The association between pharmaceutical innovation and both premature mortality and hospital utilization in Switzerland, 1996– 2019

We analyze the association that pharmaceutical innovation had with premature mortality from all diseases in Switzerland during the period 1996–2018, and its association with hospital utilization for all diseases in Switzerland during the period 2002–2019. The analysis is performed by investigating whether the diseases that experienced more pharmaceutical innovation had larger subsequent declines in premature mortality and hospitalization. Pharmaceutical innovation is measured by the growth in the number of drugs used to treat a disease ever registered in Switzerland. Utilization of a chemical substance reaches a peak 9–12 years after it was first launched, and then declines. Our estimates indicate that the number of years of potential life lost before ages 85, 75, and 65 is significantly inversely related to the number of chemical substances ever registered 6–9, 3–9, and 0–9 years earlier, respectively. The new chemical substances that were registered during the period 1990–2011 are associated with reductions in the number of years of potential life lost before ages 85, 75, and 65 in 2018 of 257 thousand, 163 thousand, and 102 thousand, respectively. The number of hospital days is significantly inversely related to the number of chemical substances ever registered 8–10 years earlier. The new chemical substances that were registered during the period 1994–2010 are associated with reductions in the number of hospital days in 2019 of 2.07 million. Average length of inpatient hospital stays is significantly inversely related to the number of chemical substances ever registered 2–10 years earlier. The new chemical substances that were registered during the period 1999–2015 are associated with reductions in the average length of stays in 2019 of 0.4 days. Under the assumption that pharmaceutical innovation is exogenous with respect to premature mortality and hospitalization, and that it is uncorrelated with other potential determinants of health outcomes, if we ignore the reduction in hospital utilization associated with previous pharmaceutical innovation, a rough estimate of the cost per life-year before age 85 gained in 2018 is € 14,310. However, about 85% of the 2018 expenditure on drugs registered during the period 1990–2011 may have been offset by the reduction in expenditure on inpatient curative and rehabilitative care. The net cost per life-year before age 85 gained in 2018 may therefore have been € 2201.


Introduction
A previous study (Lichtenberg, 2016) analyzed the association that pharmaceutical innovation had with premature mortality from cancer in Switzerland during the period 1995-2012, by investigating whether the cancer sites that experienced more pharmaceutical innovation Lichtenberg Swiss Journal of Economics and Statistics (2022) 158:7 had larger declines in premature mortality, controlling for the number of people diagnosed and mean age at diagnosis. That study found that premature cancer mortality before ages 75 and 65 was significantly inversely related to the cumulative number of drugs registered 5, 10, and 15 years earlier.
Cancer accounts for only about one-third of the years of potential life lost (YPLL) before age 75 in Switzerland. 1 In the present study, we will use similar methods to analyze the association that pharmaceutical innovation had with premature mortality from all diseases in Switzerland during a period that includes more recent years: 1996-2018. There was considerable variation across diseases in the growth in the number of drugs used to treat the diseases ever registered in Switzerland. This is illustrated by Fig. 1, which shows data for 5 diseases, for which fairly similar (between 27 and 31) numbers of drugs had been registered by 1993. During the next 25 years, 16 or fewer drugs were registered for 3 diseases, 21 drugs were registered for "other lower respiratory diseases, " and 47 drugs were registered for "other malignant neoplasms. " We will extend the analysis performed in the previous study in two additional ways. We will analyze an additional measure of premature mortality: the number of years of potential life lost before age 85 (as well as before 75 and 65). 2 And, we will analyze the association that pharmaceutical innovation had with hospital utilization for all diseases in Switzerland during the period 2002-2019. In 2018, expenditure on inpatient curative and rehabilitative care was almost three times as great as expenditure on prescribed medicines: €18.0 billion vs. €6.3 billion.
