Specifications for treatment stock weighting scheme



Changes in mortality associated with cancer drug approvals in the United States from 2000 to 2016Joanna P. MacEwan, Syvart Dennen, Rebecca Kee, Farzad Ali, Jason Shafrin, Katharine BattSupplemental materialSpecifications for treatment stock weighting schemeTo build our treatment stock measure, we assumed the weight in lagged period l takes the trapezoidal distribution given by: ωl= ul-ab-a a≤l<bu b≤l<cud-ld-c c≤l≤d0 otherwiseand assume a=1, b=4, c=12, d=25, and u=2/33≈.0606. The parameter values imply that it takes at least one year for any new indication approval to have an effect on mortality outcomes, that the effect increases from lagged year 1 to 4, a constant effect from lagged years 4 to 12, and then a declining effect between lagged years 12 to 25. We assume no effect of 25 or more years of lagged new indication approvals, which is conservative given the fact that some chemotherapies (e.g., mechlorethamine and methotrexate) have been in use since the 1950s. ADDIN EN.CITE <EndNote><Cite><Author>National Cancer Institute</Author><Year>2015</Year><RecNum>2287</RecNum><DisplayText><style face="superscript">1</style></DisplayText><record><rec-number>2287</rec-number><foreign-keys><key app="EN" db-id="f2azt92rkexrt0e90ervrezi00prx0xxstt5" timestamp="1582747152">2287</key></foreign-keys><ref-type name="Web Page">12</ref-type><contributors><authors><author>National Cancer Institute,</author></authors></contributors><titles><title>Milestones in Cancer Research and Discovery</title></titles><number>February 26, 2020</number><dates><year>2015</year></dates><urls><related-urls><url> REF _Ref33190064 \h \* MERGEFORMAT Figure S1 illustrates the shape of the lag-weight distribution and Figure 4 in the manuscript illustrates the calculated treatment stocks by tumor type and year. As a sensitivity test, we re-ran the regressions with the lag distribution shortened to 15 years and extended to 30 and 35 years. Significance levels were unchanged in almost all cases, and magnitudes tended to increase with the length of the lag distribution, as expected. One exception was thyroid cancer. The treatment stock coefficient was positive in both baseline and sensitivity analyses. This finding occurs because there are only five included drug approvals for this cancer during our period of interest (six with longer lag lengths): 1 in 1974 (which is omitted under our baseline approach), 1 in 1998, and four in the years from 2011 to 2015. As a result, the treatment stock measure is constant for this tumor type for 2002 through 2010 and declines in 2011. For the longer lag lengths, the treatment stock is declining for much of the period of interest (2002 through 2011 for the 35-year lag) due to the inclusion of the 1974 approval. This is in fact the inverse of our hypothesis about reality, which is that treatment stocks are level or increasing. This shows the limitation of the treatment stock approach when new approvals are not replacing previous treatments, indicating that our estimates are likely better when there is regular entry of NDAs for a given tumor.Figure S SEQ Figure \* ARABIC 1. Trapezoidal lag distribution of the effect of drug approvals on mortality in 2016Table S SEQ Table \* ARABIC 1. Results of sensitivity analyses using different lengths of lag distributions15 years25 years (base analysis)30 years35 yearsTumorCoeff.p-valueCoeff.p-valueCoeff.p-valueCoeff.p-valueBreast-7.29<0.001-6.36<0.001-6.75<0.001-7.51<0.001Colorectal-2.730.008-4.560.004-5.230.003-5.880.002Renal-0.43<0.001-0.69<0.001-0.77<0.001-0.86<0.001Leukemia-0.76<0.001-1.04<0.001-1.14<0.001-1.27<0.001Lung-4.440.146-18.30<0.001-21.42<0.001-24.12<0.001NHL-1.38<0.001-1.88<0.001-2.14<0.001-2.48<0.001Oral-1.310.189-1.880.189-0.610.7203.610.360Pancreas-0.220.423-1.000.054-0.960.081-1.230.074Prostate-5.340.638-44.950.075-57.49<0.001-61.42<0.001Melanoma-0.96<0.001-1.34<0.001-1.49<0.001-1.66<0.001Gastric-0.970.019-1.380.019-1.530.025-1.740.025Thyroid0.200.0060.270.0280.320.0270.330.036Bladder0.140.6041.960.002-0.670.772-1.330.403Overall, aggregated-8.81<0.001-11.25<0.001-12.240.001-13.440.001Regression specifications for the relationship between cancer treatment stocks and cancer mortalityIn the primary analysis, we modeled tumor-specific cancer mortality (per 100,000 US population) in year t and tumor type i as a function of cancer treatment stocks measured by new