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Background:  High-dose chemotherapy (HDRx) may improve the prognosis of patients with high-risk breast cancer but at the expense of increased toxicity.  However, no randomized, controlled trials have been published that clearly demonstrate the superiority of HDRx over conventional adjuvant chemotherapy.
Methods:  We developed a simple model to compare benefits and risks of HDRx with conventional adjuvant chemotherapy (SDRx).  The model integrates data on efficacy and risks of two competing treatment strategies into a single decision rule.
Results and Conclusions:  Using data from phase II studies, we show that if a disease-free survival is considered to be the most important outcome, HDRx should be administered when the probability of breast cancer relapse at five years exceeds 54% to 71% for patients with 4 to 9 positive nodes and exceeds 29% to 40% for patients with >9 positive nodes.  If the endpoint of interest is five-year overall survival, then the treatment should be administered when the probability of relapse exceeds 77% to 83% for patients with 4 to 9 nodes involved and 22% to 31% for those with >9 lymph nodes involved.  While awaiting results of randomized, controlled trials to definitively establish the efficacy rate of HDRx, we also found that HDRx could be considered in the management of high-risk breast cancer if its efficacy rate is at least 54% to 60% superior to SDRx in reducing relapse risk in breast cancer patients with 4 to 9 nodes and at least 31% to 38% for >9 positive nodes.  If survival data are used instead of disease-free survival outcomes, HDRx efficacy should be at least 47% to 48% superior to SDRx in reducing death risk in breast cancer patients with 4 to 9 nodes and at least 27% to 30% superior for >9 positive nodes to consider its use in the adjuvant setting.

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Introduction

    Optimal management of high-risk breast cancer has not yet been defined. In particular, the role of high-dose chemotherapy (HDRx) has not yet been established.^1,2 This is due, in part, to the lack of published randomized, controlled trials (RCTs) demonstrating superiority of HDRx over conventional standard-dose chemotherapy (SDRx). In addition, even if data from RCTs were available, it is often unclear how the benefits and drawbacks of competitive treatment strategies should be balanced against each other. This dilemma is especially pronounced in the setting of adjuvant chemotherapy because (1) a certain number of patients may be cured by primary surgical therapy and thus may be unnecessarily exposed to potential life-threatening treatment, and (2) when considering two competitive strategies such as HDRx and SDRx, the first therapy may be more efficacious but more toxic, thereby making it difficult to ascertain that an average benefit/risk ratio of HDRx is indeed superior to SDRx.

    In this paper, we present a method to compare the benefits and risks of alternative treatment options. Specifically, we describe how to determine circumstances under which HDRx should be used in the management of high-risk breast cancer. Due to the lack of RCTs that established the efficacy of HDRx, we also show how to calculate the minimal efficacy rate of HDRx in order to even consider its use in the management of high-risk breast cancer.

Methods

    In our model, the therapy of breast cancer in the adjuvant setting is considered. Only a single disease is considered -- the patient is assumed to either have or not have breast cancer.^3,4 Note that adjuvant therapy relates to treatment decisions that are made without the help of a diagnostic test to increase the diagnostic certainty of the presence of a disease (eg, breast cancer).^3,4 If we knew with absolute certainty that the disease will not recur, we would not administer adjuvant treatment. Since no diagnostic test is available that establishes the diagnosis of relapse, treatment decisions must be based on our estimate of the probability of a disease recurrence. If the probability of breast cancer exceeds the treatment threshold probability, we should administer therapy. When the probability is below the threshold, (adjuvant) therapy should be withheld.^3,4

    Fig 1 shows essential features of the model. A two-choice model⁴ is extended to a three-choice model: to administer HDRx (Rx1), to administer SDRx (Rx2), or to administer no treatment (NoRx). Since the benefits of adjuvant chemotherapy are well established in multiple RCTs,^5-7 the third option (NoRx) is introduced for the sake of complete representation of the clinical problem and not as a viable clinical alternative. The Appendix provides a detailed solution to the decision tree illustrated in Fig 1. Briefly, our goal is to find the threshold probability of the disease (ie, the probability of a breast cancer relapse, p_t) at which the expected value of HDRx is equal to the expected value of SDRx. As Equation 1 in the Appendix shows, this is equal to:

