The effect of new cancer drug approvals on the life expectancy of American cancer patients,

Transcription

1 Economics of Innovation and New Technology Vol. 18, No. 5, July 2009, The effect of new cancer drug approvals on the life expectancy of American cancer patients, Frank R. Lichtenberg* Graduate School of Business, Columbia University and National Bureau of Economic Research, 3022 Broadway, 614 Uris Hall, New York, NY 10027, USA (Received 14 February 2008; final version received 25 June 2008) This study attempts to determine the extent to which new cancer drugs introduced during the last 40 years have prolonged the lives of Americans diagnosed with cancer. We use a difference-in-differences approach: we analyze the correlation across cancer sites (breast, prostate, lung, etc.) between changes in the hazard rate of people previously diagnosed with that cancer and changes in the number of drugs that have been introduced to treat that cancer, controlling for variables likely to reflect changes in diagnostic techniques: cancer stage distribution, age at diagnosis, number of people diagnosed (incidence), and use of surgery and radiation. The rate of introduction of new cancer drugs varied considerably across cancer sites and over time. Data on cancer-site-specific drug introductions are constructed using the National Cancer Institute (NCI) Thesaurus and the Drugs@FDA database. Data on all other variables were obtained from the NCI s surveillance, epidemiology, and end results 9 Registries Database, an authoritative source of information on cancer incidence and survival in the USA. We find that the effect of the lagged stock of drugs on the hazard rate of cancer patients is negative and highly significant. This signifies that cancer sites with larger increases in the lagged stock of approved drugs had larger reductions in the hazard rate, ceteris paribus. The impact of the stock of Food and Drug Administration (FDA) approvals on the hazard rate tends to increase steadily for a number of years, peak about 8 12 years after launch, and then decline. This finding is consistent with evidence about the product life cycle of cancer drugs: utilization tends to increase steadily after FDA approval, peak about 6 10 years after launch, and then decline. The cancer stage, the age at diagnosis, and incidence variables have the expected effects on the hazard rate. New cancer drugs introduced during the period are estimated to have increased the life expectancy of cancer patients by almost 1 year (0.94 years). Although the health of cancer patients is less than perfect, the increase in quality-adjusted life-years is not necessarily less than the increase in life expectancy. Since the lifetime risk of being diagnosed with cancer is about 40%, the increase in the lagged stock of cancer drugs is estimated to have increased the life expectancy of the entire US population by 0.38 years. This represents about 8.8% of the overall increase in US life expectancy at birth. Estimated cost per life-year gained does not exceed $6908, which is far below recent estimates of the value of a statistical life-year. Keywords: innovation; cancer; pharmaceutical treatments; econometric methods * frank.lichtenberg@columbia.edu ISSN print/issn online 2009 Taylor & Francis DOI: /

2 408 F.R. Lichtenberg The number of drugs used to treat cancer has expanded rapidly in recent years. The number of cancer drugs launched during the 17-year period is greater than the number launched during the preceding 39-year period (40 vs. 37). The objective of this study is to determine the extent to which new cancer drugs introduced during the last 40 years have prolonged the lives of Americans diagnosed with cancer. Some clinical trials of cancer agents have demonstrated survival benefits. For example, one study showed that the 2-year survival rate of non-hodgkin s lymphoma patients treated with standard chemotherapy and rituximab (approved by the FDA in 1997) was 70%, while that of patients treated with standard chemotherapy alone was only 57%. 1 Another study showed that women who were treated with epirubicin (approved by the FDA in 1999) were 31% less likely to relapse or die within 5 years than women treated with standard chemotherapy alone. 2 A third study (New York Times 2005) reported that standard chemotherapy and hormone treatment work even better than researchers had expected... For middle-aged women with an early stage of the disease, combining the treatments can halve the risk of death from breast cancer for at least 15 years. For instance, a woman under 50 with a tumor big enough to feel, but not invading her lymph nodes, would have a 25% risk of dying of breast cancer in the next 15 years if she had surgery but no drug therapy. Adding both chemotherapy and hormone treatment would drop her risk to 11.6%. But a reliable estimate of the overall effect of new cancer drugs on the longevity of cancer patients cannot be obtained by simply surveying previous clinical studies of specific drugs and cancer sites, for several reasons. First, there is considerable variation in the methodology and metrics used in these studies, rendering comparison and aggregation difficult. Second, these studies may not provide a complete or representative picture; there may be little or no published evidence about the survival impact of some drugs. 3 Third, evidence from clinical trials cannot necessarily be extrapolated to real-world experience. As noted in the Harvard Mental Health Letter (Harvard Medical School 2007), the issue often raised by the favorable outcome of a formal clinical trial is, will the treatment work in the real world? There may be a gap between efficacy and effectiveness efficacy meaning proof in a carefully controlled trial, and effectiveness meaning success in the circumstances of everyday life. Some indicators suggest that the health outcomes of cancer patients are improving. The relative survival rate is a commonly used indicator. The relative survival rate is the ratio of the observed survival rate for a patient group to the expected survival rate for persons in the general population similar to the patient group with respect to age, sex, race, and calendar year of observation. Because it is obtained by adjusting observed survival for the normal life expectancy of the general population of the same age, the relative survival rate is an estimate of the chance of surviving the effects of cancer. 4 The 5-year relative survival rate of people diagnosed with cancer increased from 49% in 1974 to 65% in But this increase in the relative survival rate may overstate the improvement in the relative health outcomes of cancer patients, due to lead time bias. 5 The increase in relative survival could be mainly attributable to relatively earlier diagnosis. 6 Some articles in both medical journals and the popular press have concluded that little real progress has been made. In an article entitled Cancer undefeated in the New England Journal of Medicine, Bailar and Gornik (1997) argued that the effect of new treatments for cancer on mortality has been largely disappointing. A Fortune magazine article was entitled, Why we re losing the war on cancer, and how to win it (Leaf 2004). We will use a difference-in-differences approach to assess the impact of the introduction of new cancer drugs on the longevity of cancer patients: we will analyze the correlation