indication approvals in year t and tumor type i (NDAit), Kit, using a fixed effects model estimated with ordinary least squares (OLS). That is, morti,t=βi,0+βi,1incidi,t+βi,2incidi,t-1+βi,3Ki,t+εi,t To estimate the overall impact, we estimated the above model with mortality, incidence, and treatment stocks aggregated across all 15 tumor types. To account for temporal correlation in mortality rates over years, heteroscedasticity, and correlation across tumor types, we estimated Driscoll-Kraay standard errors, which are robust to general forms of spatial and temporal dependence. ADDIN EN.CITE <EndNote><Cite><Author>Driscoll</Author><Year>1998</Year><RecNum>447</RecNum><DisplayText><style face="superscript">2</style></DisplayText><record><rec-number>447</rec-number><foreign-keys><key app="EN" db-id="0z5dssaex9wssee2wsbva224s0ssx9s22pa0" timestamp="1583794056">447</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Driscoll, John C</author><author>Kraay, Aart C</author></authors></contributors><titles><title>Consistent covariance matrix estimation with spatially dependent panel data</title><secondary-title>Review of economics and statistics</secondary-title></titles><periodical><full-title>Review of Economics and statistics</full-title></periodical><pages>549-560</pages><volume>80</volume><number>4</number><dates><year>1998</year></dates><isbn>0034-6535</isbn><urls></urls></record></Cite></EndNote>2 While Driscoll-Kraay standard errors can be biased downward in small samples, simulations have shown their small-sample properties are superior to alternatives. ADDIN EN.CITE <EndNote><Cite><Author>Hoechle</Author><Year>2007</Year><RecNum>448</RecNum><DisplayText><style face="superscript">3</style></DisplayText><record><rec-number>448</rec-number><foreign-keys><key app="EN" db-id="0z5dssaex9wssee2wsbva224s0ssx9s22pa0" timestamp="1583794258">448</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hoechle, Daniel</author></authors></contributors><titles><title>Robust standard errors for panel regressions with cross-sectional dependence</title><secondary-title>The stata journal</secondary-title></titles><periodical><full-title>The stata journal</full-title></periodical><pages>281-312</pages><volume>7</volume><number>3</number><dates><year>2007</year></dates><isbn>1536-867X</isbn><urls></urls></record></Cite></EndNote>3 Estimates were produced using the Stata program xtscc. ADDIN EN.CITE <EndNote><Cite><Author>Hoechle</Author><Year>2007</Year><RecNum>448</RecNum><DisplayText><style face="superscript">3</style></DisplayText><record><rec-number>448</rec-number><foreign-keys><key app="EN" db-id="0z5dssaex9wssee2wsbva224s0ssx9s22pa0" timestamp="1583794258">448</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hoechle, Daniel</author></authors></contributors><titles><title>Robust standard errors for panel regressions with cross-sectional dependence</title><secondary-title>The stata journal</secondary-title></titles><periodical><full-title>The stata journal</full-title></periodical><pages>281-312</pages><volume>7</volume><number>3</number><dates><year>2007</year></dates><isbn>1536-867X</isbn><urls></urls></record></Cite></EndNote>3The treatment stock of tumor type i in year t, Kit depends on NDAs/BLAs for tumor type i in the years k ≤ t, NDAi,k≤t Ki,t=l=0LωlNDAi,t-ll=0Lωl=1where ωl equals the weight on new indications approved in the t–l th period and l indicates the number of lag periods. The treatment stock by tumor type and year are illustrated in REF _Ref33190053 \h \* MERGEFORMAT Figure S2 above.Then the change in the number of annual deaths for tumor type i for a one-unit increase in the treatment stock equals:?morti,t?Ki,tpopt100,000= βi,3popt100,000Substituting (2) into (1): morti,t=βi,0+βi,1incidi,t+βi,2incidi,t-1+βi,3l=0LωlNDAi,t-l+εi,t,where L = t – 1975 This implies?morti,t?NDAi,t-l= βi,3ωl.Then the change in the number of deaths in year t from tumor type i for an additional NDA/BLA approval in year t–l equals Δdeathsi,t=βi,3ωlpopt100,000,Where popi,t is the tumor relevant population size (ages 20+). Thus, the estimated total number of deaths prevented in year t from actual new indication approvals from l = 0 to L equalsΔtot_deathsi,t=l=0l=Lβi,3ωlpopt100,000NDAi,lSpecifically, the estimated number of deaths prevented from 2000-2016 from new indication approvals since 1975 equalsΔtot_deathsi,2000-2016=t=2000t=2016l=0t-1953βi,3ωlpopt100,000NDAi,lThe total