Eq 1:

p_t = (R_HDRx – R_SDRx)/( M • (E_HDRx – E_SDRx))

where R is risk (toxicity) due to HDRx or SDRx. Similarly, E is the efficacy of HDRx or SDRx, and M represents morbidity or mortality of the disease without adjuvant chemotherapy. Note that the efficacy of the therapy relates to the proportional reduction of bad events (such as a relapse or death due to breast cancer) between patients who were given adjuvant therapy and those who were not. Defined this way, the efficacy is equivalent to the therapeutic relative risk reduction⁸ (see the Appendix for further definitions of the terms relating to the treatment benefits). According to this equation, we should administer HDRx if the estimated probability of breast cancer relapse is higher than the threshold probability, p_t. Conversely, SDRx should be given if the probability of a breast cancer relapse is smaller than the p_t.

    Since high-quality data on the efficacy of HDRx are unavailable at this time, we also want to determine the minimal efficacy of HDRx at which this treatment is even worth considering. As the Appendix and Fig 2 show, this is equal to:

Eq 2

(E_HDRx – E_SDRx) >= (R_HDRx – R_SDRx )/M

or

E_HDRx >= (R_HDRx – R_SDRx) /M + E_SDRx

    Our model matches the current intuitive understanding of the factors involved in the treatment decision making: the administration of adjuvant therapy depends not only on the estimated risks and efficacy of competing management strategies, but also on the understanding of the natural history of breast cancer.

Natural History of High-Risk Breast Cancer

    For our analysis, we studied the outcomes of patients with either 4 to 9 or >9 positive axillary lymph nodes who were treated by surgery with or without postoperative radiotherapy. Five-year disease-free survival and overall survival were used as the outcomes of interest for our analysis, which allows comparison between HDRx and SDRx at the same endpoints (given the fact that long-term data on the efficacy of HDRx are lacking). We used data from prospective RCTs^6,9-12 and a large natural-history database that collected outcomes on stage II breast cancer.^13,14 As summarized in Table 1, five-year disease-free survival for patients with 4 to 9 nodes involved with tumor ranges from 17% to 37%. For those with >9 lymph nodes involved, five-year disease-free survival ranges from 0% to 29%. Overall five-year survival ranges from 46% to 50% for patients with 4 to 9 nodes involved and from 23% to 44% for patients with >9 lymph nodes involved. Note that higher values were reported from the natural-history database,¹³ which is retrospective in nature, than from the National Surgical Adjuvant Breast and Bowel Project (NSABP)^9-11 or the Milan National Institute prospective RCTs.^6,7,12 However, prospective data had considerably smaller numbers of patients than did the natural-history database. Also, the NSABP separated high-risk breast cancer patients by those with 7 to 12 lymph nodes involved and those with >12 nodes involved. Given the fact that a considerable overlap exists among all these data, we used both lower and upper bounds to investigate the effects of HDRx vs SDRx.

Table 1. -- Data Used in Analysis of Outcomes Without Adjuvant Chemotherapy
Five-Year Disease-Free Survival:		Five-Year Overall Survival:		Comments and References
4-9 Lymph Nodes	>=10 Lymph Nodes	4-9 Lymph Nodes	>=10 Lymph Nodes
37%	29%	50%	44%	All patients, historical data13,14
25%	20%	Not reported	Not reported	Postmenopausal patients6
17%	0%	Not reported	Not reported	Premenopausal patients6
28% (7-12 nodes)	16% (>=13 nodes)	50% (7-12 nodes)	28% (>=13 nodes)	All patients9,11
30.5% (7-12 nodes)	22% (>=13 nodes)	52% (7-12 nodes)	32.5% (>=13 nodes)	Postmenopausal patients9,11
21% (7-12 nodes)	9.6% (>=13 nodes)	46% (7-12 nodes)	23.5% (>=13 nodes)	Premenopausal patients9,11
Morbidity Range:*		Mortality Range:**
4-9 lymph nodes	>=10 lymph nodes	4-9 lymph nodes	>=10 lymph nodes
63%-83%	71%-100%	50%-54%	56%-77%
* Calculated as 100% – disease-free survival (DFS) (eg, if 5-year DFS is 37%, then morbidity at 5 years is 63%).
** Calculated as 100% – overall survival.

