To investigate the impact that new chemical entity (NCE) launches had on the number of YPLL at different ages and other mortality measures, I will estimate models based on the following triple-differences model:

${\text{MORT}}_{ict}={\beta}_{k}ln\left({\text{CUM}\mathrm{\_}\text{NCE}}_{ic,t-k}\right)+{\alpha}_{ic}+{\delta}_{it}+{\pi}_{ct}+{\epsilon}_{ict}$(1)

where MORT_{ict} is one of the following variables:

ln(YPLL75_{ict}) | = the log of the number of YPLL before age 75 due to disease *i* in country *c* in year *t* (*y* = 2007, 2015)^{8} |

ln(YPLL65_{ict}) | = the log of the number of YPLL before age 65 due to disease *i* in country *c* in year *t* |

ln(N_DEATHS_{ict}) | = the log of the number of deaths due to disease *i* in country *c* in year *t* |

AGE_DEATH_{ict} | = mean age at death due to disease *i* in country *c* in year *t* |

and

CUM_NCE_{ic,}_{t-k} | = ∑_{m} IND_{mi} LAUNCHED_{mc,}_{t-k} = the number of post-1992 NCEs to treat disease *i* that had been launched in country *c* by the end of year *t-k*^{9} |

IND_{mi} | = 1 if NCE *m* is used to treat (indicated for) disease *i* = 0 if NCE *m* is not used to treat (indicated for) disease *i* |

LAUNCHED_{mc,}_{t-k} | = 1 if NCE *m* had been launched in country *c* by the end of year *t-k* = 0 if NCE *m* had not been launched in country *c* by the end of year *t-k* |

*α*_{ic} | = a fixed effect for disease *i* in country *c* |

*δ*_{it} | = a fixed effect for disease *i* in year *t* |

*π*_{ct} | = a fixed effect for country *c* in year *t*^{10} |

Eq. (1) will be estimated using data on 17 major diseases comprising the disease classification used in World Health Organization (2017).

Due to data limitations, the number of NCEs is the only country- and disease-specific and time-varying explanatory variable in eq. (1). But both a patient-level U.S. study and a longitudinal country-level study have shown that controlling for numerous other potential determinants of longevity does not reduce, and may even increase, the estimated effect of pharmaceutical innovation. The study based on patient-level data (Lichtenberg 2013) found that controlling for race, education, family income, insurance coverage, Census region, BMI, smoking, the mean year the person started taking his or her medications, and over 100 medical conditions had virtually no effect on the estimate of the effect of pharmaceutical innovation (the change in drug vintage) on life expectancy. The study based on longitudinal country-level data (Lichtenberg 2014a) found that controlling for ten other potential determinants of longevity change (real per capita income, the unemployment rate, mean years of schooling, the urbanization rate, real per capita health expenditure (public and private), the DPT immunization rate among children ages 12–23 months, HIV prevalence and tuberculosis incidence) *increased* the coefficient on pharmaceutical innovation by about 32 %.

Failure to control for non-pharmaceutical medical innovation (e. g. innovation in diagnostic imaging, surgical procedures, and medical devices) is also unlikely to bias estimates of the effect of pharmaceutical innovation on premature mortality, for two reasons. First, more than half of U.S. funding for biomedical research came from pharmaceutical and biotechnology firms (Dorsey 2010). 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 (2017) says that it “has played a vital role in cancer drug discovery and development, and, today, that role continues.” Second, previous research based on U.S. data (Lichtenberg 2014a, 2014b) indicates that non-pharmaceutical medical innovation is not positively correlated across diseases with pharmaceutical innovation.

Estimates of eq. (1) will provide evidence about the impact of the launch of drugs for a disease on mortality from that disease, but they will not capture possible spillover effects of the drugs on mortality from *other* diseases. These spillovers may be either positive or negative. For example, the launch of cardiovascular drugs could reduce mortality from cardiovascular disease, but increase mortality from the “competing risk” of cancer. On the other hand, the launch of drugs for mental disorders could reduce mortality from other medical conditions. Prince et al. (2007) argued that “mental disorders increase risk for communicable and non-communicable diseases, and contribute to unintentional and intentional injury. Conversely, many health conditions increase the risk for mental disorder, and comorbidity complicates help-seeking, diagnosis, and treatment, and influences prognosis.”

My data on drug launches are left-censored: I only have data on drugs launched after 1992. I therefore define CUM_NCE_{ic,}_{t-k} as the number of post-1992 NCEs (i. e. NCEs first launched anywhere in the world after 1992) used to treat disease *i* that had been launched in country *c* by the end of year *t-k*. Consequently, this measure is subject to error, because CUM_NCE_{ic,}_{t-k} will not (but should) include pre-1993 NCEs that were first launched in country *c* after 1992. If this measurement error is random, it is likely to bias estimates of *β*_{k} toward zero.

