In his model of endogenous technological change, Romer [17] 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. The premature mortality model that I will estimate may be considered a health production function, in which premature mortality is an inverse indicator of health output or outcomes, and the cumulative number of drugs approved is analogous to the stock of ideas. The first model will be of the following form:
$${ \ln }({\text{YPLL75}} _{{{\text{s}},t}} ) = \beta_{k} {\text{CUM}}\_{\text{NCE}}_{{{\text{s}},t - k}} + \gamma { \ln }({\text{CASES}}\_{\text{LT75}} _{{{\text{s}},t - 1}} ) + \pi {\text{AGE}}\_{\text{DIAG}}_{{{\text{s}},t - 1}} + \alpha_{\text{s}} + \delta_{t} + \varepsilon_{{{\text{s}},t}}$$
(1)
where
YPLL75s,t
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= years of potential life lost before age 75 from cancer at site s per 100,000 people below age 75 in year t (t = 1995, … , 2012)
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CUM_NCEs,t–k
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= ∑d INDds REGISTEREDd,t−k
= the number of new chemical entities (drugs) to treat cancer at site s that had been registered in Switzerland by the end of year t − k
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INDds
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= 1 if drug d is used to treat (indicated for) cancer at site s
= 0 if drug d is not used to treat (indicated for) cancer at site s
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REGISTEREDd,t–k
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= 1 if drug d was registered in Switzerland by the end of year t − k
= 0 if drug d was not registered in Switzerland by the end of year t – k
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CASES_LT75s,t−1
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= the number of new cases of cancer at site s diagnosed in people below age 75 per 100,000 people below age 75 in year t − 1
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AGE_DIAGs,t−1
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= the mean age at which people who were diagnosed with cancer at site s in year t − 1 were diagnosed
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α
s
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= a fixed effect for cancer at site s
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δ
t
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= a fixed effect for year t
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- The most recent available incidence data are for the year 2011
Inclusion of year and cancer-site fixed-effects controls for the overall decline in premature cancer mortality and for stable between-disease differences in premature mortality.Footnote 5 A negative and significant estimate of β
k
in Eq. (1) would signify that diseases for which there was more pharmaceutical innovation had larger declines in premature mortality. \(\beta_{k} \times \, \left( {{\text{CUM}}\_{\text{NCE}}.,_{2012 - k} - {\text{CUM}}\_{\text{NCE}}.,_{1995 - k}}\right)\), where CUM_NCE.,
t−k
is the mean of CUM_NCEs,t−k
, is an estimate of the decline in Swiss premature cancer mortality during the sample period (1995–2012) that can be attributed to the introduction of new drugs. The functional form of Eq. (1) has the property of diminishing marginal productivity: the absolute reduction in premature mortality declines with each successive increase in the number of drugs.
As illustrated by Fig. 6, the data exhibit heteroskedasticity: cancer sites with larger total premature mortality during 1995–2012 had smaller (positive and negative) annual percentage fluctuations in YPLL75. Equation (1) will therefore be estimated by weighted least-squares, weighting by the mean premature mortality rate during 1995–2012 ((Σt YPLL75s,t)/18). The standard errors of Eq. (1) will be clustered within cancer sites.
Although one would expect an increase in true cancer incidence to increase premature cancer mortality, cancer incidence rates are subject to measurement error, so one should not necessarily expect the coefficient on measured cancer incidence (γ) to be positive. Let I and I* represent measured and true cancer incidence, respectively. Then I = (I/I*) × I*, and log(I) = log(I/I*) + log(I*). Measured cancer incidence can increase for two reasons: an increase in true cancer incidence, or an increase in the ratio of measured incidence to true incidence. The latter could occur as a result of increasing quantity or quality of cancer screening. More and better cancer screening could lead to earlier diagnosis, which might reduce premature mortality. Therefore the effect on premature mortality of increases in I* and increases in (I/I*) may offset one another: the former is likely to increase premature mortality, but the latter may reduce it. For this reason, although controlling (in an unrestrictive manner) for measured incidence in the premature mortality model seems appropriate, we should not be surprised if we don’t find a significant effect of measured incidence on premature mortality.
