Optimal breast cancer risk reduction policies tailored to personal risk level

Abstract

Depending on personal and hereditary factors, each woman has a different risk of developing breast cancer, one of the leading causes of death for women. For women with a high-risk of breast cancer, their risk can be reduced by two main therapeutic approaches: 1) preventive treatments such as hormonal therapies (i.e., tamoxifen, raloxifene, exemestane); or 2) a risk reduction surgery (i.e., mastectomy). Existing national clinical guidelines either fail to incorporate or have limited use of the personal risk of developing breast cancer in their proposed risk reduction strategies. As a result, they do not provide enough resolution on the benefit-risk trade-off of an intervention policy as personal risk changes. In addressing this problem, we develop a discrete-time, finite-horizon Markov decision process (MDP) model with the objective of maximizing the patient’s total expected quality-adjusted life years. We find several useful insights some of which contradict the existing national breast cancer risk reduction recommendations. For example, we find that mastectomy is the optimal choice for the border-line high-risk women who are between ages 22 and 38. Additionally, in contrast to the National Comprehensive Cancer Network recommendations, we find that exemestane is a plausible, in fact, the best, option for high-risk postmenopausal women.

Appendices

Appendix:

Appendix A: Detailed description of the estimation of the disutility associated with hormonal therapy

We estimate δ_t(a) in four steps:

• 1. For each non-breast cancer event, count number of extra events in a population uses hormonal therapy a compared to non-drug users (both populations are assumed to be of size 100,000). Let c_e denote extra event count for event e. These differences are calculated by using the relative risk values from the literature corresponding to age group that t falls into.

• 2. Classify events as “life threatening” (E_lt), “severe” (E_s) and “mild” (E_m). Life threatening events are assumed to have same disutility as a breast cancer. Calculate total adjusted extra event count (c_tot) as follows:

  $$c_{tot} = \sum\limits_{e \in E_{lt}} c_{e} + 0.5 \sum\limits_{e \in E_{s}} c_{e} + 0.25 \sum\limits_{e \in E_{m}} c_{e}$$

  Note: the coefficients are taken from [55].

• 3. Calculate the probability of a breast-cancer-like event (i.e., life threatening event):

  $$p_{e}=1-e^{(-c_{tot}/100,000)}$$

• 4. Calculate δ_t(a) using the disutility of breast cancer (d_BC) [26]:

  $$\delta_{t}(a)= p_{e} d_{BC}$$

Appendix B: One-way sensitivity analyses on the hazard ratio of risk reduction interventions

We conduct a one-way sensitivity analysis for each preventive treatment alternative by varying the hazard ratio between the lower and upper bounds of the corresponding 95% confidence interval. Figure 6 presents the optimal policy considering the upper and lower bounds of the 95% confidence interval of the hazard ratios of mastectomy. When the HR of mastectomy is equal to its upper bound estimate (i.e., effectiveness of mastectomy in reducing the risk of breast cancer is less compared to that assumed in the base-case estimate), the breast cancer lifetime risk threshold for mastectomy increases across all ages (Fig. 6a). For example, the breast cancer lifetime risk threshold for mastectomy increases from 47% to 59% for a 28 year-old woman. Consequently, mastectomy becomes suboptimal at age 61. As the optimality region of mastectomy becomes smaller, only the adjacent optimality regions of the other risk reduction interventions become larger. Specifically, while the optimality regions for tamoxifen and exemestane become larger, there is no impact on the optimality region of raloxifene.

Fig. 6

Optimal policies considering the upper and lower HR bounds of mastectomy. a The HR of mastectomy is equal to its upper bound estimate (0.292). b The HR of mastectomy is equal to its lower bound estimate (0.021)

On the other hand, breast cancer lifetime risk threshold drops to 43% for a 28 year-old woman when the HR of mastectomy is equal to its lower bound estimate (i.e., effectiveness of mastectomy in reducing breast cancer risk is higher compared to that assumed in the base-case estimate) (Fig. 6b). As a result, mastectomy becomes the optimal action for a 71 year-old woman with breast cancer lifetime risk of 85%.