Treatment Risks (Harms)

    The main outcome of interest was mortality. Mortality reported in the literature with HDRx vary from as low as 0% to as high as 22%.^15,16 In 1993, the largest single-arm, prospective study of HDRx reported a therapy-related mortality of 12%.¹⁷ However, a recent analysis of 5,886 patients in North America who were treated with HDRx found a statistically significant trend in decline in mortality with time secondary due to HDRx,¹⁵ with the latest mortality reported to be 5%. We believe that this decline is real and therefore adopted a 5% mortality rate due to HDRx in our analysis.

    Mortality secondary to SDRx is rare and varies from 0% to 1.9%, depending on the regimen used.^6,12,18,19 Since we are interested in comparison of two regimens, we assume that the mortality difference between HDRx and SDRx regimens is 5%.

    Other outcomes of interest are long-term morbidities. However, making decisions on adjuvant therapy based on morbidity data is problematic. Few data have been published on this subject,²⁰ and morbidity outcome measures are often less precise than mortality endpoints because they generally do not occur as discrete events.²¹ Similarly, measures of quality of life, although increasingly recognized to be important in clinical decision making, are less precise, and uniformly accepted methodology for its measurement is still under development.²² Ideally, we would like to combine all treatment-related morbidities such as hepatic, renal, and pulmonary morbidities into a single morbidity/quality-of-life score. However, patients with single vs multiple organ abnormalities usually are not reported separately, making it impossible to combine them in a single useful measure. Likewise, data do not allow distinction whether morbidity from renal dysfunction, for example, is worse than morbidity from pulmonary impairment. For these reasons, our model is well suited for decision making based on mortality endpoints but has limitations when "softer" data are compared. Nevertheless, we performed our benefit/risk analysis using data on the effect of adjuvant therapy on patients’ cognitive functions, which likely represent "the worst-case scenario" of the toxic side effects of a therapy under consideration. In a recently reported study, van Dam et al²³ found that 32% of patients treated with HDRx suffered from a long-term cognitive impairment compared with 17% of patients treated with SDRx and 9% of control patients; thus, the toxicity (risk) is 23% for HDRx and 8% for SDRx. Although this study involved a small number of patients and needs to be confirmed, we adopted these rates as the highest morbidity rates secondary due to these respective treatments in our base case analysis of "a worst-case scenario."

Treatment Benefits

    Care is needed in understanding measures and parameters that are commonly used to express benefit of the treatment. The Appendix shows how equations 1 and 2 change depending on the types of measures used to define the benefits of the treatment. We use three measures to express treatment efficacy: relative risk reduction, the number of patients needed to treat, and the relative benefit increase⁸ (see Appendix). However, main results are presented in terms of relative risk reduction.

Efficacy of Conventional Adjuvant Chemotherapy (E_SDRx)

    We express the efficacy of adjuvant therapy in terms of reducing the risk of relapse and death due to breast cancer.⁸ The most reliable data for estimating efficacy of any treatment are derived from meta-analysis of multiple RCTs.⁵ However, while there are many RCTs evaluating effectiveness of adjuvant chemotherapy, few data randomized only those patients with >4 lymph nodes involved vs no adjuvant chemotherapy. Consequently, the efficacy of SDRx for high-risk breast cancer will have to be extrapolated from subgroup analysis of RCTs that also include patients with fewer than 4 nodes involved and from historical data.^6,7,12,13,24 Using combinations of these data, an average efficacy for relapse reduction can be calculated as 35% (range = 11% to 62%) for 4 to 9 positive lymph nodes and 15% (5% to 25%) for >9 involved nodes, respectively. Efficacy in terms of mortality reduction was calculated as 38% (20% to 74%) for patients with 4 to 9 involved lymph nodes and 21% (3.5% to 34%) for patients with >9 positive lymph nodes.