3 Economics of Innovation and New Technology 409 Table 1. FDA approval years of chemotherapy agents with approved uses for six cancer sites. 151 Malignant neoplasm of stomach Leucovorin calcium 1952 Methotrexate sodium 1953 Fluorouracil 1962 Doxorubicin hydrochloride 1974 Cisplatin 1978 Mitomycin 1981 Etoposide 1983 Docetaxel 1996 Epirubicin hydrochloride Malignant neoplasm of trachea, bronchus, and lung Cyclophosphamide 1959 Vincristine sulfate 1963 Vinblastine sulfate 1965 Doxorubicin hydrochloride 1974 Cisplatin 1978 Mitomycin 1981 Etoposide 1983 Carboplatin 1989 Paclitaxel 1992 Vinorelbine tartrate 1994 Docetaxel 1996 Gemcitabine hydrochloride 1996 Irinotecan hydrochloride Malignant neoplasm of bone and articular cartilage Methotrexate sodium 1953 Cyclophosphamide 1959 Vincristine sulfate 1963 Doxorubicin hydrochloride 1974 Cisplatin 1978 Etoposide 1983 Ifosfamide 1988 Topotecan hydrochloride Malignant neoplasm of female breast Methotrexate sodium 1953 Cyclophosphamide 1959 Fluorouracil 1962 Doxorubicin hydrochloride 1974 Carboplatin 1989 Paclitaxel 1992 Vinorelbine tartrate 1994 Docetaxel 1996 Gemcitabine hydrochloride 1996 Capecitabine 1998 Trastuzumab 1998 Epirubicin hydrochloride Malignant neoplasm of bladder Methotrexate sodium 1953 Cyclophosphamide 1959 Vinblastine sulfate 1965 Doxorubicin hydrochloride 1974 Cisplatin 1978 Gemcitabine hydrochloride Malignant neoplasm of kidney and other and unspecified urinary organs Cyclophosphamide 1959 Vincristine sulfate 1963 Dactinomycin 1964 Doxorubicin hydrochloride 1974 Etoposide 1983 Carboplatin 1989

4 410 F.R. Lichtenberg Figure 1. Cumulative number of chemotherapy agents approved by the FDA with accepted uses for six types of cancer, across cancer sites (breast, prostate, lung, etc.) between changes in the hazard rate of people previously diagnosed with that cancer and changes in the number of drugs that have been introduced to treat that cancer, controlling for variables is likely to reflect changes in diagnostic techniques: cancer stage distribution, age at diagnosis, number of people diagnosed (incidence), 7 and use of surgery and radiation. As illustrated by Table 1 and Figure 1, the change in the number of previously introduced drugs varied considerably across cancer sites. 8 By 1975, four chemotherapy agents with accepted use for malignant neoplasm of the stomach had been approved by the FDA. Four chemotherapy agents had also been approved for five other cancer sites by By 1983, three additional chemotherapy agents had been approved to treat lung cancer, but none had been approved to treat breast cancer. By 2004, the number of approved chemotherapy agents ranged between 6 and 13. Section 1 describes the econometric model. Section 2 of the paper describes the data that will be used to estimate the model. Estimates of the model are presented in Section 3. Interpretation and implications of the estimates are considered in Section Econometric model To investigate the impact of the introduction of new cancer drugs on the survival of patients diagnosed with cancer, we will estimate models of the following form: ln(hazard it ) = β 1 DRUG_STOCK i,t k + β 2 LOC_REG% it + β 3 DISTANT% it + β 4 AGE_MEAN it + β 5 ln(n_diag it ) + β 6 SURGERY% it + β 7 RADIATION% it + α i + δ t + ε it (i = 1,..., 25; t = 1978,..., 2004) (1) where HAZARD it is the hazard rate in year t of people diagnosed with cancer at site i within the previous 5 years; DRUG_STOCK i,t k the cumulative number of drugs approved by the end of year t k that are (currently) used to treat cancer type i; LOC_REG% it the fraction

