Risk of heart disease following treatment for breast cancer – results from a population-based cohort study

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    Evaluation Summary:

    This manuscript will be of interest to oncologists, cardiologists, cardio-oncologists, and primary care providers who treat patients with breast cancer and adds to the growing body of literature that identifies the increased risk for cardiotoxicity associated with breast cancer treatment and does so at the general population level. The results of this study are interesting and supported by the data provided, however they must be interpreted with caution as the database utilized includes intended treatment regimens (chemotherapy, radiotherapy) rather than the confirmed treatments patients received.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

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Abstract

There is a rising concern about treatment-associated cardiotoxicities in breast cancer patients. This study aimed to determine the time- and treatment-specific incidence of arrhythmia, heart failure, and ischemic heart disease in women diagnosed with breast cancer.

Methods:

A register-based matched cohort study was conducted including 8015 breast cancer patients diagnosed from 2001 to 2008 in the Stockholm-Gotland region and followed up until 2017. Time-dependent risks of arrhythmia, heart failure, and ischemic heart disease in breast cancer patients were assessed using flexible parametric models as compared to matched controls from general population. Treatment-specific effects were estimated in breast cancer patients using Cox model.

Results:

Time-dependent analyses revealed long-term increased risks of arrhythmia and heart failure following breast cancer diagnosis. Hazard ratios (HRs) within the first year of diagnosis were 2.14 (95% CI = 1.63–2.81) for arrhythmia and 2.71 (95% CI = 1.70–4.33) for heart failure. HR more than 10 years following diagnosis was 1.42 (95% CI = 1.21–1.67) for arrhythmia and 1.28 (95% CI = 1.03–1.59) for heart failure. The risk for ischemic heart disease was significantly increased only during the first year after diagnosis (HR = 1.45, 95% CI = 1.03–2.04). Trastuzumab and anthracyclines were associated with increased risk of heart failure. Aromatase inhibitors, but not tamoxifen, were associated with risk of ischemic heart disease. No increased risk of heart disease was identified following locoregional radiotherapy.

Conclusions:

Administration of systemic adjuvant therapies appears to be associated with increased risks of heart disease. The risk estimates observed in this study may aid adjuvant therapy decision-making and patient counseling in oncology practices.

Funding:

This work was supported by the Swedish Research Council (grant no: 2018-02547); Swedish Cancer Society (grant no: CAN-19-0266); and FORTE (grant no: 2016-00081).

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  1. Author Response

    Reviewer #1 (Public Review):

    Yang, Bhoo-Pathy, Brand et al detail their investigation of a large Swedish cohort compared with age matched controls to estimate the risk of short- and long-term cardiotoxicities of breast cancer therapies in a general breast cancer patient population. They find that breast cancer patients are at significantly increased risk of developing arrhythmia and heart failure both within the first year of cancer diagnosis as well as at least 10 years after. Interestingly, they find that there is an increased risk of ischemic heart disease within the first year after diagnosis, but no increased risk of ischemic heart disease in the long term.

    The authors should be commended for this large cohort study that achieves its goal of identifying the incidence and hazard ratio of cardiotoxicity associated with breast cancer treatment within a general breast cancer population. Their findings of increased risk of heart failure in patients treated with anthracyclines and trastuzumab is consistent with multiple prior studies in the field of cardio-oncology and adds to the validity of the data.

    The finding that there is only a slightly increased (and statistically insignificant) risk of ischemic heart disease after left sided radiotherapy is quite interesting, and as noted by the authors, differs from prior understandings about risk of ischemic heart disease associated with breast radiation therapy. Without data on mean heart dose or total radiation administered the results are hypothesis generating, but should not be utilized to guide medical decision making.

    One of the major limitations of this study is that the authors' goal is to identify the incidence and risk of cardiotoxicity associated with the various breast cancer treatment regimens and determine these risks over time, and as noted by the authors, the registry utilized only includes planned treatment not whether patients did receive this therapy (and what dose of therapy). This is a key point that should be emphasized when interpreting the results.

    As noted by the reviewer, the Stockholm-Gotland Breast Cancer Register only included the intended treatment without a detailed dosage of the therapy. However, the agreement between intended and administrated treatment was about 95% in Sweden (Löfgren,L et, al BMC Public Health. 2019). We have now further explained this in the discussion section.