In the next section, we will describe the econometric model that we will use to analyze the association that pharmaceutical innovation had with premature mortality and hospitalization due to all diseases in Switzerland during the period 1996-2019. The data sources used to estimate this model are discussed on Sect. 3. Empirical results are presented in Sect. 4. Some implications of the estimates are discussed on Sect. 5. Section 6 provides a summary.  Economics and Statistics (2022) 158:7 2 Econometric model of premature mortality and hospital utilization We begin with the following general model of the association between health outcomes and the history of pharmaceutical innovation: where Y ct a measure of premature mortality or hospital utilization due to medical condition c in year t N_NEW c,t−k the number of new drugs used to treat medical condition c that were approved in year t − k (k = 0, 1, 2, …); α c a fixed effect for medical condition c δ t a fixed effect for year t.
According to Eq. (1), premature mortality and hospitalization due to a medical condition depends on the logarithm of a distributed lag function of the number of new drugs approved to treat the disease, controlling for fixed medical condition and year effects. This specification allows the effect of a new drug approval on outcomes to (1) ln (Y ct ) = β ln γ 0 N _NEW c,t + γ 1 N _NEW c,t−1 + γ 2 N _NEW c,t−2 + · · · + α c + δ t + ε ct depend upon how long ago the drug was approved. For example, (γ 2 /γ 1 ) = 2 would imply that a drug approved 2 years ago has twice as great an impact as a drug approved one year ago.
The lag structure of Eq. (1)-in particular, whether recently approved drugs have a smaller or larger impact than drugs approved longer ago-is likely to depend on several factors. Two considerations suggest that recently approved drugs should have a smaller impact. First, utilization of recently-launched drugs tends to be lower than utilization of drugs launched many years earlier. Evidence about the shape of the age (number of years since launch)-utilization profile can be obtained by estimating the following equation: where N_SU mn the number of standard units of chemical substance m sold n years after it was first launched (n = 0, 1, …, 20) ρ m a fixed effect for chemical substance m δ n a fixed effect for age n.
(2) ln (N _SU mn ) = ρ m + δ n + ε mn Page 4 of 24 Lichtenberg Swiss Journal of Economics and Statistics (2022) 158:7 The expression exp(δ n − δ 12 ) is a "relative utilization index": it is the mean ratio of the quantity of a drug sold n years after it was launched to the quantity of the same drug sold 12 years after it was launched. We estimated Eq. (2), using annual data for the period 2010-2020 on 1015 chemical substances. Estimates of the "relative utilization index" are shown in Fig. 2. These estimates indicate that utilization of a chemical substance reaches a peak 9-12 years after it was first launched, and then declines. It is used about twice as much 9 years after launch as it was one year after launch. Due to gradual diffusion of new drugs, recently launched drugs may have a smaller impact than previously launched drugs.
A second reason why recently launched drugs may have a smaller impact on outcomes is that some drugs for chronic diseases (e.g. statins) may have to be consumed for several years to achieve full effectiveness.
But there is also a reason why recently launched drugs may have a larger impact than previously launched drugs: quality change. The impact of a drug on disease burden is likely to depend on its quality (or effectiveness) as well as on its quantity (utilization), and drugs launched more recently are likely to be of higher quality than earlier-vintage drugs. 3,4 However, the average annual rate of pharmaceutical quality change is unknown.
Although we think that Eq. (1) is a good theoretical model of the impact of pharmaceutical innovation on outcomes, estimation of that equation is not practical. Without imposing restrictions on the γ k parameters, Eq. (1) is a nonlinear (and non-log-linear) function of the parameters. Aside from that, to our knowledge, no statistical packages enable estimation of distributed lag models from panel data with clustered standard errors.
However, we think we can obtain some insight about the lag structure by estimating different versions of Eq. (1) under simple, alternative assumptions about γ k . In the first version, we assume that γ k = 1, ∀ k. In this case, the model reduces to ln(Y ct ) = β ln(CUM_DRUG Outcomes in year t depend on the sum of the number of drugs ever launched until the end of year t. In the second version, γ 0 = 0, γ k = 1, k ≥ 1. In this case, the model reduces to ln(Y ct ) = β ln(CUM_DRUG Outcomes in year t depend on the sum of the number of drugs ever launched until the end of year t − 1.