5 Economics of Innovation and New Technology 411 of people diagnosed with cancer at site i within the previous 5 years whose cancer was at the localized or regional stage; DISTANT% it the fraction of people diagnosed with cancer at site i within the previous 5 years whose cancer was at the distant stage; AGE_MEAN it the mean age of people diagnosed with cancer at site i within the previous 5 years; N_DIAG it the average number of people diagnosed with cancer at site i within the previous 5 years; SURGERY% it the fraction of people diagnosed with cancer at site i within the previous 5 years whose initial treatment included surgery; RADIATION% it the fraction of people diagnosed with cancer at site i within the previous 5 years whose initial treatment included radiation; α i a fixed effect for cancer site i; δ t a fixed effect for year t; and ε it a disturbance. Since the model includes the cancer site and fixed year effects, it is a difference-indifferences model. Negative and significant estimates of β x would indicate that, ceteris paribus, cancer sites with above-average increases in the lagged cumulative number of drugs approved had above-average declines in the hazard rates of recent-diagnosed cancer patients. All models will be estimated via weighted least-squares, weighting by the number of people at risk, i.e. the number of people previously diagnosed who are still alive. Clustered (within cancer-site) standard errors will be reported. Since the dependent variable is the logarithm of the hazard rate, we are, in effect, estimating a proportional hazards model. Such a model assumes that changing an explanatory variable has the effect of multiplying the hazard rate by a constant. Introduced by Cox (1972), 9 the proportional hazards model was developed in order to estimate the effects of different covariates influencing the times-to-failure of a system, and has been widely used in the biomedical field. In his model of endogenous technological change, Romer (1990) hypothesized an aggregate production function such that an economy s output depends on the stock of ideas that have previously been developed, as well as on the economy s endowments of labor and capital. Equation (1) may be considered a health production function, in which the hazard rate is an (inverse) indicator of health output or outcomes, and the cumulative number of drugs approved (DRUG_STOCK) is analogous to the stock of ideas. Note that the hazard rate is hypothesized to depend on the cumulative number of drugs approved k years earlier. This is because utilization of a drug is expected to increase for a number of years after it has been approved. We will estimate Equation (1) using eight different assumed values of k: k = 0, 2, 4,..., 14. We would expect the shape of the relationship between β 1 and k to be similar to the shape of the drug age-sales profile, i.e. the relationship between the utilization of a drug and the number of years since the drug was launched. Thanks to data from the IMS Health, we can provide evidence about the shape of the drug age-sales profile for cancer drugs sold in the USA during the period The shape of the profile is indicated by the drug-age parameters (γ a s) in the following model: ln(util dt ) = γ a + π d + ρ t + ε dt (a = 0, 1, 2,...; d = 1,..., 93; t = 1995,..., 2005) (2) where UTIL dt is the number of standard units of cancer drug d sold in year t; γ a = 1 if drug d was a years old in year t, 0 otherwise; π d a fixed effect for drug d; ρ t a fixed effect for year t; and ε dt a disturbance. We estimated this equation via weighted least squares, weighting by the total number of standard units of the drug sold during Estimates of utilization of cancer drugs, relative to their utilization in the year they were launched (approved by the FDA), are shown in Figure The graph shows that utilization of a drug tends to increase steadily for about 7 years after launch. In years 7 10, annual utilization is about 20 times as high as it was in year 0, and about twice as high as it was in year 4. Utilization appears to

6 412 F.R. Lichtenberg Figure 2. Estimates of utilization of cancer drugs, relative to their utilization in the year they were launched (approved by the FDA). Note: The plotted values are the values of exp(γ a γ 0 ) for a = 0, 1, 2, from the equation ln(util dt ) = γ a + π d + ρ t + ε dt. decline sharply after a drug is about 10 years old. Figure 2 suggests that cancer drugs like many other products follow a product life cycle, which consists of four stages: a market introduction stage, a growth stage, a mature stage, and a decline stage. 11 Since it generally takes about 7 years for a cancer drug to reach peak utilization, we expect the hazard rate to depend more on DRUG_STOCK i,t 7 than it will on DRUG_STOCK i,t or DRUG_STOCK i,t 3, for example. Note that Equation (1) is semi-logarithmic with respect to DRUG_STOCK i,t k, i.e. the log of the hazard rate depends on DRUG_STOCK i,t k. One might specify a log log model instead, whereby the log of the hazard rate depends on ln(drug_stock i,t k ). However for some cancer sites, the value of DRUG_STOCK i,t k was zero early in the sample period; these observations would have to be excluded when estimating a log log model. Moreover the semi-logarithmic model, like the log log model, imposes the reasonable condition of diminishing the marginal impact of new drug introductions on the hazard rate. 12 It is well known that the hazard rate of people diagnosed with cancer is directly related to how far advanced the cancer was at the time of diagnosis. It is conceivable that the rate of chemotherapy innovation is positively correlated, across cancer sites, with the rate of diagnostic innovation. If this is the case, failure to control for site-specific diagnostic innovation could result in overestimation of the impact of chemotherapy innovation on the hazard rate. We therefore include a number of variables that are likely to indicate how far advanced the cancer was at the time of diagnosis. The first two of these variables (LOC_REG% and DISTANT%) are measures of the distribution of patients, by stage at diagnosis. Cancer diagnosed at a distant stage is more advanced than cancer advanced at a localized or regional stage. 13 One would therefore expect (β 2 β 3 ) to be negative: an increase in the ratio of localized/regional cases to distant cases should result in a reduction in the hazard rate. Diagnostic advances are also likely to result in a reduction in the mean age at which people are diagnosed, and an increase in the number of people diagnosed. We therefore expect β 4 > 0 and β 5 < 0. We also control for the fractions of diagnosed patients whose initial treatment included surgery and/or radiation.