    In Discussion: “Overall, our results indicate only small risk of heart disease due to radiotherapy in women treated in Sweden after year 2000. Further studies with detailed information on the mean heart dose of radiation or total cumulative radiation dose administered are therefore needed to confirm and provide more context to this finding.”

    In Discussion: “Besides, the Stockholm-Gotland Breast Cancer Register only records intended treatment, not whether patients actually received these therapies. However, the agreement between the intended and administered breast cancer treatment in Sweden has been previously reported to be about 95% (Löfgren et al., 2019).”

    There are several conclusions included in the discussion section that are not supported by the data from the results section and the authors should be careful to suggest mechanisms of cardiotoxicity from an observational population-based study. Examples include suggesting anthracyclines cause cardiotoxicity of the myocardium but not the cardiac vessels; attributing early increased risk of ischemic heart disease to emotional distress alone; and that inhibition of HER2 receptors in myocytes may explain cardiotoxicity caused by trastuzumab. These are interesting hypotheses that would be better supported by references to lab/animal model studies.

    We thank the reviewer for the suggestions and have now added the reference for the suggested mechanisms of cardiotoxicity with lab/animal model studies in the discussion section.

    In Discussion: “As the long-term risk was observed for heart failure but not ischemic heart disease, the cardiotoxic effect of chemotherapy might be mainly on the myocardium mediated by the effect of DNA double-strand breaks through topoisomerase (Top) 2β, but not the cardiac vessels. (Lyu et al., 2007)”

    In Discussion: “The finding that risk of ischemic heart disease in breast cancer patients was only transiently elevated after diagnosis is not unexpected, considering the emotional distress of dealing with a new cancer diagnosis in the patients, which may lead to higher short-term rates of ischemic heart disease (Fang et al., 2012; Schoormans, Pedersen, Dalton, Rottmann, & van de Poll-Franse, 2016). In addition, surgery after breast cancer diagnosis might increase the risk of arterial thromboembolism (Gervaso, Dave, & Khorana, 2021), which includes myocardial infarction, and the effect appears to attenuate one year after diagnosis. (Navi et al., 2017; Navi et al., 2019).”

    In Discussion: “The cardiotoxic effect of trastuzumab meanwhile may be explained by inhibition of the HER2 receptors in myocytes, that activates the mitochondrial apoptosis pathway through modulation of Bcl-xL and -xS, which regulates cell development and growth (Grazette et al., 2004; Yeh & Bickford, 2009)”

    The authors succeed in highlighting the increased risk of cardiotoxicity associated with breast cancer treatment in the observed patient population. Rather than exploring the mechanism of cardiotoxicity for the treatment regimens observed, the data presented may be more useful to propose a longitudinal cardiac monitoring schedule for patients who have been treated for breast cancer, and who the current data suggest, are at long term risk for heart failure and arrhythmia.

    As we found increased long-term risk of heart failure in breast cancer patients, especially for those treated with Anthracyclines +Taxanes and Trastuzumab, we therefore suggest for a prolonged longitudinal cardiac monitoring schedule for ten or more years in these treated patients. We have added the suggestion in the discussion section.

    In Discussion: “Analysis by time since diagnosis revealed long-term increased risks of arrhythmia and heart failure following breast cancer diagnosis, suggesting that a longitudinal cardiac monitoring schedule might be helpful to improve cardiac health in breast cancer patients.”

    Reviewer #2 (Public Review):

    This is a registry based study in which patients diagnosed with locoregional breast cancer ( stage 1-111) from 2001-2008, between the ages of 25-75 were compared to a randomly sampled cohort of 10 women matched by the year of birth and for three specific cardiac conditions as outlined in the key objective. Data was gathered by cross referencing Subject's unique identification numbers in Swedish Cancer Register, Patient Register, Cause of Death, and Migration Register. Prescribed Drug Register was reviewed to gather information about prescribed medication to perhaps infer the medical comorbid conditions for which medication was prescribed. Breast cancer treatment specific information was missing in cases and presumption of use of Anti Her2 therapy was made based on HER2 neu status in some cases. While the primary objective of the study to show increased evidence primarily Heart failure and arrythmias seem to have been met in this patient registry based study, there is some question of the specificity of the data since it was gathered from the various registers and is subject to operator dependent biases.