Efficacy of High-Dose Adjuvant Chemotherapy (E_HDRx)

    The lack of published RCTs is even more apparent when trying to establish efficacy of HDRx in the management of high-risk breast cancer. Again, we used historical data to calculate the efficacy of HDRx. Using data from Peters et al¹⁷ against this historical mark, the efficacy of HDRx in reducing the five-year relapse is calculated to be 71% for patients with 10 or more involved lymph nodes, and the overall death reduction with this regimen at five-year survival is 50%. We assume the same efficacy rate in the treatment of high-risk breast cancer with 4 to 9 positive lymph nodes, although calculation of efficacy from a smaller European study against historical data resulted in efficacy of 77%.²⁵

    Tables 1 and 2 summarize data used in our analysis. Our calculations of relative risk reduction resulted in approximately a 20% difference in efficacy of SDRx between the subgroup of patients with 4 to 9 positive lymph nodes and those with 10 or more positive nodes. At the same time, we assumed no difference in efficacy rates between these two groups of patients for HDRx. While these assumptions introduced a potential bias in analysis, we believe they are based on calculations using the best current available data in the literature. We also express some of our results in terms of NNT (number of patients needed to be treated to prevent one poor outcome) -- a popular therapeutic summary measure of the treatment under consideration (Table 3, see Appendix).²⁶

Table 2. -- Benefit/Risk Data Used in Analysis of Adjuvant Chemotherapy
Benefits: Treatment Efficacy
Relapse Reduction at 5 Years:		Death Reduction at 5 Years:		Comments and References:
4-9 Lymph Nodes	>=10 Lymph Nodes	4-9 Lymph Nodes	>=10 Lymph Nodes
71%	71%	50%	50%	Efficacy of HDRx6,12,13,16,17,25
35% (11%-62%)	15% (5%-25%)	38% (20%-74%)	21% (3.5%-34%)	Efficacy of SDRx6,12,13,16,17
36%	56%	12%	29%	Difference between HDRx and SDRx
Harm: Treatment Toxicity
Chronic: Long-Term Morbidity		Acute: Mortality
23%		5% (0%-22%)		Due to HDRx,15 chronic morbidity refers to cognitive impairment with HDRx23 (projected at 5 years)
8%		0% (0%-2%)		Due to SDRx,6,12,18,19 chronic morbidity refers to cognitive impairment with SDRx19 (projected at 5 years)
15%		5%		Difference between HDRx and SDRx
HDRx = high-dose chemotherapy
SDRx = standard-dose chemotherapy
Efficacy = relative risk reduction (see Appendix for definition)

Table 3. -- NNT (Number of Patients Needed to Be Treated) to Prevent One Additional Relapse or Death in High-Risk Breast Cancer Patients
	Conventional Chemotherapy:		High-Dose Chemotherapy:
	Relapse	Death	Relapse	Death
4-9 Lymph Nodes	5*	5	2	4
>9 Lymph Nodes	9	9	2	4
* This means that we may need to treat an additional 5 patients to prevent 1 relapse.

Results

    How great should the efficacy of HDRx be before it is worth considering in the management of breast cancer? Using comparisons against historical data, Table 2 shows that HDRx can reduce the death risk due to breast cancer by 50% and the relapse of breast cancer by 71% to 77%. These high efficacy rates were reported in nonrandomized, single-arm, prospective studies and could be due to a selection bias favoring the enrollment of patients with better prognostic factors in phase II trials. Garcia-Carbonero et al² recently showed that when selection criteria commonly used in high-dose consolidation chemotherapy trials were applied to high-risk breast cancer treated with SDRx, no difference between disease-free and overall survival was seen in a retrospective comparison between HDRx and SDRx. This study further added to the uncertainty of a true efficacy of HDRx that can be sorted out only in a well-designed, prospective RCT.