More generally, to assess the association that pharmaceutical innovation had with premature mortality and hospital utilization under 13 different assumed lag structures, we will estimate models based on the following 2-way fixed effects equation: where Y ct is one of the following variables: YPLL85 ct the number of years of potential life lost before age 85 due to cause c in year t (t = 1996, 1997, …, 2018); YPLL75 ct the number of years of potential life lost before age 75 due to cause c in year t (t = 1996, 1997, …, 2018); YPLL65 ct the number of years of potential life lost before age 65 due to cause c in year t (t = 1996, 1997, …, 2018); HOSP_DAYS ct the number of hospital days due to cause c in year t (t = 2002, 2003,…, 2019); ALOS ct the average length of hospital stays due to cause c in year t (t = 2002, 2003, …, 2019) and CUM_DRUG c,t−k ∑ m IND mc LAUNCHED m,t−k = the number of chemical substances to treat medical condition c that had been launched in Switzerland by the end of year t − k (k = 0, 1, 2,…,12) 5 IND mc = 1 if chemical substance m is used to treat (indicated for) medical Grossman and Helpman (1991) argued that "innovative goods are better than older products simply because they provide more 'product services' in relation to their cost of production. " Bresnahan and Gordon (1996) stated simply that "new goods are at the heart of economic progress, " and Bils (2004) said that "much of economic growth occurs through growth in quality as new models of consumer goods replace older, sometimes inferior, models. " As noted by Jovanovic and Yatsenko (2012), in "the Spence-Dixit-Stiglitz tradi-tion…new goods [are] of higher quality than old goods. ". 4 The impact on disease burden may depend on the interaction (quantity * quality) of the two variables. The impact will increase with respect to drug age (time since launch) if the rate of increase of quantity with respect to age is greater than the rate of decline of quality with respect to age; otherwise the impact will decline. 5 The Swiss process of marketing authorization and reimbursement takes place in two steps.
Step one: Drug is reviewed for safety, effectiveness and approval by Swissmedic. If approved, the drug receives market authorization.
Step 2: The producer negotiates a price for the drug with the Federal Office of Public Health. Once the price is determined, the drug is put on the Specialty List for reimbursement. Virtually all drugs that receive marketing authorization are put on the Specialty List. This process takes longer for some drugs than it does for others. An intermediary/broker (the Federal Drug Commission (EAK)) is responsible for recommending a price for a newly approved drug. According to Paris and Docteur (2007), "the Swiss tend to be early adopters of new pharmaceutical products. ".
Page 5 of 24 Lichtenberg Swiss Journal of Economics and Statistics (2022) 158:7 condition c 6 = 0 if chemical substance m is not used to treat (indicated for) medical condition c LAUNCHED m,t−k 1 if chemical substance m had been registered in Switzerland by the end of year t − k = 0 if chemical substance m had not been registered in Switzerland by the end of year t − k α c a fixed effect for medical condition c δ t a fixed effect for year t This formulation of the "health production function" (Koç, 2004) is consistent with Romer's (1990) model of endogenous technological change, in which "growth in income per person is tied to growth in the total stock of ideas" (Jones (2019, p. 861), emphasis added). Equation (3) will be estimated by weighted leastsquares. For the first four dependent variables, the weight will be ∑ t Y ct . For the last dependent variable, the weight will be N_DISCHARGES ct = the number of inpatient hospital discharges due to cause c in year t. Disturbances will be clustered by cause.
The year fixed effects (δ t 's) in Eq.