7 Economics of Innovation and New Technology Data Data on all variables except DRUG_STOCK were obtained from the surveillance, epidemiology, and end results (SEER) 9 Registries Database, part of the SEER program of the National Cancer Institute (NCI), an authoritative source of information on cancer incidence and survival in the USA. SEER currently collects and publishes cancer incidence and survival data from population-based cancer registries covering approximately 26% of the US population. The SEER program registries routinely collect data on patient demographics, primary tumor site, tumor morphology, and stage at diagnosis, first course of treatment, and follow-up for vital status. The SEER program is the only comprehensive source of population-based information in the USA that includes stage of cancer at the time of diagnosis and patient survival data. The SEER 9 registries are Atlanta, Connecticut, Detroit, Hawaii, Iowa, New Mexico, San Francisco-Oakland, Seattle-Puget Sound, and Utah. In this data set, cases diagnosed from 1973 through 2005 are available for all registries except Seattle Puget Sound (1974+) and Atlanta (1975+). The database contains one record for each of 3,553,244 tumors. We calculated estimates of DRUG_STOCK by combining data from two different sources: the NCI Thesaurus 14 and the Drugs@FDA database. 15 The NCI Thesaurus provides definitions, synonyms, and other information on nearly 10,000 cancers and related diseases, 8000 single agents and combination therapies, and a wide range of other topics related to cancer and biomedical research. It is maintained by a multidisciplinary team of editors, who add about 900 new entries each month. The NCI Thesaurus contains information about relationships between treatments and diseases. In particular, it enumerates the chemotherapy regimens that have accepted uses for specific types of cancer, and the active ingredients contained in those regimens. For example, three chemotherapy regimens (containing a total of four ingredients) are currently used to treat cervical carcinoma: the Cisplatin Taxol (Paclitaxel) regimen, the Cisplatin Topotecan regimen, and the Gemcitabine Cisplatin regimen. We determined the dates at which each active ingredient was approved by the FDA from the Drugs@FDA database. The FDA approval years of the four ingredients were 1978 (Cisplatin), 1992 (Paclitaxel), and 1996 (Topotecan and Gemcitabine). Hence, DRUG_STOCK for cervical carcinoma was zero before 1978, one from 1978 to 1991, two from 1992 to 1995, and four from 1996 to the present. DRUG_STOCK t 7, which due to gradual diffusion of new treatments may be more relevant to survival than contemporaneous DRUG_STOCK, was zero before Sample means, by year, are shown in Table 2. Means are weighted by the number of people at risk, i.e. the number of people diagnosed within the previous 5 years who are still alive. The hazard rate of people diagnosed with cancer within the previous 5 years declined from 22% in 1978 to 14% in The cumulative number of drugs approved by the end of year t 10 increased from 2.8 to 8.0. The fraction of people diagnosed with localized or regional cancer increased from 55% to 74%. Mean age at diagnosis increased from 63.1 in 1978 to 65.3 in 1995 and then declined slightly. The fraction of patients having surgery declined slightly, while the fraction having radiation increased about 19%. Table 3 shows values of the variables in 1978 and 2004 for each of the 25 cancer sites, ranked by a number of patients diagnosed in A few of the hazard rates exceed 100% because following the convention adopted in the statistical software we used (the LIFETEST procedure in SAS version 9.1.3), the hazard is computed at the midpoint of a time interval, i.e. h t = (s t s t+1 )/((s t + s t+1 )/2)), where h t is the hazard rate during period t and s t the probability of survival until the beginning of period t. For example, if s 0 = 100% and s 1 = 24.5%, h 0 = 121%.

8 Table 2. Sample means, by year. Number of Year people at risk HAZARD(%) DRUG STOCK t 10 LOC REG(%) DISTANT(%) AGE MEAN N DIAG Surgery% Radiation% , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , F.R. Lichtenberg Note: Means are weighted by the number of people at risk, i.e. the number of people diagnosed within the previous 5 years who are still alive.