    Several trials are currently underway to compare HDRx with SDRx. When planning RCTs, investigators usually try to establish what difference in efficacy rates should be detected between two treatment alternatives. Historical data serve as anchor points to set up efficacy rates for the experimental and control arms. Investigators then calculate the sample size needed to provide enough power to detect the difference in efficacy between the new and established treatments. The toxicities of these treatments are usually not considered at this planning stage. Our equation shows that the minimal efficacy rate that needs to be detected also depends on the toxicity of two treatments that are being compared, along with the data on the outcomes without treatment. Thus, if one regimen is indeed more effective but also more toxic, the equation allows us to show how much more effective a regimen needs to be to compensate for its increased toxicity. Using the baseline assumptions shown in Table 2, Equation 2 shows that HDRx should have an efficacy rate of at least 54% to 60% to be superior to SDRx in reducing relapse risk in breast cancer patients with 4 to 9 nodes and at least 31% to 38% for those with >9 positive nodes. Its efficacy should result in a reduction of death risk of at least 47% to 48% in breast cancer patients with 4 to 9 positive nodes and at least 27% to 30% for those with >9 positive nodes to be superior to SDRx.

    Fig 2 represents a graph to determine the minimal efficacy rate of HDRx with respect to other possible values of SDRx and outcomes without treatment. All current trials sponsored by the National Cancer Institute (NCI) are powered to detect much smaller differences in efficacy rates.¹ It is likely that one of these NCI trials will produce a statistically significant result at the smaller efficacy rate but at the increased toxicity risks (see Discussion). Our method enables the calculation of the magnitude of efficacy needed to offset its increased toxicity. The Appendix also shows another useful measure of clinical interest: the minimally required net efficacy/risk (E/R) ratio, defined as:

(E_HDRx – E_SDRx)/(R_HDRx – R_SDRx)

 is at least as large as the reciprocal value of the probability of a clinical outcome for untreated disease (1/M). In another words, if the five-year survival of patients with 10 or more positive nodes is 20%, the net E/R ratio should be at least 5 (= 1/0.2) in order to consider the use of HDRx. In this case, HDRx should not be considered if its E/R ratio is not at least five times greater than that of SDRx. Minimal efficacy of HDRx can also be expressed in terms of NNT -- as the lowest NNT at which HDRx may be administered (Table 4).

Table 4. -- Lowest NNT at Which High-Dose Chemotherapy May Be Administered*
	To Prevent Relapse:	To Prevent Death:
4-9 Lymph Nodes	4	4
>9 Lymph Nodes	6	6
* Calculated for fixed mortality difference between HDRx and SDRx of 5%. If NNT is greater than that shown above, HDRx should never be administered (see Appendix).

    When should a high-dose chemotherapy be administered? Assuming that the data in Table 2 will stand the scrutiny of RCTs, under which circumstances should HDRx -- a potentially fatal treatment that may be unnecessary in approximately 30% of patients -- be administered? As discussed in the Methods section and the Appendix, it is better on average to administer therapy to the patient if the probability of a relapse is greater than the threshold probability. If only disease-free survival is considered, then we should administer HDRx when the probability of breast cancer relapse at five years exceeds approximately 54% to 71% for patients with 4 to 9 positive nodes and 29% to 40% for patients with 10 or more positive lymph nodes. If the probability of a relapse in patients with more than 9 positive lymph nodes is 100%, the threshold for action decreases to 29%. Therefore, our analysis confirms the current practice of most physicians, which is the tendency to have a lower threshold for administering HDRx in patients with >9 positive lymph nodes than in those with 4 to 9 positive nodes.

    If the endpoint of interest is five-year overall survival, then the treatment should be administered when the probability of relapse is above 77% to 83% for patients with 4 to 9 nodes involved and 22% to 31% for those with 10 or more lymph nodes involved. In current practice, most patients have such poor prognostic factors that HDRx appears to be justified in most clinical circumstances (see Discussion). Using somewhat different assumptions, Elfenbein and colleagues²⁷ found the treatment threshold for administering HDRx to be 47%. Fig 3 shows a method to determine the action treatment thresholds depending on assumptions about difference in efficacy of HDRx and SDRx for various values of the relapse risk.