(3) control for the effects of changes in macroeconomic variables (e.g. population size, GDP, educational attainment), to the extent that those variables have similar effects on mortality and hospitalization caused by different diseases. The year fixed effects capture the change in the dependent variable, holding lagged CUM_DRUG constant, i.e., in the absence of previous pharmaceutical innovation. The ("counterfactual") estimated aggregate value of the dependent variable in year t in the absence of previous pharmaceutical innovation is ((∑ c Y c,1996 ) × exp(δ t −δ 1996 )). We can estimate the ("actual") aggregate value of the dependent variable in year t in the presence of previous pharmaceutical innovation as is the year fixed effect of the following equation 7 : For each dependent variable, we will estimate 13 versions of Eq. (3): one for each value of the lag length k (k = 0, 1, 2,…,12). We will also estimate a version that includes multiple lag lengths.
Equation (3) includes a measure of pharmaceutical innovation (CUM_DRUG c,t−k ), but it does not include measures of other types of biomedical innovation (e.g. innovation in diagnostic imaging, surgical procedures, and medical devices). Dorsey (2010) showed that 88% of private U.S. funding for biomedical research came from pharmaceutical and biotechnology firms. 8 Also, some previous research indicated that non-pharmaceutical medical innovation is not positively correlated across diseases with pharmaceutical innovation. Some studies have found no mortality benefit from more intensive screening. For example, data from the Prostate, Lung, Colorectal and Ovarian randomized screening trial showed that, after 13 years of follow up, men who underwent annual prostate cancer screening with prostate-specific antigen testing and digital rectal examination had a 12 percent higher incidence of prostate cancer than men in the control group but the same rate of death from the disease. No evidence of a mortality benefit was seen in subgroups defined by age, the presence of other illnesses, or pre-trial PSA testing (National Cancer Institute, 2012). Also, a large U.S. government study found that drug therapy alone may save the lives of heart disease patients with blocked coronary arteries as effectively as bypass or stenting procedures (Kolata, 2019). Nevertheless, controlling for non-pharmaceutical medical innovation would be desirable, but measuring non-pharmaceutical medical innovation is far more difficult than measuring pharmaceutical innovation.

Data sources and descriptive statistics
Data on the Swiss approval dates (1933-present) of molecules (WHO ATC5 chemical substances) were obtained from Swissmedic (2021). Data on approved ICD-10 indications of WHO ATC5 chemical substances were obtained from Thériaque, a database produced by France's Centre National Hospitalier d'Information sur le Médicament (2021). Data on Swiss drug expenditure, by molecule and year (2010-2020), were obtained from the IQVIA MIDAS database. Data on the number of years of potential life lost before ages 85, 75, and 65, by cause and year , were constructed from data contained in the Eurostat hlth_cd_aro and hlth_cd_anr files (European Commission, 2021). Data on population, by age group and year, were obtained from the Eurostat demo_pjangroup file. Data on the number of days of hospital care, by cause and year (2002-2019), were obtained from the Eurostat hlth_co_hosday file. Data on inpatient average length 6 Many drugs have multiple indications: 50% of drugs have 2 or more indications (causes of disease in the WHO Global Health Estimates disease classification), and 7% of drugs have 5 or more indications. 7 Both measures control for changes in the distribution of YPLL or hospital utilization, by cause. 8 Much of the rest came from the federal government (i.e. the NIH), and new drugs often build on upstream government research (Sampat and Lichtenberg 2011). The National Cancer Institute (2021) says that it "has played a vital role in cancer drug discovery and development, and, today, that role continues".  Table 1. Between 1996 and 2018, YPLL85 declined by 20%, and the population below age 85 increased by 19%, so the premature (before age 85) mortality rate declined by 33%, from 9789 to 6573 per 100,000 population. The pre-age-75 and pre-age-65 mortality rates declined even more, by 38% and 44%, respectively. Data on mortality by cause in 2018 are shown in Table 5 in Appendix. 9 Annual data on hospitalization for all causes during 2002-2019 are shown in Table 2. Between 2002 and 2019, the number of hospital days was essentially constant, and the population increased by 18%, so the number of hospital days per 1000 population declined by 15%, despite the aging of the population. The average length of inpatient hospital stays declined even more, by 29%. Data on the number of hospital days and average length of stay, by cause, in 2019 are shown in Table 6 in Appendix.