    Strengths: Study is a long term follow up of patients treated with potential cardiotoxic drugs, confirming the previously known association of specific heart disease to the use of these drugs. Longest follow up seems to be for 16 yrs for the earliest cohort of 2001 and minimum approximately 10 yrs for the cohort of 2008. This study does confirm that long term risk that remains even after the treatment is completed and potentially suggests that more robust cardiac function monitoring guidelines for survivors may be warranted.

    Weaknesses: This is a patient register based study. As outlined above, data was extracted by cross referencing various patient registers. Since the data was dependent on the ICD codes entered in the patient register, there seems to be potential for missed information.

    The Swedish Patient Register has quite high validity for the heart diseases analyzed in this study, with a positive predictive value between 88%-98%, by using the main diagnosis in the register. However, it is still possible that we have missed some information for heart disease and we have emphasized this limitation in the discussion section.

    In discussion: “The Swedish Patient Register has high validity for heart failure, arrhythmia and ischemic heart disease (with positive predictive value between 88%-98%) (Hammar et al., 2001; Ludvigsson et al., 2011), by analysing main diagnoses only. However, misclassification of heart diseases may still have occurred.”

    Preexisting comorbidities were also extracted through Patient Registers hence may be subject to same potential for missed information.

    The Swedish Patient Register has relatively high validity for the majority of comorbid diseases. However, patients without severe symptoms of the diseases might be treated in the primary health care centers, which were not included in the patient register. We have therefore pointed out this limitation in the discussion section.

    In discussion: “In addition, preexisting comorbidities extracted from the patient registers may not include those patients with slight symptoms.”

    In addition, information for use of Trastuzumab was extrapolated from the Her2neu status of the patient when such information may not have been accessible through Prescribed Drug Registers.

    As the majority of HER-2 positive patients were treated in the clinics, the Swedish Prescribed Drug Register does not register their information. Because ~90% of HER-2 positive cancers were treated with trastuzumab between 2005 and 2008 in the Stockholm-Gotland region, we therefore used HER-2 positivity as a proxy for trastuzumab treatment. We have now further explained this in the methods section.

    In Materials and Methods: “As ~90% of HER-2 positive cancers were treated with trastuzumab between 2005 and 2008 in the Stockholm-Gotland region and the Swedish Prescribed Drug Register does not cover data on treatment with trastuzumab, HER-2 positivity was used as a proxy when no registry data on trastuzumab was available during this time period (30% of the HER-2 positive patients had missing information on trastuzumab).

    It is also unclear if there was any protocol in place for cardiac monitoring for patients receiving cardiotoxic chemotherapy or Anti Her2neu agents.

    In Sweden, there is no cardiac monitoring for chemotherapy in routine clinical practice. For HER2-therapy, cardiac monitoring with a thorough cardiac assessment prior to treatment, including history, physical examination, and determination of left ventricular ejection fraction before, during and right after treatment has been mandatory since introduction in clinical routine. We have now added this information to the discussion.

    In discussion: “As there is no cardiac monitoring for chemotherapy in routine clinical practice and cardiac assessment is only performed prior to and during the treatment period for HER-2 positive patients in Sweden, a longer-term cardiac monitoring program might be helpful for these patients.”

    Reviewer #3 (Public Review):

    This matched analysis uses data from patients newly diagnosed with breast cancer the Stockholm-Gotland Breast Cancer Register and data from patients in the general female population in Sweden to ask the question of whether breast cancer diagnosis (and subsequent treatments of breast cancer) is associated with an increased rate of heart disease after treatment. It is impossible to answer this question in a randomized controlled setting and would be unethical to randomize patients to not be treated for their cancer, thus a matched approach in theory would seem to make sense at face value. However, I have some concerns about the analysis that I believe impede their answering the research aims.

    1. With regard to the matched analysis of time to heart disease diagnosis, I have several critiques/questions. First, for the breast cancer cohort, were patients with a diagnosis of heart disease prior to cancer diagnosis included in the analysis? If so, how was the event (which precedes time = 0) incorporated into the analysis? If not, please make sure to make note of this important restriction. I think the latter approach is the better / correct.