9 Table 3. Values of the variables in 1978 and 2004 for each of the 25 cancer sites, ranked by number of patients diagnosed in HAZARD DRUG DRUG Number of (%) STOCK t STOCK t 10 LOC REG% DISTANT% AGE MEAN N DIAG SURGERY% RADIATION% people at risk Cancer site Malignant neoplasm of trachea, bronchus, and lung 174 Malignant neoplasm of female breast 185 Malignant neoplasm of prostate Malignant neoplasm of colon, rectum, rectosigmoid junction, and anus 188 Malignant neoplasm of bladder 182 Malignant neoplasm of body of uterus 157 Malignant neoplasm of pancreas 151 Malignant neoplasm of stomach ,058 16, ,773 34, , , , , , , ,915 57, ,357 24, ,113 17, (Continued) Economics of Innovation and New Technology 415

10 Table 3. Continued. HAZARD DRUG DRUG Number of (%) STOCK t STOCK t 10 LOC REG% DISTANT% AGE MEAN N DIAG SURGERY% RADIATION% people at risk Cancer site Malignant neoplasm of ovary and other uterine adnexa 189 Malignant ,964 neoplasm of kidney and other and unspecified urinary organs 172 Malignant ,067 melanoma of skin 180 Malignant neoplasm of cervix uteri 200,202 Lymphosarcoma, ,318 reticulosarcoma, and other malignant neoplasms of lymphoid and histiocytic tissue 191 Malignant neoplasm of brain 204 Lymphoid leukemia 205 Myeloid leukemia F.R. Lichtenberg

11 203 Multiple myeloma and immunoproliferative neoplasms 150 Malignant neoplasm of esophagus 201 Hodgkin s disease Malignant neoplasm of liver and intrahepatic bile ducts 171 Malignant neoplasm of connective and other soft tissue 186 Malignant neoplasm of testis Malignant ,506 neoplasm of lip, oral cavity, and pharynx 170 Malignant neoplasm of bone and articular cartilage 163 Malignant neoplasm of pleura Economics of Innovation and New Technology 417

12 418 F.R. Lichtenberg Table 4. Estimates of five different versions of Equation (1): ln(hazard it ) = β x DRUG STOCK i,t k + β y LOC REG% it + β z DISTANT% it + β 4 AGE MEAN it + β 5 ln(n DIAG it ) + β 6 SURGERY% it + β 7 RADIATION% it + α i + δ t + ε it. Column k (DRUG STOCK lag) DRUG STOCK t k Stderr ProbZ < < LOC REG% Stderr ProbZ DISTANT% Stderr ProbZ AGE MEAN Stderr ProbZ ln(n DIAG) Stderr ProbZ < < < SURGERY% Stderr ProbZ RADIATION% Stderr ProbZ < < Note: All models were estimated via weighted least-squares, weighting by the number of people at risk, i.e. the number of people previously diagnosed who were still alive. Clustered (within cancer-site) standard errors are reported. Figure 3. Estimates of β 1 based on eight different values of k (the DRUG_STOCK lag length). Note: Effect on hazard rate is the value of β 1 from Equation (1). Relative utilization is the value of γ a from Equation (2).

13 Economics of Innovation and New Technology 419 Table 5. Estimates of β 1 in Equation (1) based on 10-year lag of DRUG STOCK when each cancer site is excluded. Excluded cancer site Estimate Stderr LowerCL UpperCL Z ProbZ Malignant neoplasm of < lip, oral cavity, and pharynx 150 Malignant neoplasm of < esophagus 151 Malignant neoplasm of < stomach Malignant neoplasm of < colon, rectum, rectosigmoid junction, and anus 155 Malignant neoplasm of liver < and intrahepatic bile ducts 157 Malignant neoplasm of < pancreas 162 Malignant neoplasm of < trachea, bronchus, and lung 163 Malignant neoplasm of < pleura 170 Malignant neoplasm of bone < and articular cartilage 171 Malignant neoplasm of < connective and other soft tissue 172 Malignant melanoma of skin < Malignant neoplasm of < female breast 180 Malignant neoplasm of < cervix uteri 182 Malignant neoplasm of body < of uterus 183 Malignant neoplasm of ovary < and other uterine adnexa 185 Malignant neoplasm of prostate 186 Malignant neoplasm of testis < Malignant neoplasm of < bladder 189 Malignant neoplasm < of kidney and other and unspecified urinary organs 191 Malignant neoplasm of brain < ,202 Lymphosarcoma and reticulosarcoma, Other malignant neoplasms of lymphoid and histiocytic tissue 201 Hodgkin s disease < Multiple myeloma < and immunoproliferative neoplasms 204 Lymphoid leukemia < Myeloid leukemia <0.0001