Data on the number of chemical substances ever registered in Switzerland, by medical condition (hospital classification), 1989-2019, are shown in Table 7 in Appendix.

Premature mortality model estimates
Estimates of β k from 2-way fixed-effects premature mortality models [Eq. (3)] are presented in Table 3 and plotted in Fig. 3. Each estimate is from a separate model.
Panel A of the table and figure show estimates when the dependent variable is ln(YPLL85 ct ). The estimates of β k are not statistically significant when k ≤ 5, but they are negative and significant when 6 ≤ k ≤ 9: premature (before age 85) mortality is significantly inversely related to the number of chemical substances ever registered 6-9 years earlier. It is most strongly inversely related to the number of chemical substances ever registered 8 years earlier. This is consistent with the evidence discussed above that utilization of a chemical substance reaches a peak 9-12 years after it was first launched, and that drugs launched more recently are likely to be of higher quality than earlier-vintage drugs. Panel B of Table 3 and Fig. 3 shows estimates when the dependent variable is ln(YPLL75 ct ). In this case, the estimates are negative and significant when 3 ≤ k ≤ 9: the number of years of potential life lost before age 75 is significantly inversely related to the number of chemical substances ever registered 3-9 years earlier. It is most strongly inversely related to the number of chemical substances ever registered 7 years earlier.
Panel C of Table 3 and Fig. 3 shows estimates when the dependent variable is ln(YPLL65 ct ). In this case, the estimates are negative and significant when 0 ≤ k ≤ 9: the number of years of potential life lost before age 65 is significantly inversely related to the number of chemical substances ever registered 0-9 years earlier. Once again, it is most strongly inversely related to the number of chemical substances ever registered 7 years earlier. But the finding that YPLL65 is significantly inversely related to the number of chemical substances ever registered just a few years earlier may indicate that access to new drugs for diseases that kill patients at lower ages may occur earlier than access to new drugs for diseases that kill patients at higher ages.
As discussed above, by estimating both Eqs. (3) and (4), we can compute both the ("counterfactual") aggregate value of the dependent variable in year t in the absence of previous pharmaceutical innovation, and the ("actual") aggregate value of the dependent variable in year t in the presence of previous pharmaceutical innovation. The results of these calculations for the three premature mortality measures are shown in Fig. 4. For each measure, we use the estimate of Eq. (3) in which ln(CUM_DRUG c,t−k ) is most strongly related to ln(Y ct ).
Panels A and B of Fig. 4 compare the evolution of aggregate YPLL85 (= ∑ c YPLL85 ct ) controlling for CUM_DRUG c,t−7 (i.e., if CUM_DRUG c,t−7 had remained constant) to the actual evolution of aggregate YPLL85. Between 1996 and 2018, YPLL85 declined by 20%, from 679 to 544 thousand. The estimate of β 7 implies that, if CUM_DRUG c,t−7 had not increased, YPLL85 would have increased by 18%, to 801 thousand. As shown in Table 1, during that period, the population below age 85 increased by 19%, which implies that, if CUM_DRUG c,t−7 had not increased, there would  Solid squares denote significant (p-value < .05) esƟmates; hollow squares denote insignificant esƟmates.
EsƟmates of β k from 2-way fixed-effects premature mortality models (eq. (3) Panels C and D of Fig. 4 show similar calculations for YPLL75. Between 1996 and 2018, YPLL75 declined by 26%, from 366 to 271 thousand. The estimate of β 7 implies that, if CUM_DRUG c,t−7 had not increased, YPLL75 would have increased by 18%, to 431 thousand. As shown in Table 1, during that period, the population below age 75 increased by 18%, which implies that, if CUM_DRUG c,t−7 had not increased, there would have been almost no change in the premature (before age 75) mortality rate. The new chemical substances that were registered during the period 1990-2011 are associated with a reduction in the number of years of potential life lost before age 75 in 2018 of 163 thousand (= 430 thousand-267 thousand).