Discussion

    Breast cancer remains a major public health problem. The number of deaths resulting from breast cancer in 1998 is estimated to be approximately 43,500.²⁸ More than 25% of these patients will present with >4 axillary positive lymph nodes for breast cancer.¹ These patients have an extremely poor prognosis with an estimated five-year relapse-free survival of only 37% for patients with 4 to 9 positive nodes and 29% for patients with >9 positive nodes (Table 1).¹³ HDRx with autologous/stem cell rescue has been proposed as a promising treatment strategy based on initial results of phase II studies.^16,17,25 However, it is unclear if these encouraging results reflect a true superiority of HDRx compared to conventional therapy or if they represent the impact of selection criteria that are used to enroll patients into phase II studies with HDRx.^1,2 One RCT reported in abstract form has not yet resulted in a clear advantage of HDRx over SDRx.²⁹ Several more RCTs are in progress that hopefully will definitively establish the efficacy of HDRx in the management of high-risk breast cancer. However, these trials will not address the issue of how to integrate the benefits and risks of competing treatment alternatives into a practical decision-making strategy. In this paper, we show that it is possible to incorporate the benefits and risks of HDRx and SDRx to calculate practical threshold for the treatment action, and we also show that if the probability of relapse of breast cancer at five years is above the calculated threshold, then HDRx should be administered. Depending on the data used (Tables 1 and 2), this threshold for action varies from as low as 22% to as high as 83%. This wide range for the action threshold reflects not only current uncertainty about data quality used for our analysis, but also the difficulties in estimating long-term morbidities due to both HDRx and SDRx. The latter also represents the major limitation of our model, which does not consider patient preferences toward a variety of side effects. Our model does not distinguish between which side effect is worse (renal impairment vs cardiac dysfunction, for example). Similarly, the model is neutral between the immediate risk of dying and the prospect for a long-term survival that can be obtained with HDRx.³⁰ However, after understanding these constraints, the model is very effective when mortality data are used and may help to integrate benefits and harms into practical treatment action.

    How do we propose to use our model in actual clinical practice? We developed this model to assist practicing physicians in deciding whether or not to administer HDRx in patients with high-risk breast cancer. As shown above, the physician must first incorporate published data on benefits and risks related to treatment from a large group of patients with breast cancer to calculate the threshold probability of action (Tables 1 and 2, Equation 1, Fig 3). The physician must then estimate the probability of breast cancer relapse for the individual patient. SDRx is indicated if the probability is lower than the treatment threshold. HDRx should be given if the probability of breast cancer relapse is greater than the action threshold. The key then becomes the assessment of the probability of breast cancer relapse in the individual patient. Numerous prognostic factors have been identified during last several decades that help to predict the course of breast cancer in individual patients.³¹ Of the multiple factors identified, involvement of axillary nodes with tumors has been consistently shown to be the most important predictor of survival and disease-free survival in breast cancer.³¹ In many analyses, tumor size follows axillary node status in importance when predicting posttreatment recurrence and death³¹ in breast cancer. Taken together, these two simple parameters have a strong predicting value. For example, a patient with tumor size >5 cm and with >4 positive lymph nodes has approximately a 55% probability of dying due to breast cancer at five years. In this particular patient, HDRx should be only 16.5% more efficacious from SDRx in order to be recommended to the patient. In an Italian study,⁶ none of the premenopausal patients without treatment who had >10 positive lymph nodes was disease-free beyond one year. Assuming that we will accept this figure of virtual certainty of breast cancer relapse in this subset of patients (and that we would administer HDRx only at the threshold probability of 100%), then we should administer HDRx if it is only 5% more efficacious than SDRx (see Appendix).

    Similarly, other prognostic factors (eg, tumor grade, hormonal and epidermal growth factor receptor status, oncogene and tumor suppressor gene expression) can be used to help in assessing the probability of relapse in an individual patient.³¹ However, no prognostic system was developed to assess the probability of recurrence and death in the setting of adjuvant HDRx for high-risk breast cancer. Further study is needed to better predict the course of breast cancer in individual patients with >4 positive lymph nodes.

    As mentioned above, the true efficacy of HDRx is unknown. Therefore, our practical recommendations will have to be tentative until more definitive data are collected. To answer the question about whether HDRx is even worth considering, we developed a simple formula showing the circumstances under which the presumably higher efficacy of HDRx will offset the higher risk associated with this therapy. We also believe that this formula may be beneficial in the planning and design of clinical trials. In clinical trials, investigators usually design the study based on comparison of efficacy rates and do not consider risks associated with each of the interventions studied. For example, the trial often demonstrates that treatment A is more efficacious than treatment B but is also more toxic. Physicians must then decide if the more efficacious or the less risky treatment should be given. No method has been developed to show how much more efficacious a treatment should be in order to compensate for its increased toxicity. We believe that Equation 2 and Fig 2 can be used for these purposes.

