or curative intent treatment (i.e. radical prostatectomy or radiation therapy) at diagnosis. Patients were simulated to receive intensity modulated radiation therapy or brachytherapy [8]. (ii) Intermediate risk -these patients were simulated to receive either radical prostatectomy or radiation therapy at diagnosis. Patients were simulated to receive intensity modulated radiation therapy as monotherapy or in combination with brachytherapy or androgen deprivation therapy. The median duration of ADT use was 8 months [8,17]. (iii) High risk -these patients were simulated to receive intensity modulated radiation therapy and androgen deprivation therapy with (or without) brachytherapy. The median duration of ADT use was 15 months [8,17].
Following the failure of initial treatments (i.e. cancer recurrence), patients from all risk groups were simulated to received subsequent treatments. Subsequent treatment simulated following the failure of initial treatment with radical prostatectomy was radiation therapy with (or without) androgen deprivation therapy. Further, following the failure of initial radiation therapy patients were simulated to receive androgen deprivation as subsequent treatment [8]. State transition probabilities for subsequent treatments were ascertained during simulation.

State-transition probabilities
The state-transition probabilities used to develop the model were derived from peer-reviewed literature [17][18][19][20][21][22]. Study findings were reported as rates over a time period (i.e. cumulative incidence). These were converted to annual rates followed by annual probabilities. Annual rates (r 1y ) were derived using the formula r 1y 52[ln (1-r)/t], where 'r' was the rate reported by studies and 't' was the time period corresponding to the rate. Annual probabilities of the event (p 1y ) were derived from annual rates using the formula p 1y 51-exp (2r 1y ), where 'p 1y ' was the annual probability and 'r 1y ' was the annual rate. [14] Health states transited by patients during the simulated periods were counted by tracker variables [23].

Model overview and assumptions
Initial treatment distributions were adapted from peer-reviewed literature that reflected the clinical practice in Quebec, Canada. [17][18][19][20][21][22] Simulated patients were assigned to initial treatments specific to level of risk at diagnosis. In the low risk cohort, 10% were assumed to undergo active surveillance and 90% were assumed to receive initial treatments. [24,25] Patients on active surveillance were assumed to receive a delayed treatment at an annual probability of 0.08 for first 2 years, 0.04 for 3 to 5 years, and 0.02 for 5 to 10 years. [18] The 90% of patients simulated to receive curative intent treatment were distributed as follows: 0.30 for radical prostatectomy, 0.30 for intensity modulated radiation therapy, and 0.30 for brachytherapy. [21,26] In contrast, intermediate and high risk patients were assumed to receive a curative intent initial treatment following diagnosis. The distribution of initial treatments received by intermediate risk cohort was 0.49 for radical prostatectomy, 0.24 for intensity modulated radiation therapy, 0.19 for intensity modulated radiation therapy+androgen deprivation therapy, and 0.08 for intensity modulated radiation therapy+brachytherapy. [17,20,27] The distribution of initial treatments received by high risk cohort was 0.77 for intensity modulated radiation therapy+androgen deprivation therapy and 0.23 for intensity modulated radiation therapy+androgen deprivation therapy+brachytherapy [17,20].
The disease management trajectory for low, intermediate, and high risk groups were simulated using data on subsequent treatments following time to recurrence by risk group, [17][18][19][20] time to mCRPC following disease recurrence (after subsequent treatment), [21] time to PCa death following mCRPC, [22] and time to overall death following active surveillance or disease recurrence/nonrecurrence. [28] Patients who progressed to mCRPC were assumed to only die from PCa. [7] For low risk, annual probability of recurrence for all treatments was assumed alike. [18] For intermediate risk, annual probability of recurrence for Table 1. Treatment distribution by risk groups.

Annual probability Refs
Active treatment R PCa recurrence

Health state
Base case [refs] Sensitivity analyses [refs] Active surveillance/treatments

Validation of the model
Internal validation examined model's internal consistency and assumptions at the population level [31]. The model predicted rates on treatments for PCa recurrence by risk group at diagnosis, mCRPC, overall and PCa deaths were compared with rates derived from peer-reviewed literature used to develop the model. Predicted annual rates and observed annual rates were compared with t-tests. A two sided pvalue of 0.05 was set as the level of significance.

Sensitivity analyses
Sensitivity analyses were performed to examine robustness of model findings.
One-way sensitivity analyses were performed by varying the input value of a parameter at a time while the rest were held at their base case values (Table 3). Following transition probabilities of base case were varied over values reported in the literature: (i) low risk cohort received primary androgen deprivation therapy, (ii) active treatment distribution, (iii) PCa recurrence following initial treatments, (iv) PCa death following mCRPC, and (v) overall death following active surveillance or PCa recurrence free. Two-way analysis assessed clinically relevant interaction between parameters and its bearing on survival.

Outcome assessment
The model predicted clinical outcomes were: rate of recurrence following initial treatment, rate of mCRPC, rate of PCa death and overall death. These rates were predicted for the overall cohort, by risk groups and initial treatment strategies over specified time periods. Monte Carlo microsimulations of 1000 samples were used to stabilize model predicted estimate (e.g. mean) and the variability in results across simulated cohorts generated the 95% confidence interval (95% CI) [32].

Model validation
Validation demonstrated good internal consistency of the model. The outcomes predicted by overall, low, intermediate, and high risk cohorts were similar to the observed outcomes derived from the literature, (p50.49), (p50.62), (p50.47), (p50.51), respectively. The annual rates predicted by the model were comparable to the observed annual rates derived from the literature ( Table 4). The model predicted outcomes demonstrated good concordance with the disease evolution and observed outcomes.