Panels E and F of Fig. 4 show similar calculations for YPLL65. Between 1996 and 2018, YPLL65 declined by 35%, from 200 to 129 thousand. The estimate of β 7 implies that, if CUM_DRUG c,t−7 had not increased, YPLL65 would have increased by 16%, to 231 thousand. As shown in Table 1, during that period, the population below age 65 increased by 15%, which implies that, if CUM_DRUG c,t−7 had not increased, there would have been almost no change in the premature (before age 65) mortality rate. The new chemical substances that were registered during the period 1990-2011 are associated with a reduction in the number of years of potential life lost before age 65 in 2018 of 102 thousand (= 231 thousand-129 thousand).
As stated earlier, we also estimated a version of Eq. (3) that includes multiple lag lengths: CUM_DRUG c,t , CUM_DRUG c,t−8 , and CUM_DRUG c,t−12 . These estimates are shown in Table 8 in Appendix. In model 1 in that table, the dependent variable is ln(YPLL85 ct ). The coefficient on CUM_DRUG c,t−8 is negative and significant (p value = 0.0025); the coefficients on CUM_DRUG c,t and CUM_DRUG c,t−12 are insignificant. The magnitude of the coefficient on CUM_DRUG c,t−8 is slightly (8%) larger than the coefficient shown in Table 3 (reproduced in model 2 of Table 8 in Appendix). In models 3 and 4 of Table 8 in Appendix, the dependent variable is ln(YPLL75 ct ); in models 5 and 6, the dependent variable is ln(YPLL65 ct ). In those models as well, the coefficient on CUM_DRUG c,t−8 is negative and significant, and the coefficients on CUM_DRUG c,t and CUM_DRUG c,t−12 are insignificant.

Hospital utilization model estimates
Estimates of β k from 2-way fixed-effects hospital utilization models [Eq. (3)] are presented in Table 4 and plotted in Fig. 5.
Panel A of the table and figure shows estimates when the dependent variable is ln(HOSP_DAYS ct ). The estimates of β k are negative and significant when 8 ≤ k ≤ 10: the number of hospital days is significantly inversely related to the number of chemical substances ever registered 8-10 years earlier. (The estimates of β 7 and β 11 are marginally significant (p value < 0.07).) It is most strongly inversely related to the number of chemical substances ever registered 9 years earlier.
Panel B of the table and figure shows estimates when the dependent variable is ln(ALOS ct ). The estimates of β k are negative and significant when 2 ≤ k ≤ 10: average length of stay is significantly inversely related to the number of chemical substances ever registered 2-10 years earlier. It is most strongly inversely related to the number of chemical substances ever registered 4 years earlier.
This relatively short lag might be due to more rapid diffusion of new drugs in the hospital sector than in the retail sector, which is the case in the U.S. Panels A and B of Fig. 6 compare the actual evolution of aggregate hospital utilization to the estimated evolution, in the absence of previous pharmaceutical innovation. Between 2002 and 2019, controlling for the changing mix of causes of hospitalization, HOSP_DAYS increased by 4%, from 11.5 million to 12.0 million. The estimate of β 9 implies that, if CUM_DRUG c,t−9 had not increased, HOSP_DAYS would have increased by 22%, to 14.0 million. As shown in Table 2, during that period, the population increased by 18%, which implies that, if CUM_DRUG c,t−9 had not increased, there would have been a small (3%) increase in the number of hospital days per 1000 population. The new chemical substances that were registered during the period 1994-2010 are associated with a reduction inthe number of hospital days in 2019 by 2.07 million (= 14.02 million-11.95 million).