Fig. 7

Optimal action maps considering the upper and lower hazard ratio bounds of tamoxifen. a The 0-5 year HRs of tamoxifen are equal to their upper bound estimate 0.73 and 0.97, respectively. b The 0-5 year HRs of tamoxifen are equal to their lower bound estimate 0.53 and 0.62, respectively

For the sensitivity analysis in which we assume that the 0-5 year and 5-10 year HRs of tamoxifen are equal to their respective upper bound estimates, tamoxifen becomes suboptimal (Fig. 7a). However, the optimality region of tamoxifen significantly enlarges when the 0-5 year and 5-10 year HRs are set to their respective lower bound estimates (Fig. 7b). We observe that tamoxifen becomes optimal even for postmenopausal women with high breast cancer lifetime risk.

Fig. 8

Optimal action maps considering the upper and lower hazard ratio bounds of raloxifene. a The HR of raloxifene is equal to its upper bound estimate (0.79). b The HR of raloxifene is equal to its lower bound estimate (0.51)

Similar to the sensitivity analysis on tamoxifen, raloxifene is not optimal for any breast cancer lifetime risk and age combination when the HR of raloxifene is equal to its upper bound estimate (Fig. 8a). On the other hand, if the HR of raloxifene is equal to its lower bound estimate (Fig. 8b), raloxifene becomes optimal even for women at their early postmenopausal period when the breast cancer lifetime risk is relatively low.

Due to the wide 95% confidence interval of exemestane HR, we observe a significant difference between the two optimal policies in Fig. 9. When the HR of exemestane is equal to its upper bound estimate (Fig. 9a), the optimality regions of both raloxifene and tamoxifen become larger and they both dominate exemestane. On the other hand, if the HR of exemestane is equal to its lower bound, tamoxifen is no longer optimal for premenopausal women because it is more effective for women to wait and initiate exemestane therapy after menopause (Fig. 9b). Also, the optimality region of mastectomy becomes smaller due to the high effectiveness of exemestane.

Fig. 9

Optimal action maps considering the upper and lower hazard ratio bounds of exemestane. a The HR of exemestane is equal to its upper bound estimate (0.70). b The HR of exemestane is equal to its lower bound estimate 

Appendix C: One-way sensitivity analysis on the disutility of risk reduction interventions

We conduct a one-way sensitivity analysis for each preventive treatment alternative by varying the disutility between the lower and upper bound of the corresponding 95% confidence interval (Figs. 10, 11, 12, 13). The one-way sensitivity analyses show that the optimality of an intervention is highly sensitive to its disutility and the optimal decisions change even within the disutility confidence intervals. Hence, these results advocate the use of our modeling framework to personalize the breast cancer risk reduction strategy for each patient.

4.1 D.1: One-way sensitivity analysis on the disutility of exemestane

Fig. 10

Optimal policies considering the upper and lower bounds on the disutility of exemestane. a The disutility of exemestane is equal to its lower bound estimate (from 0.0000001 at age 20 and linearly increase to 0.00002 at age 100). b The disutility of exemestane is equal to its upper bound estimate (from 0.0016 at age 20 and linearly increase to 0.169 at age 100)

4.2 D.2: One-way sensitivity analysis on the disutility of mastectomy

Fig. 11

Optimal policies considering the upper and lower bounds on the disutility of mastectomy. a The disutility of mastectomy is equal to its lower bound estimate (i.e., $\delta_t$ (M) = 0.11 and decreases linearly to 0 in 5 years). b The disutility of mastectomy is equal to its upper bound estimate (i.e., $\delta_t$ (M) = 0.37 and decreases linearly to 0 in 5 years)

4.3 D.3: One-way sensitivity analysis on the disutility of tamoxifen

Fig. 12

Optimal policies considering the upper and lower bounds on the disutility of tamoxifen. a The disutility of tamoxifen is equal to its lower bound estimate (from 0.0008 at age 20 and linearly increase to 0.0047 at age 100). b The disutility of tamoxifen is equal to its upper bound estimate (from 0.0033 at age 20 and linearly increase to 0.2073 at age 100)

4.4 D.4: One-way sensitivity analysis on the disutility of raloxifene

Fig. 13

Optimal policies considering the upper and lower bounds on the disutility of raloxifene. a The disutility of raloxifene is equal to its lower bound estimate (from 0.0004 at age 20 and linearly increase to 0.0007 at age 100). b The disutility of raloxifene is equal to its upper bound estimate (from 0.0026 at age 20 and linearly increase to 0.1702 at age 100)