    In conclusion, we have presented a simple benefit/risk analysis for the setting of adjuvant chemotherapy of high-risk breast cancer. The model also can be applied to other clinical situations such as consolidation treatment with high-dose therapy in acute myelogenous leukemia and acute lymphoblastic leukemia. The model’s power will improve as more definitive data on treatments efficacy and risks are collected.

APPENDIX

Deriving Threshold Equations

    We derived our analysis from a simple decision model with six different outcomes (Fig 1):

D+,Rx1     D–,Rx1     D+,Rx2
D–,Rx2     D+,NoRx     D–,NoRx

    A detailed description of the decision dilemma facing two treatment alternatives is presented elsewhere.⁴

    The three alternatives are to administer treatment Rx1, to administer treatment Rx2, or to administer no treatment (NoRx). The state [D+,Rx1] or the state [D+,Rx2] represents the outcome for those patients who have the disease and were given the first (or second) treatment, and the state [D–,Rx1] or [D–,Rx2] relates to the outcome for those patients who are given the first (or second) treatment and have no disease. If a treatment is not administered, the state [D–,NoRx] relates to the outcome for those patients who do not have disease and were not given any treatment. On the other hand, [D+,NoRx] describes outcomes for those patients who have the disease and are not given any treatment.

Defining the Treatment Benefits

    The treatment itself may have beneficial effects (ie, it exerts its effects on the disease) and adverse effects (risks or toxicity). In general, this beneficial effect can be expressed in terms of reducing the risk of a poor outcome (eg, adjuvant chemotherapy reduces death risk due to breast cancer) or increasing the probability of a good outcome (eg, adjuvant chemotherapy increases the probability of survival). Both of these probabilities (reducing poor outcome or increasing good outcome) can be presented in terms of NNT (number of patients needed to be treated) to prevent one poor outcome or to increase one good outcome (see below).⁸

    The effect of the treatment on the mortality/morbidity (Mrx) can be expressed through the efficacy (E) of the treatment and the mortality/morbidity without treatment (M) as:

Mrx = (1 – E ) • M

    Note that our E is equivalent to the treatment relative risk reduction (RRR) (the proportionate reduction in the probability of adverse outcome resulting from treatment), which is a customary way to express the efficacy of a therapy:

E = RRR = (M – Mrx )/M

    Also, note that if E = 1, then the treatment completely eliminates the disease, and if E = 0, then the mortality/morbidity is unchanged from the baseline risk of a disease. For example, if E = 30%, this means that a particular treatment reduces the probability of undesirable effect of the disease by 30%.

    If survival data is tracked instead of the morbidity/mortality data, the relative benefit increase (RBI) is calculated as:

RBI = (M – Mrx)/(1 – M )

    Note that instead of RBI, we can also use survival data with (S_rx = 1 – M_rx) and without (S = 1 – M) treatment.

    The number of patients needed to be treated (NNT) has emerged as an attractive concept that can provide a real understanding about the effectiveness of therapy.²⁶ A reciprocal of the difference in absolute probability of outcomes between two treatment alternatives is equal to the number of patients needed to be treated (NNT) to produce a therapeutic difference for one patient:

NNT = 1 /(M – Mrx)

Defining Outcome Utilities

    Each of the outcomes shown in Fig 1 has a certain value, and this relative value is noted as the utility of the outcome.^3,30 Utilities associated with a particular clinical outcome can be expressed in different units such as length of life, absence of pain, dollar value, or the strength of individual patient preference for an outcome.^3,30 We will express utilities for the six outcomes as the percentage of the number (or the probability) of patients who will be free from consequences of the disease or toxicity of the treatment. When considering the utility for the state [D+,Rx] (where Rx could be the first or second treatment), we must consider the effects of the disease and treatment on the state of health.

    The utility for the health state [D+,Rx] is equal to:

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