Panels C and D of Fig. 6 compare the actual evolution of the average length of inpatient hospital stays to the estimated evolution, in the absence of previous pharmaceutical innovation. Between 2002 and 2019, controlling for the changing mix of causes of hospitalization, ALOS declined by 3.3 days, from 11.4 to 8.1 days. The estimate of β 4 implies that, if CUM_DRUG c,t−4 had not increased, ALOS would have declined by 2.9 days, to 8.5 days. The new chemical substances that were registered during the period 1999-2015 are associated with a reduction in ALOS in 2019 of 0.4 (= 8.5-8.1) days.
Estimates of hospital utilization models that include multiple lag lengths (CUM_DRUG c,t , CUM_DRUG c,t−8 , and CUM_DRUG c,t−12 ) are shown as models 7 and 9 in  Table 8 in Appendix. In model 7, the dependent variable is ln(HOSP_DAYS ct ). The coefficient on CUM_DRUG c,t is positive and significant. Perhaps this is due to reverse causality: an exogenous increase in hospital utilization for a medical condition could stimulate an acceleration or increase in new drug approvals for that condition. The coefficient on CUM_DRUG c,t−8 remains negative and significant; its magnitude is 25% larger than the coefficient shown in Table 4 (reproduced in model 8 of Table 8 in Appendix). The coefficient on CUM_DRUG c,t−12 is insignificant. In model 9, the dependent variable is ln(ALOS ct ). The coefficient on CUM_DRUG c,t−8 is negative and significant; the coefficients on CUM_DRUG c,t and CUM_DRUG c,t−12 are insignificant.

Discussion
As shown in Panels A and B of Fig. 4, the new chemical substances that were registered during the period 1990-2011 are associated with a reduction in the number of years of potential life lost before age 85 in 2018 of 257 thousand. Now we will obtain rough estimates of the incremental cost-effectiveness (cost per life-year before age 85 gained) of those chemical substances in 2018. First, we will estimate cost-effectiveness if we ignore the reduction in hospital utilization attributable to previous pharmaceutical innovation. Then, we will estimate costeffectiveness if we account for this reduction in hospital utilization.
As noted above, according to Eurostat, expenditure on prescribed medicines in Switzerland in 2018 was € 6288 million. Data from the IQVIA MIDAS database indicate As noted by Bertram et al (2016), authors writing on behalf of the WHO's Choosing Interventions that are Cost-Effective project (WHO-CHOICE) suggested in 2005 that "interventions that avert one disability-adjusted life-year (DALY) for less than average per capita income for a given country or region are considered very costeffective; interventions that cost less than three times average per capita income per DALY averted are still considered cost-effective. " Switzerland's per capita GDP in 2018 was € 73,436, so the new chemical substances that were registered during the period 1990-2011 appear to have been very cost-effective overall, even if we ignore the reduction in hospital utilization attributable to previous pharmaceutical innovation.
EsƟmates of β k from 2-way fixed-effects hospital uƟlizaƟon models (eq. (3) As shown in Panels A and B of Fig. 6, the new chemical substances that were registered during the period 1994-2010 are associated with a reduction in the number of hospital days in 2019 of 2.07 million (= 14.02 million-11.95 million). In other words, if no new chemical substances had been registered during the period 1994-2010, the number of hospital days might have been 17.3% (= (14.02 million/11.95 million) − 1) higher in 2019. It is plausible that expenditure on inpatient curative and rehabilitative care would also have been 17.3% higher. According to Eurostat, expenditure on inpatient curative and rehabilitative care in 2018 was € 17,965 million. Therefore, we estimate that, if no new chemical substances had been registered during the period 1994-2010, expenditure on inpatient curative and rehabilitative care in 2018 might have been € 3112 million (= 17.3% × € 17,965 million) higher. About 85% (= € 3112 million/€ 3678 million) of the 2018 expenditure on drugs registered during the period 1990-2011 may have been offset by the reduction in expenditure on inpatient curative and rehabilitative care. The net cost per life-year before age 85 gained in 2018 may have been € 2201 (= (1-85%) × € 14,309). 12

Summary and conclusions
In this study, we analyzed the association that pharmaceutical innovation had with premature mortality from all diseases in Switzerland during the period 1996-2018, and its association with hospital utilization for all diseases in Switzerland during the period 2002-2019. Most private biomedical research funding comes from pharmaceutical and biotechnology firms. Page 15 of 24 Lichtenberg Swiss Journal of Economics and Statistics (2022) 158:7 The analysis was performed by investigating whether the diseases that experienced more pharmaceutical innovation had larger declines in premature mortality and hospitalization. Pharmaceutical innovation was measured by the growth in the number of drugs used to treat a disease ever registered in Switzerland. We allowed the association of innovation to be subject to a substantial lag because utilization of recently-launched drugs tends to be lower than utilization of drugs launched many years earlier. Utilization of a chemical substance reaches a peak 9-12 years after it was first launched, and then declines.