    As suggested by Referee 3, we have now excluded those patients with a diagnosis of heart disease prior to cancer diagnosis. We have updated the results and the methods section accordingly.

    In Materials and Methods:

    “We included all patients diagnosed with non-metastatic breast cancer (stages I-III) and without prior diagnosis of heart disease at age 25 to 75 years (N = 8015).”

    Second, for the matched cohort, what is time = 0 for these persons? i.e. how does one interpret "Time since diagnosis" on Figure 1 for a patient who has not been diagnosed with breast cancer?

    We apologize for this misunderstanding and have revised it to “Time since index date (= date of diagnosis, which is the same date for corresponding matched individual from the general population) ” in Figure 1.

    Third, how was the matching incorporated into the FPM? Presumably there should be a frailty term of some sort to indicate the matched groups, within which there is expected to be correlation.

    In the flexible parametric survival model for matched cohort data, a shared frailty term was incorporated into the model to indicate the matched cluster. The maximum (penalized) marginal likelihood method is used to estimate the regression coefficients and the variance for the frailty. We have added this explanation in the methods part.

    In Materials and Methods: “Considering the correlation within the matched clusters, a shared frailty term (as random effects) was incorporated into the model and the maximum (penalized) marginal likelihood method was used to estimate the regression coefficients and the variance for the frailty.”

    1. It is noted that Kaplan Meier curves were used to estimate the cumulative incidence of heart disease. How was death of the patient prior to diagnosis of heart disease handled? I do not think that Kaplan Meier is the correct approach here but rather a Aaalen-Johansen-type estimator that treats death as a competing event. See e.g. https://pubmed.ncbi.nlm.nih.gov/10204198/ A Kaplan Meier will tend to overestimate the event rate when competing events are counted as censoring.

    As suggested by the reviewer, we have now used the Aalen-Johansen method to estimate the cumulative incidence of heart disease and revised the text in the Methods, as well as the tables and figures in the supplement.

    In Materials and Methods,: “Aalen-Johansen estimation was used to assess the cumulative incidences of heart diseases in breast cancer patients and matched reference individuals, while other causes of death were considered as competing events.”

    1. The sentence "Missing indicators were included for the analysis of these covariates in the model" and the results in Table 3 suggest that some missing values were analyzed 'as is', meaning that missingness was used as a category itself. This of course is not desirable and there exists methodology+software for more appropriately handling these data, e.g. multiple imputation with chained equations. For example, how does one interpret that 'unknown chemotherapy' status is positively associated with heart failure but less so than anthracycline based chemo.

    Missingness of the type of adjuvant treatment was considered as a category in the previous version of our manuscript. To address potential biases resulting from missing data, we have now used multiple imputation with chained equations and revised the methods and Table 3 accordingly.

    In Materials and Methods: “Multiple imputation with chained equations was used to deal with the treatment categories with missing information. We replaced the missing data with 10 rounds of imputations and all the covariates were included in the imputation model.”

    1. The reported HRs at the top of page 10 seem incongruous with the FPM model demonstrated in Figure 1, since there is clearly a non-linear relationship between the hazard and the outcome. In other words, there is little sense in which the hazards are proportional at all time points.

    As shown in the FPM model in Fig. 1, HRs were not constant according to time since index date. Therefore, in the revised version, we only showed the HRs separately in <1, 1-2, 2-5, 5-10 and 10-17 years after diagnosis. We have revised the abstract, methods, and Table 2.

    In Abstract: “Time-dependent analyses revealed long-term increased risks of arrhythmia and heart failure following breast cancer diagnosis. Hazard ratios (HRs) within the first year of diagnosis were 2.14 (95% CI = 1.63-2.81) for arrhythmia and 2.71 (95% CI = 1.70-4.33) for heart failure. HR more than 10 years following diagnosis was 1.42 (95% CI = 1.21-1.67) for arrhythmia and 1.28 (95% CI = 1.03-1.59) for heart failure. The risk for ischemic heart disease was significantly increased only during the first year after diagnosis (HR=1.45, 95% CI = 1.03-2.04).”

    In Materials and Methods: “We compared the risk of heart diseases in breast cancer patients with that observed in the matched cohort, using flexible parametric model (FPM) with time since index date as underlying time scale.”