14 420 F.R. Lichtenberg 3. Empirical results Estimates of five different versions of Equation (1) are shown in Table 4. The equation in column 1 does not include a DRUG_STOCK measure. The equation in column 2 includes the contemporaneous stock of drugs, DRUG_STOCK t. The equations in columns 3 5 include the stock of drugs 5, 10, and 15 years earlier, respectively. To conserve space, we do not report estimates of the 25 cancer-site fixed effects (α i s) and 27 year fixed effects (δ t s) of all equations; complete estimates of the equation in column 4, which includes DRUG_STOCK t 10, are shown in the Appendix, Table A1. In all equations, the cancer stage, age at diagnosis, and incidence variables have the expected effects on the hazard rate. Cancer sites with above-average increases in (LOC_REG% DISTANT%) had above-average declines in the hazard rate. 16 Lower mean age at diagnosis, and higher growth in incidence, reduce the hazard rate. Changes in the fraction of patients having surgery are not correlated with changes in the hazard rate, but cancer sites that had above-average increases in radiation therapy had above-average declines in the hazard rate. Now let us consider the coefficients on the DRUG_STOCK measures in columns 2 5. The coefficient on the contemporaneous stock of drugs in column 2 is not statistically significant: the hazard rate in year t of people diagnosed with cancer within the previous 5 years is not related to the number of drugs approved by the FDA by year t. However the coefficient on DRUG_STOCK t 5 in column 3 is negative and highly significant (p = 0.003). The coefficient on DRUG_STOCK t 10 in column 4 is 60% larger in magnitude than the coefficient on DRUG_STOCK t 5 in column 3. The coefficient on DRUG_STOCK t 15 in column 5 is also negative and significant (p < ), but it is smaller in magnitude than the coefficient on DRUG_STOCK t 10 in column 4. We estimated Equation (1) using eight different values of k (the DRUG_STOCK lag length): k = 0, 2, 4,, 14. The eight resulting estimates of β 1 are plotted in Figure 3. Also shown are estimates of the cancer drug age-utilization profile (γ a, a = 0, 2, 4,, 14) reproduced from Figure 2. The shapes of these two curves are quite similar. Utilization of a cancer drug tends to increase steadily after FDA approval, peak about 6 10 years after launch, and then decline. The impact of the stock of FDA approvals on the hazard rate also tends to increase steadily for a number of years, peak about 8 12 years after launch, and then a decline. As a robustness check, we also estimated Equation (1) based on a 10-year lag of DRUG_STOCK when each cancer site is excluded from the sample. The estimates of β 1 from these 25 regressions are shown in Table 5. In every case, the estimate of β 1 is negative and significant (p 0.012). The largest changes in β 1 occur when two of the most common cancer sites (prostate and lung) are excluded; the magnitude of the estimate of β 1 declines by 34% and 17%, respectively. 4. Implications of the estimates As shown in Table 2, during the period , the hazard rate declined by about a third, from 22% to 14%. Part of this decline was due to changes in variables other the stock of drugs. As shown in Figure 4, the estimates imply that if there had been no changes in LOC_REG%, DISTANT%, AGE_MEAN, N_DIAG, SURGERY%, and RADIATION%, the hazard rate would have declined by about %. If there had also been no change in DRUG_STOCK t 10, the hazard rate would have declined by about %. The increase in the lagged stock of drug accounts for about one-third of the decline in the hazard rate that is not accounted for by the other covariates.

15 Economics of Innovation and New Technology 421 Figure 4. Estimated decline in weighted mean hazard rate: controlling vs. not controlling for DRUG_STOCK t 10. Table 2 shows that mean DRUG_STOCK t 10 increased from 2.8 in 1978 to 8.0 in The coefficient on DRUG_STOCK t 10 in column 4 of Table 4 is Therefore the increase in the lagged drug stock is estimated to have reduced the hazard rate of people diagnosed with cancer within the previous 5 years by 12% (= 1 exp[ ( )]) between 1978 and This allows us to obtain a rough estimate of how much the life expectancy of people diagnosed with cancer has been increased by the introduction of new cancer drugs. These calculations are shown in Table 6. Columns 2 4 show the actual survival, hazard, and density functions of patients diagnosed with cancer in 1978 (N = 77, 918). The 3-year observed survival rate of these patients was 51.8%; their 5-year survival rate was 44.0%. Since 15.0% of these patients were still alive by 31 December 2004 (the cut-off date of the SEER limited-use data set), we cannot calculate the precise life expectancy of this cohort of patients. However, if we assume that patients who died more than 25 years after diagnosis died exactly 30 years after diagnosis, we may conclude that the life expectancy of people diagnosed with cancer in 1978 was 9.1 years. Columns 6 8 show the predicted survival, hazard, and density functions of patients diagnosed with cancer in 1978 if the mean drug stock in 1978 had been equal to its 2004 value (8.0), rather than its 1978 value (2.8). The hazard rates in years 0 4 would have been 12% lower. As a result, the 3-year survival rate would have been 56.8%, and the 5-year survival rate would have been 49.3%. If we assume that the introduction of new cancer drugs had no effect on the hazard rates of patients more than 5 years after diagnosis, and that patients who died more than 25 years after diagnosis died exactly 30 years after diagnosis, we may conclude that the life expectancy of people diagnosed with cancer in 1978 would have been 10.0 years if the mean drug stock in 1978 had been equal to its 2004 value, rather than its 1978 value. Thus, new cancer drugs introduced during the period are estimated to have increased the life expectancy of cancer patients by almost 1 year (0.94 years). 17 According to the NCI, the lifetime risk of being diagnosed with cancer is about 40%. 18 This implies that the increase in the lagged stock of cancer drugs increased the life expectancy of the entire US population by 0.38 years (= 40% 0.94 years). Between