Outcome assessment
The predicted mean life expectancy was 20.9 years (95%CI 20.

Discussion
This study delineates for the first time the development, validation, and outcomes predicted by a simulation model for the contemporary management of PCa from diagnosis to the end-of-life. Internal validation demonstrated good internal consistency of the model whereas sensitivity analyses indicated robustness of base case findings. Of note, the findings reported by this study extend to include longterm forecasted outcomes over 15-years whereas no comparable data exist in the literature. It would be of interest to verify if the long-term follow up of cohorts would concur these predicted rates. This model differed from its predecessors on various key aspects. [9][10][11] Preceding decision analytic models lacked contemporary management options such as active surveillance, intensity modulated radiation therapy, and systemic treatments for mCRPC. [5,[8][9][10][11][12] Further, preceding models embraced Markov cohort simulation framework that is memory less to simulate a hypothetical cohort at risk of PCa. [9][10][11] In contrast the current model, (i) from a clinical perspective, this study simulated the contemporary management options of PCa and its bearing on the clinical burden of the disease, and (ii) from a methodological perspective, a Markov model with Monte Carlo microsimulation framework was used. Moreover, the microsimulation with tracker variables overcame the memory less property of Markov cohort simulation embraced by preceding models. [9][10][11] Further, tracker variables enabled individual patient level simulation by integrating transition probabilities based on disease evolution [23]. The contemporary life expectancy at 65 years predicted by the model was comparable to life expectancy reported for Canadian men and other developed nations (17.8-19.3 years) for 2011. [33,34] The predicted HALE for 2013 was higher compared to 13.8 years reported for Canadian men in 2005/2007. [35] The model predicted survival at 5-and 10-year was comparable to contemporary studies. [36][37][38][39][40][41][42][43] Study findings corroborated with the evidence that contemporary management options conferred improved survival. [5,7,8] The existing literature lacked studies on clinical outcomes and survival associated with intensity modulated radiation therapy strategies over long follow-up periods (e.g. 15-year) and this prevented adequate comparisons. Further, comparing predicted outcomes was confronted with heterogeneity in reported rates in the literature. This heterogeneity potentially stemmed from patient characteristics (e.g. age, clinical, pathological parameters, and preferences), definition of outcomes, clinical practice, and length of follow-up [19,40,[44][45][46][47][48][49].
This simulation synthesized evidence on contemporary treatment strategies pertaining to low, intermediate, and high risk groups. For low risk, active surveillance conferred improved clinical outcomes and overall survival compared to active treatments. Clinical outcomes and survival were comparable between radical prostatectomy and brachytherapy followed by intensity modulated radiation therapy in the low risk group. These differences potentially stemmed from disparity in patient characteristics specific to treatment options in the low risk group. [19, 44-46, 50, 51] For intermediate group, the outcomes and survival associated with radical prostatectomy were comparable to intensity modulated radiation therapy+brachytherapy followed by intensity modulated radiation therapy used as monotherapy, and intensity modulated radiation therapy+androgen deprivation therapy. Patients selected for radical prostatectomy compared to radiation therapies were relatively younger with a less severe disease that may explain the difference in predicted outcomes and survival. [45,46,52] For this group and high risk category, addition of brachytherapy to intensity modulated radiation therapy+androgen deprivation therapy improved clinical outcomes and survival compared to intensity modulated radiation therapy+androgen deprivation therapy. These findings are in agreement with preceding studies reporting that addition of brachytherapy to external beam radiation/intensity modulated radiation therapy might have conferred better clinical outcomes and survival. [20,53] The predicted overall survival associated with intensity modulated radiation therapy+androgen deprivation was marginally decreased compared to other multimodal treatment options with intensity modulated radiation. This disparity potentially stemmed from androgen deprivation that may exacerbate cardiometabolic risks and potentially lead to marginal increase in overall mortality. [54][55][56][57][58][59][60] The outcomes associated with treatment options predicted by the model should be generalized with caution since data used to develop the model was retrieved from studies showing differences between treatment groups. Moreover, this study was designed to integrate contemporary treatment options to develop a new decision analytic model and not to evaluate the effectiveness.
There were potential limitations associated with the development of the simulation model. First, assumptions were considered to overcome limitations of the existing literature on observed rates and thereby affect predicted rates. Second, methodological limitations to studies used to develop and validate the model potentially influence the accuracy of state-transition probabilities and predicted outcomes. Third, variation in the epidemiology of the disease, adoption (and reimbursement) of health technologies, and clinical practice across geographic regions limit the generalizability of study findings to healthcare systems from which the model input data was not garnered. However, such a limitation is akin to other disease models. [61][62][63][64] Finally, management complications associated with treatment choices were not accounted by the model.
In conclusion, this study concurrently integrated the evidence from a wide range of contemporary treatment options to manage PCa to generate a new model where predicted rates corroborated observed rates. Study findings demonstrated contemporary PCa management options conferred life expectancy to patients comparable to general population in Canada and other developed nations. This validated model could be used to assess long-term effectiveness of various PCa management strategies. The flexible structure of the model would permit evaluation of outcomes associated with these health technologies in diverse cohorts. This simulation based study identified limitations to the existing clinical literature. Clinical decision making will greatly benefit from simulation based study given the absence of empirical studies that concurrently evaluated active surveillance and contemporary treatment options for low, intermediate, and high risk PCa from diagnosis to end-of-life.