    In Results: “A short-term increase in risks of arrhythmia and heart failure was found in breast cancer patients (Table 2, Figure 1, HR at first year for arrhythmia= 2.14; 95% CI = 1.63-2.81, for heart failure =2.71; 95% CI = 1.70-4.33, respectively).”

    1. It seems unlikely that breast cancer diagnosis could ever be 'protective' for ischemic heart disease. A more constrained model that does not allow for the possibility of HR < 1 could provide a more sensible estimate of this time-dependent HR.

    To the best of our knowledge, the inverse association between breast cancer and the long-term risk of ischemic heart disease is possible considering that some of the reproductive risk factors for breast cancer have protective effect on the risk of ischemic heart disease. We have now discussed about this in Discussion.

    In Discussion: “The long term lower risk of ischemic heart disease in breast cancer patients compared to age-matched women might be explained by the opposite role of reproductive factors in breast cancer and ischemic heart disease. Women with younger age at menarche and older age at menopause were associated with increased risk of breast cancer, while decreased risk of ischemic heart disease were found among these women (Collaborative Group on Hormonal Factors in Breast, 2012; Okoth et al., 2020).”

  2. Evaluation Summary:

    This manuscript will be of interest to oncologists, cardiologists, cardio-oncologists, and primary care providers who treat patients with breast cancer and adds to the growing body of literature that identifies the increased risk for cardiotoxicity associated with breast cancer treatment and does so at the general population level. The results of this study are interesting and supported by the data provided, however they must be interpreted with caution as the database utilized includes intended treatment regimens (chemotherapy, radiotherapy) rather than the confirmed treatments patients received.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

  3. Reviewer #1 (Public Review):

    Yang, Bhoo-Pathy, Brand et al detail their investigation of a large Swedish cohort compared with age matched controls to estimate the risk of short- and long-term cardiotoxicities of breast cancer therapies in a general breast cancer patient population. They find that breast cancer patients are at significantly increased risk of developing arrhythmia and heart failure both within the first year of cancer diagnosis as well as at least 10 years after. Interestingly, they find that there is an increased risk of ischemic heart disease within the first year after diagnosis, but no increased risk of ischemic heart disease in the long term.

    The authors should be commended for this large cohort study that achieves its goal of identifying the incidence and hazard ratio of cardiotoxicity associated with breast cancer treatment within a general breast cancer population. Their findings of increased risk of heart failure in patients treated with anthracyclines and trastuzumab is consistent with multiple prior studies in the field of cardio-oncology and adds to the validity of the data.

    The finding that there is only a slightly increased (and statistically insignificant) risk of ischemic heart disease after left sided radiotherapy is quite interesting, and as noted by the authors, differs from prior understandings about risk of ischemic heart disease associated with breast radiation therapy. Without data on mean heart dose or total radiation administered the results are hypothesis generating, but should not be utilized to guide medical decision making.

    One of the major limitations of this study is that the authors' goal is to identify the incidence and risk of cardiotoxicity associated with the various breast cancer treatment regimens and determine these risks over time, and as noted by the authors, the registry utilized only includes planned treatment not whether patients did receive this therapy (and what dose of therapy). This is a key point that should be emphasized when interpreting the results.

    There are several conclusions included in the discussion section that are not supported by the data from the results section and the authors should be careful to suggest mechanisms of cardiotoxicity from an observational population-based study. Examples include suggesting anthracyclines cause cardiotoxicity of the myocardium but not the cardiac vessels; attributing early increased risk of ischemic heart disease to emotional distress alone; and that inhibition of HER2 receptors in myocytes may explain cardiotoxicity caused by trastuzumab. These are interesting hypotheses that would be better supported by references to lab/animal model studies.

    The authors succeed in highlighting the increased risk of cardiotoxicity associated with breast cancer treatment in the observed patient population. Rather than exploring the mechanism of cardiotoxicity for the treatment regimens observed, the data presented may be more useful to propose a longitudinal cardiac monitoring schedule for patients who have been treated for breast cancer, and who the current data suggest, are at long term risk for heart failure and arrhythmia.