16 Table 6. Calculation of life expectancy of patients diagnosed in 1978: actual vs. predicted with DRUG STOCK Column Actual: patients diagnosed in 1978 Predicted: patients diagnosed in 1978 with DRUG STOCK 1994 Years after Survival Density Hazard Adjustment due to Hazard Survival Density diagnosis MIDPOINT (S t ) (%) (S t S t+1 ) (%) (S t S t+1 )/S t (%) increase in DRUG STOCK t 10 (S t S t+1 )/S t (%) (S t ) (%) (S t S t+1 ) (%) > F.R. Lichtenberg

17 Economics of Innovation and New Technology and 2004, US life expectancy at birth increased by 4.3 years, from 73.5 to 77.8 years (Arias 2007, Table 12). Thus, new cancer drugs accounted for 8.8% of the overall increase in life expectancy at birth. How much did it cost to achieve this additional year of life per person diagnosed with cancer? To determine this cost, I will estimate the average amount spent on cancer drugs for Medicare cancer patients from time of diagnosis until death. According to the NCI, 11.1 million Americans previously diagnosed with cancer were alive on 1 January 2005; 19 60% of them were at least 65 years old. 20 Hence, there were about 6.7 million Medicare-eligible Americans previously diagnosed with cancer. Medicare spent about $2.9 billion on chemotherapy in Hence, annual Medicare chemotherapy expenditure per Medicare-eligible patient previously diagnosed with cancer was $435 (= $2.9 billion/6.7 million). Even if the life expectancy of people diagnosed with cancer were 15 years, average (undiscounted) cancer drug expenditure per cancer patient from diagnosis till death would be $6520 (= 15 years $435/year). The cost per life-year gained would not exceed $6908 (= $6520/0.94 life-years). This is far below recent estimates of the value of a statistical life-year. Murphy and Topel (2003) and Nordhaus (2003) estimate that this value is in the neighborhood of $150,000. Moreover, since drug expenditures calculated above include expenditures on old as well as new drugs, this range represents an upper bound on the cost per life-year gained. Data from the Medical Expenditure Panel Survey suggest that, in general, new drugs drugs approved within the previous years account for about half of total drug expenditure. If this applied to cancer drugs, we should divide the cost per life-year estimates by two. However, given the rapid increase in the number of cancer drugs, new cancer drugs may account for more than half of total cancer drug expenditure. We have examined the effect of new cancer drugs on the life expectancy or number of remaining life-years of cancer patients at the time of diagnosis. Ideally, we would like to measure the effect on the number of quality-adjusted life-years (QALYs). Health economists generally postulate a quality-of-life index (QOL) that ranges between 1 (corresponding to perfect health) and 0 (corresponding to death). The number of QALYs is the number of years multiplied by the average value of the QOL index during those years. For example, 10 years lived at mean QOL = 0.7 equals 7 QALYs. Unfortunately, SEER does not collect any data on the QOL of cancer survivors, so calculating the impact of new cancer drugs on the number of QALYs is not feasible. While new cancer drugs appear to have increased the longevity of cancer survivors by about a year, QOL in that additional year is likely to have been much less than one. However, it is also plausible that, in addition to delaying death, new cancer drugs increased the QOL of people at a given number of years after diagnosis. If this is the case, the increase in QALYs is not necessarily less than the increase in life expectancy. This is illustrated by Figure 5. Suppose that new cancer drugs shifted the time-qol profile from the curve labeled 1978 to the curve labeled This shift reflects the estimated increase in life expectancy, from 9.1 to 10.0 years. The increase in life-years is equal to the sum of areas A and B. This is significantly larger than area A alone the QOL-adjusted value of the additional 0.94 years. But we hypothesize that new drugs also increased average QOL from year 0 to year 9.1. The increase in QALYs during that period is measured by area C. Clearly A <(A + B), but (A + C) is not necessarily smaller than (A + B). Whether it depends on the relative magnitudes of B and C: average QOL in the marginal years versus QOL improvement in the inframarginal years. One might suppose that increasing the longevity of cancer patients will inevitably result in an increase in medical expenditure on them. But Lubitz et al. (2003) found that although