Equation (1) also includes mean age at time of diagnosis (AGE_DIAG) as an explanatory variable. Like the number of cases diagnosed, mean age at time of diagnosis could change for two reasons. First, the true mean age of onset of the disease could change; a reduction in the true mean age of onset would be likely to increase premature mortality. Second, the lag from time of onset to time of diagnosis could change; a reduction in this lag, which would reduce mean age at time of diagnosis, would be likely to reduce premature mortality. Hence, the sign of the coefficient (π) on AGE_DIAGs,t−1 in Eq. (1) is ambiguous, a priori. Nevertheless, it seems desirable to control for mean age at time of diagnosis in the premature mortality equation.Footnote 6
The measure of pharmaceutical innovation in Eq. (1)—the number of chemical substances previously commercialized to treat a disease—is not the theoretically ideal measure. Premature mortality is presumably more strongly related to the drugs actually used to treat a disease than it is to the drugs that could be used to treat the disease. A preferable measure is the mean vintage of drugs used to treat cancer at site s in year t, defined as \({\text{VINTAGE}}_{\text{st}} = \sum_{\text{d}} Q_{\text{dst}} {\text{LAUNCH}}\_{\text{YEAR}}_{\text{d}}/{\sum_{\text{d}}} Q_{\text{dst}}\), where Q
dst = the quantity of drug d used to treat cancer at site s in year t, and LAUNCH_YEARd = the world launch year of drug d.Footnote 7 Unfortunately, measurement of VINTAGEst is infeasible: even though data on the total quantity of each drug in each year (Q
d.t
= Σs Qdst) are available, many drugs are used to treat multiple diseases,Footnote 8 and there is no way to determine the quantity of drug d used to treat cancer at site s in year t.Footnote 9 However, Lichtenberg [9] showed that in France, there is a highly significant positive correlation across drug classes between changes in the (quantity-weighted) vintage of drugs and changes in the number of chemical substances previously commercialized within the drug class.
Pharmaceutical innovation is not the only type of medical innovation that is likely to reduce premature mortality. Other medical innovation, such as innovation in diagnostic imaging, surgical procedures, and medical devices, is also likely to affect premature mortality. Therefore, measures of these other types of medical innovation should be included in the Eq. (1). Unfortunately, longitudinal disease-level measures of non-pharmaceutical medical innovation are not available for Switzerland. However, failure to control for non-pharmaceutical medical innovation is unlikely to bias estimates of the effect of pharmaceutical innovation on premature mortality, for two reasons. First, more than half of US funding for biomedical research came from pharmaceutical and biotechnology firms [4]. Much of the rest came from the federal government (i.e., the NIH), and new drugs often build on upstream government research [18]. The National Cancer Institute [14] says that it “has played an active role in the development of drugs for cancer treatment for 50 years… [and] that approximately one half of the chemotherapeutic drugs currently used by oncologists for cancer treatment were discovered and/or developed” at the National Cancer Institute.
Second, previous research based on US data indicates that non-pharmaceutical medical innovation is not positively correlated across diseases with pharmaceutical innovation. Lichtenberg [9] showed that, in the US during the period 1997–2007, the rate of pharmaceutical innovation was not positively correlated across diseases with the rate of medical procedure innovation and may have been negatively correlated with the rate of diagnostic imaging innovation. Also, Lichtenberg [10] found that estimates of the effect of pharmaceutical innovation on US cancer mortality rates were insensitive to the inclusion or exclusion of measures of non-pharmaceutical medical innovation. This suggests that failure to control for other medical innovation is unlikely to result in overestimation of the effect of pharmaceutical innovation on longevity growth.
In Eq. (1), premature mortality from cancer at site s in year t depends on the number of new chemical entities (drugs) to treat cancer at site s launched in Switzerland by the end of year t − k, i.e., there is a lag of k years. Eq. (1) will be estimated for different values of k: k = 0, 5, 10, 15, 20, 25, 30.Footnote 10 One would expect there to be a substantial lag because new drugs diffuse gradually—they won’t be used widely until years after commercialization. Figure 7 shows data on the mean number of standard unitsFootnote 11 of cancer drugs sold (in thousands) in Switzerland in 2012, by period of launch in Switzerland. Mean utilization in 2012 of drugs launched after 2000 is only 19 % as high as mean utilization of drugs launched during 1951–1990, and 11 % as high as mean utilization of drugs launched during 1991–2000.
The effect of a drug’s launch on premature mortality is likely to depend on both the quality and the quantity of the drug. Indeed, it is likely to depend on the interaction between quality and quantity: a quality improvement will have a greater impact on mortality if drug utilization (quantity) is high. Although newer drugs tend to be of higher quality than older drugs (see [11]), the relative quantity of very new drugs is quite low, so the impact on mortality of very new drugs is lower than the impact of older drugs.