Eq. (1) includes a large number of parameters, mainly due to 153 (17 diseases × 9 countries) disease/country fixed effects (α_{ic}'s). These “nuisance” parameters are not of interest to us, and estimation of a (simpler) “difference-in-differences” model, which can be derived from the triple-difference model (eq. (1)), is less computationally burdensome. Setting MORT_{ict} = ln(YPLL75_{ict}), and *t* equal to 2007 and 2015, yields eq. (2) and eq. (3), respectively:

$ln\left(\text{YPLL}{75}_{ic,2007}\right)={\beta}_{k}ln\left({\text{CUM}\mathrm{\_}\text{NCE}}_{ic,2007-k}\right)+{\alpha}_{ic}+{\delta}_{i,2007}+{\pi}_{c,2007}+{\epsilon}_{ic,2007}$(2)

$ln\left(\text{YPLL7}{\text{5}}_{ic,2015}\right)={\beta}_{k}ln\left(\text{CUM}\mathrm{\_}\text{NC}{\text{E}}_{ic,2015-k}\right)+{\alpha}_{ic}+{\delta}_{i,2015}+{\pi}_{c,2015}+{\epsilon}_{ic,2015}$(3)

Subtracting eq. (2) and eq. (3), yields:

$\mathrm{\Delta}ln\left(\text{YPLL}{75}_{ic}\right)={\beta}_{k}\phantom{\rule{thinmathspace}{0ex}}\mathrm{\Delta}ln\left(\text{CUM}\mathrm{\_}\text{NCE}\mathrm{\_}{k}_{ic}\right)+{\delta}_{i}^{\prime}+{\pi}_{c}^{\prime}+{\epsilon}_{ic}^{\prime}$(4)

where

Δln(YPLL75_{ic}) | = ln(YPLL75_{ic,}_{2015}) − ln(YPLL75_{ic,}_{2007}) = the log change from 2007 to 2015 in the number of YPLL before age 75 due to disease *i* in country *c* |

Δln(CUM_NCE_k_{ic}) | = ln(CUM_NCE_{ic,}_{2015−k}) − ln(CUM_NCE_{ic,}_{2007−k}) = the log change from 2007 − *k* to 2015 − *k* in the number of post-1992 NCEs for disease *i* that had ever been launched in country *c* |

*δ'*_{i} | = *δ*_{i,}_{2015} − *δ*_{i,}_{2007} = the difference between the 2007 and 2015 fixed effects for disease *i* |

*π'*_{c} | = *π*_{c,}_{2015} − *π*_{c,}_{2007} = the difference between the 2007 and 2015 fixed effects for country *c* |

More generally,

$\mathrm{\Delta}\text{MOR}{\text{T}}_{ic}={\beta}_{k}\mathrm{\Delta}ln\left(\text{CUM}\mathrm{\_}\text{NCE}\mathrm{\_}{\text{k}}_{ic}\right)+{\delta}_{i}^{\prime}+{\pi}_{c}^{\prime}+{\epsilon}_{ic}^{\prime}$(5)

where

$\mathrm{\Delta}\text{MOR}{\text{T}}_{ic}=\text{MOR}{\text{T}}_{ic,2015}-\text{MOR}{\text{T}}_{ic,2007}$

To address the issue of heteroskedasticity,^{11} eq. (5) will be estimated by weighted least squares, using the following weights:

Dependent variable | Weight |
---|

Δln(YPLL75_{ic}) | (YPLL75_{ic,}_{2007} + YPLL75_{ic,}_{2015})/2 |

Δln(YPLL65_{ic}) | (YPLL65_{ic,}_{2007} + YPLL65_{ic,}_{2015})/2 |

Δln(N_DEATHS_{ic}) | (N_DEATHS_{ic,}_{2007} + N_DEATHS_{ic,}_{2015})/2 |

ΔAGE_DEATH_{ic} | (N_DEATHS_{ic,}_{2007} + N_DEATHS_{ic,}_{2015})/2 |

The disturbances of eq. (5) will be clustered in a two-way cluster on country and disease.

Eq. (5) will be estimated for different values of *k: k* = 0, 1, …, 5. A separate model is estimated for each value of *k*, rather than including multiple values (CUM_NCE_{i,}_{t}, CUM_NCE_{i,}_{t-1}, CUM_NCE_{i,}_{t-2}, …) in a single model because CUM_NCE is highly serially correlated (by construction), which would result in extremely high multicollinearity if multiple values were included.

The lag structure of the relationship between MORT_{ict} and CUM_NCE_{ic,}_{t-k} (e. g. whether the magnitude of *β*_{5} (|*β*_{5}|) is larger or smaller than the magnitude of *β*_{0}) is likely to depend on several factors. New drugs diffuse gradually – they aren't used widely until some years after launch; this would cause |*β*_{5}| > |*β*_{0}|. But the effect of a drug's launch on mortality is likely to depend on the *quality* as well as on 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. If newer drugs tend to be of higher quality than older drugs (see Lichtenberg 2014b), this would cause |*β*_{5}| < |*β*_{0}|. Also, because our data on drug launches are left-censored, CUM_NCE_{ic,}_{t-k} is subject to greater measurement error for large *k* (e. g. *k* = 5) than it is for small *k* (e. g. *k* = 0). Due to the potentially offsetting effects of utilization, quality improvement, and measurement error, the shape of the lag structure is theoretically indeterminate.

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