Our estimates indicated that the number of years of potential life lost before ages 85, 75, and 65 is significantly inversely related to the number of chemical substances ever registered 6-9, 3-9, and 0-9 years earlier, respectively. The new chemical substances that were registered during the period 1990-2011 are associated with reductions inthe number of years of potential life lost before ages 85, 75, and 65 in 2018 of 257 thousand, 163 thousand, and 102 thousand, respectively.
The number of hospital days is significantly inversely related to the number of chemical substances ever registered 8-10 years earlier. The new chemical substances that were registered during the period 1994-2010 are associated with a reduction inthe number of hospital days in 2019 of 2.07 million. Average length of inpatient hospital stays is significantly inversely related to the number of chemical substances ever registered 2-10 years earlier. The new chemical substances that were registered during the period 1999-2015 are associated with a reduction inALOS in 2019 of 0.4 days.
If we ignore the reduction in hospital utilization attributable to previous pharmaceutical innovation, a rough estimate of the cost per life-year before age 85 gained in 2018 is € 14,310.
Moreover, about 85% of the 2018 expenditure on drugs registered during the period 1990-2011 may have been offset by the reduction in expenditure on inpatient curative and rehabilitative care. The net cost per life-year before age 85 gained in 2018 may therefore have been € 2201.
Our estimates are predicated on the assumption that pharmaceutical innovation is exogenous with respect to premature mortality and hospitalization, and that it is uncorrelated with other potential determinants of health outcomes. For several reasons, this assumption could be violated. 13 One reason is that Switzerland implemented a mandatory health insurance system in 1996, with several reforms since then that affected the quality of health services and the drug admission process. The potential endogeneity of pharmaceutical innovation in Switzerland due to changes in the Swiss health insurance system might be addressed by using an instrument for the number of new drugs approved for a disease in Switzerland. One potential instrument is the number of new drugs approved in the U.S. 14 (There is a very strong positive correlation across 58 diseases between the 1996-2018 growth in number of drugs ever approved in the USA and Switzerland: R 2 = 0.59; p value < 0.0001.) We estimated Eq. (3) using instrumental variables (IV); the instrument for the number of new drugs ever approved for a disease in Switzerland was the number of new drugs ever approved for a disease in the United States three years earlier. While the IV and OLS estimates had different magnitudes and lag structures, both sets of estimates revealed highly significant inverse associations across diseases between both premature mortality and hospital days and the lagged number of drugs ever registered.
A second potential reason for violation of the assumption is implementation of non-pharmaceutical medical innovations (e.g. medical devices) and new disease-specific treatment guidelines. A previous study (Lichtenberg, 2014) indicated that controlling for non-pharmaceutical medical innovation did not affect estimates of the effect of pharmaceutical innovation on U.S. cancer mortality. We are not aware of evidence for the hypothesis that, in general, changes in guidelines have reduced mortality or hospitalization, or that they are correlated across diseases with new drug approvals. Future studies of Swiss mortality and hospitalization should attempt to control for nonpharmaceutical medical innovation and for changes in guidelines.