Premature mortality in year t presumably depends more on the number of drugs actually used to treat patients in year t (N_NCE_TREATs,t
) than it does on the number of drugs registered by year t (or t − k). (Some drugs are not used until several years after registration.) CUM_NCE
s,t−k
might be considered a “noisy indicator” of N_NCE_TREAT
s,t
. In other words, CUM_NCE
s,t−k
is subject to measurement error. Measurement error often biases coefficients towards zero. McKinnish [12] argued that when explanatory variables in panel data models are subject to measurement error, long-difference estimates may be less downward biased than fixed-effects estimates,Footnote 12 and that “it seems prudent for researchers to estimate both fixed-effects and long-differences models whenever feasible”. Therefore, in addition to estimating the fixed-effects model of the level of premature mortality (Eq. 1) using annual data, I will estimate a long-difference model that can be derived from Eq. (1). A special case of Eq. (1), when t = 2012 (the final year of the sample period) and incidence and mean age at diagnosis are excluded (for simplicity) is:
$${ \ln }\left( {{\text{YPLL75}} _{{{\text{s}}, 20 1 2}} } \right) = \beta_{k} {\text{CUM}}\_{\text{NCE}}_{{{\text{s}}, 20 1 2- k}} + \alpha_{\text{s}} + \delta_{ 20 1 2} + \varepsilon_{{{\text{s}}, 20 1 2}}$$
(2)
When t = 1995 (the initial year of the sample period) and incidence and mean age at diagnosis are excluded:
$${ \ln }\left( {{\text{YPLL75}} _{{{\text{s}}, 1 9 9 5}} } \right) = \beta_{k} {\text{CUM}}\_{\text{NCE}}_{{{\text{s}}, 1 9 9 5- k}} + \alpha_{\text{s}} + \delta_{ 1 9 9 5} + \varepsilon_{{{\text{s}}, 1 9 9 5}}$$
(3)
Subtracting (3) from (2) yields a simple linear regression:
$${ \ln }\left( {{\text{YPLL75}} _{{{\text{s}}, 20 1 2}} } \right) - { \ln }\left( {{\text{YPLL75}} _{{{\text{s}}, 1 9 9 5}} } \right) = \beta_{k} \left( {{\text{CUM}}\_{\text{NCE}}_{{{\text{s}}, 20 1 2- k}} - {\text{CUM}}\_{\text{NCE}}_{{{\text{s}}, 1 9 9 5- k}} } \right) + \, \left( {\delta_{ 20 1 2} - \delta_{ 1 9 9 5} } \right) + \left( {\varepsilon_{{{\text{s}}, 20 1 2}} - \varepsilon_{{{\text{s}}, 1 9 9 5}} } \right)$$
(4)
It is quite plausible that (CUM_NCE
s,2012−k
− CUM_NCE
s,1995−k) is subject to less measurement error than CUM_NCE
s,t−k
: the long-run (12-years) change in the number of drugs used to treat a condition can be measured more reliably than the number of drugs used to treat a condition in a particular year.
The measure of pharmaceutical innovation, CUM_NCE
s,t−k
= ∑d INDds LAUNCHd,t−k
, is based on whether drug d had an indication for cancer at site s at the end of 2011. One would prefer to base the measure on whether drug d had an indication for cancer at site s at the end of year t − k. FDA data indicate that about one in four new molecular entities has supplemental indications, i.e., indications approved after the drug was initially launched.Footnote 13
In Eq. (1), the measure of premature mortality is the number of years of potential life lost before age 75. To assess the robustness of my results, I will estimate models similar to Eq. (1), using the age threshold 65 as well as 75.
Chemical substances are divided into different groups according to the organ or system on which they act and their therapeutic, pharmacological, and chemical properties. In the anatomical therapeutic chemical (ATC) classification system developed by the World Health Organization Collaborating Centre for Drug Statistics Methodology, drugs are classified in groups at five different levels. The highest (1st) level is the “anatomical main group” level; there are 14 anatomical main groups. The 2nd, 3rd, 4th, and 5th levels are “therapeutic subgroup”, “pharmacological subgroup”, “chemical subgroup”, and “chemical substance”, respectively.Footnote 14 Premature mortality from a disease may depend on the number of chemical (or pharmacological) subgroups that have previously been developed to treat the disease rather than, or in addition to, the number of chemical substances (drugs) that have previously been developed to treat the disease. This will be investigated by estimating versions of Eq. (4) in which (CUM_SUBGROUPs,2012 − k
− CUM_SUBGROUPs,1995 − k
) is included in addition to or instead of (CUM_NCEs,2012 − k
− CUM_NCEs,1995 − k
), where
CUM_SUBGROUPs,t−k
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= ∑g IND_SUBGROUPgs REGISTERED_SUBGROUPg,t−k
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IND_SUBGROUPgs
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= 1 if any drugs in chemical subgroup g are used to treat (indicated for) cancer at site s
= 0 if no drugs in chemical subgroup g are used to treat (indicated for) cancer at site s
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REGISTERED_SUBGROUPg,t−k
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= 1 if any drugs in chemical subgroup g had been registered in Switzerland by the end of year t − k
= 0 if no drugs in chemical subgroup g had been registered in Switzerland by the end of year t − k
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