  4. Reviewer #2 (Public Review):

    This is a registry based study in which patients diagnosed with locoregional breast cancer ( stage 1-111) from 2001-2008, between the ages of 25-75 were compared to a randomly sampled cohort of 10 women matched by the year of birth and for three specific cardiac conditions as outlined in the key objective. Data was gathered by cross referencing Subject's unique identification numbers in Swedish Cancer Register, Patient Register, Cause of Death, and Migration Register. Prescribed Drug Register was reviewed to gather information about prescribed medication to perhaps infer the medical comorbid conditions for which medication was prescribed. Breast cancer treatment specific information was missing in cases and presumption of use of Anti Her2 therapy was made based on HER2 neu status in some cases. While the primary objective of the study to show increased evidence primarily Heart failure and arrythmias seem to have been met in this patient registry based study, there is some question of the specificity of the data since it was gathered from the various registers and is subject to operator dependent biases.

    Strengths:

    Study is a long term follow up of patients treated with potential cardiotoxic drugs, confirming the previously known association of specific heart disease to the use of these drugs. Longest follow up seems to be for 16 yrs for the earliest cohort of 2001 and minimum approximately 10 yrs for the cohort of 2008. This study does confirm that long term risk that remains even after the treatment is completed and potentially suggests that more robust cardiac function monitoring guidelines for survivors may be warranted.

    Weaknesses:

    This is a patient register based study. As outlined above, data was extracted by cross referencing various patient registers. Since the data was dependent on the ICD codes entered in the patient register, there seems to be potential for missed information.

    Preexisting comorbidities were also extracted through Patient Registers hence may be subject to same potential for missed information.

    In addition, information for use of Trastuzumab was extrapolated from the Her2neu status of the patient when such information may not have been accessible through Prescribed Drug Registers.

    It is also unclear if there was any protocol in place for cardiac monitoring for patients receiving cardiotoxic chemotherapy or Anti Her2neu agents.

    In the last, I would also like to suggest an external review of biostatistical methods.

  5. Reviewer #3 (Public Review):

    This matched analysis uses data from patients newly diagnosed with breast cancer the Stockholm-Gotland Breast Cancer Register and data from patients in the general female population in Sweden to ask the question of whether breast cancer diagnosis (and subsequent treatments of breast cancer) is associated with an increased rate of heart disease after treatment. It is impossible to answer this question in a randomized controlled setting and would be unethical to randomize patients to not be treated for their cancer, thus a matched approach in theory would seem to make sense at face value. However, I have some concerns about the analysis that I believe impede their answering the research aims.

    1. With regard to the matched analysis of time to heart disease diagnosis, I have several critiques/questions. First, for the breast cancer cohort, were patients with a diagnosis of heart disease prior to cancer diagnosis included in the analysis? If so, how was the event (which precedes time = 0) incorporated into the analysis? If not, please make sure to make note of this important restriction. I think the latter approach is the better / correct. Second, for the matched cohort, what is time = 0 for these persons? i.e. how does one interpret "Time since diagnosis" on Figure 1 for a patient who has not been diagnosed with breast cancer? Third, how was the matching incorporated into the FPM? Presumably there should be a frailty term of some sort to indicate the matched groups, within which there is expected to be correlation.

    2. It is noted that Kaplan Meier curves were used to estimate the cumulative incidence of heart disease. How was death of the patient prior to diagnosis of heart disease handled? I do not think that Kaplan Meier is the correct approach here but rather a Aaalen-Johansen-type estimator that treats death as a competing event. See e.g. https://pubmed.ncbi.nlm.nih.gov/10204198/ A Kaplan Meier will tend to overestimate the event rate when competing events are counted as censoring.

    3. The sentence "Missing indicators were included for the analysis of these covariates in the model" and the results in Table 3 suggest that some missing values were analyzed 'as is', meaning that missingness was used as a category itself. This of course is not desirable and there exists methodology+software for more appropriately handling these data, e.g. multiple imputation with chained equations. For example, how does one interpret that 'unknown chemotherapy' status is positively associated with heart failure but less so than anthracycline based chemo.

    4. The reported HRs at the top of page 10 seem incongruous with the FPM model demonstrated in Figure 1, since there is clearly a non-linear relationship between the hazard and the outcome. In other words, there is little sense in which the hazards are proportional at all time points.

    5. It seems unlikely that breast cancer diagnosis could ever be 'protective' for ischemic heart disease. A more constrained model that does not allow for the possibility of HR < 1 could provide a more sensible estimate of this time-dependent HR.