18 424 F.R. Lichtenberg Figure 5. Hypothetical effect on new drugs on time-qol profile. elderly persons in better health had a longer life expectancy than those in poorer health, they had similar cumulative health care expenditures until death. 5. Summary and conclusions This study has attempted to determine the extent to which new cancer drugs introduced during the last 40 years have prolonged the lives of Americans diagnosed with cancer. A reliable estimate of the overall effect of new cancer drugs on the longevity of cancer patients cannot be obtained by simply surveying previous clinical studies of specific drugs and cancer sites. We used a difference-in-differences approach to assess the impact of the introduction of new cancer drugs on the longevity of cancer patients: we analyzed the correlation across cancer sites (breast, prostate, lung, etc.) between changes in the hazard rate of people previously diagnosed with that cancer and changes in the number of drugs that have been introduced to treat that cancer, controlling for variables likely to reflect changes in diagnostic techniques: cancer stage distribution, age at diagnosis, number of people diagnosed (incidence), and use of surgery and radiation. The rate of introduction of new cancer drugs varied considerably across cancer sites and over time. Data on cancer-site-specific drug introductions were constructed using the NCI Thesaurus and the Drugs@FDA database. Data on all other variables were obtained from the NCI s SEER 9 Registries Database, an authoritative source of information on cancer incidence and survival in the USA. The effect of the lagged stock of on the hazard rate of cancer patients was negative and highly significant. This signifies that cancer sites with larger increases in the lagged stock of approved drugs had larger reductions in the hazard rate, ceteris paribus. The impact of the stock of FDA approvals on the hazard rate tends to increase steadily for a number of years, peak about 8 12 years after launch, and then decline. This finding is consistent with evidence about the product life cycle of cancer drugs: utilization tends to increase steadily after FDA approval, peak about 6 10 years after launch, and then decline. Cancer stage, age at diagnosis, and incidence variables had the expected effects on the hazard rate. New cancer drugs introduced during the period were estimated to have increased the life expectancy of cancer patients by almost 1 year (0.94 years). Although the health of cancer patients is less than perfect, the increase in QALYs is not necessarily less than the increase in life expectancy.

19 Economics of Innovation and New Technology 425 Since the lifetime risk of being diagnosed with cancer is about 40%, the increase in the lagged stock of cancer drugs increased the life expectancy of the entire US population by 0.38 years. This represents about 8.8% of the overall increase in US life expectancy at birth. The cost per life-year gained would not exceed $6908, which is far below recent estimates of the value of a statistical life-year. Notes 1. New England Journal of Medicine highlights survival benefit of new treatment for non-hodgkin s lymphoma, 2. Drug regime boosts breast cancer survival, stm. 3. Johnson et al. (2003) reported that only one-fourth of the oncology drug marketing applications approved by the FDA during the period 1 January 1990 to 1 November 2002 were based on direct evidence of survival benefits; 75% of approvals were based on surrogate end points (e.g. reduction in tumor size) However, mean age at time of diagnosis was higher in 2004 than it was in 1978 (64.6 vs. 63.1). 7. As noted in the SEER Cancer Statistics Review, improved earlier detection and diagnosis of cancers may produce an increase in both incidence rates and survival rates. 8. Our procedure for constructing these data is described below. 9. See also Cox and Oakes (1984). 10. The graph shows the estimates of exp(γ a γ 0 ) for a = 0, 1, 2, See Wikipdeia, Product life cycle management, management. 12. Let Y = HAZARD and X = DRUG_STOCK. Then ln Y = β X (dy /dx ) = Y β. The marginal effect of X on Y (dy /dx ) is proportional to Y. Since Y is declining, a diminishing marginal impact of new drug introductions on the hazard rate is a maintained hypothesis. 13. The stages are defined as follows: Localized. An invasive neoplasm confined entirely to the organ of origin. It may include intraluminal extension where specified. For example for colon, intraluminal extension limited to immediately contiguous segments of the large bowel is localized, if no lymph nodes are involved. Localized may exclude invasion of the serosa because of the poor survival of the patient once the serosa is invaded. Regional. A neoplasm that has extended (1) beyond the limits of the organ of origin directly into surrounding organs or tissues; (2) into regional lymph nodes by way of the lymphatic system; or (3) by a combination of extension and regional lymph nodes. Distant. A neoplasm that has spread to parts of the body remote from the primary tumor either by direct extension or by discontinuous metastasis (e.g. implantation or seeding) to distant organs, issues, or via the lymphatic system to distant lymph nodes. We combine localized and regional stages because only the combined figure is reported for prostate cancer, one of the most prevalent cancers. The omitted cancer stage category is unstaged: cases in which information is not sufficient to assign a stage Estimates of the difference (β 2 β 3 are negative and highly significant. 17. Assuming that patients who died more than 25 years after diagnosis died exactly 35 years after diagnosis implies a slightly larger gain in life expectancy from new cancer drugs: 1.03 years. 18. NCI, Lifetime Risk of Developing or Dying of Cancer, find/lifetime_risk.html Medicare Part B Physician/Supplier Data by BETOS, Calendar Year 2004, gov/medicarefeeforsvcpartsab/downloads/betos04.pdf. Data provided by Hoffman et al. (2005) suggest lower expenditure on cancer drugs. They report that total 2003 expenditure on antineoplastic agents by non-federal hospitals was $2.3 billion.

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