estimated number of deaths prevented for the years 2000 to 2016 from new indication approvals equalsΔtot_deathsi,2016=t=2000t=2016l=0l=t-2000βi,3ωlpopt100,000NDAi,lIn a sensitivity analysis of the overall impact of treatment stock on mortality, we estimated average impact of treatment stock using a fixed effects model at the tumor year-level. Namely, we estimated the following equation using weighted least squaresmorti,t=βi,0+βi,1incidi,t+βi,2incidi,t-1+β3Ki,t+εi,twhere each tumor type was weighted by tmorti,t to account for differences in the magnitude of average mortality rates over the period.Note that equation (4) differs from (1) by holding the impact of treatment stock (β3) constant across all tumor types, and from the aggregated approach by allowing each covariate to take on tumor-specific values.As a further sensitivity analysis we estimated a beta regression model, which is appropriate in cases where the dependent variable is a rate, proportion, or fraction—i.e., takes values between but not including 0 and 1. ADDIN EN.CITE <EndNote><Cite><Author>Ferrari</Author><Year>2004</Year><RecNum>2290</RecNum><DisplayText><style face="superscript">4</style></DisplayText><record><rec-number>2290</rec-number><foreign-keys><key app="EN" db-id="f2azt92rkexrt0e90ervrezi00prx0xxstt5" timestamp="1582748377">2290</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Ferrari, Silvia</author><author>Cribari-Neto, Francisco</author></authors></contributors><titles><title>Beta Regression for Modelling Rates and Proportions</title><secondary-title>Journal of Applied Statistics</secondary-title></titles><periodical><full-title>Journal of Applied Statistics</full-title></periodical><pages>799-815</pages><volume>31</volume><number>7</number><dates><year>2004</year><pub-dates><date>2004/08/01</date></pub-dates></dates><publisher>Taylor &amp; Francis</publisher><isbn>0266-4763</isbn><urls><related-urls><url> In this model the deaths per 100,000 were expressed as a rate, e.g., 50 deaths per 100,000 was expressed as 0.0005, but the specification was otherwise the same as in Equation (1). The mean mortality for tumor type i in year t conditional on the covariate matrix x, μx, i, t, was modeled using a logit link function:μx, i, t=expβi,0+βi,1incidi,t+βi,2incidi,t-1+βi,3Ki,t+εi,t1+expβi,0+βi,1incidi,t+βi,2incidi,t-1+βi,3Ki,t+εi,t.Since the magnitude of the effect size cannot be determined from the estimated coefficients from the beta regression model, the average effect sizes for each tumor type and year were estimated using the margins command in Stata 16.0. ADDIN EN.CITE <EndNote><Cite><Author>StataCorp</Author><Year>2020</Year><RecNum>2288</RecNum><DisplayText><style face="superscript">5,6</style></DisplayText><record><rec-number>2288</rec-number><foreign-keys><key app="EN" db-id="f2azt92rkexrt0e90ervrezi00prx0xxstt5" timestamp="1582747673">2288</key></foreign-keys><ref-type name="Web Page">12</ref-type><contributors><authors><author>StataCorp,</author></authors></contributors><titles><title>betareg — Beta regression</title></titles><number>February 26, 2020</number><dates><year>2020</year></dates><urls><related-urls><url> app="EN" db-id="f2azt92rkexrt0e90ervrezi00prx0xxstt5" timestamp="1582747922">2289</key></foreign-keys><ref-type name="Web Page">12</ref-type><contributors><authors><author>StataCorp,</author></authors></contributors><titles><title>margins — Marginal means, predictive margins, and marginal effects</title></titles><number>February 26, 2020</number><dates><year>2020</year></dates><urls><related-urls><url> We used the margins command to predict mortality for each tumor type and year conditional on the treatment stock in that year (mi,t|si,t), then calculated the difference in the expected mortality (mi,t) if the treatment stock had been 0. We multiplied this difference by the population in year t (popt) to calculate the change in deaths by year and tumor type. That is:Δdeathsi,t=mi,t×popt.The total/cumulative deaths prevented from 2002–2016 by tumor type were calculated as:Δdeathsi=t=20022016mi,t×popt.Figure S2 below shows the total deaths averted by year estimated via the beta regression, while Table S4 provides the coefficients and p-values for the tumor-level results.Figure S SEQ Figure \* ARABIC 2. Number of deaths prevented per year from 2002–2016 in the US from treatment stocks, beta regression sensitivity analysisTable S2. Coefficients from beta regression sensitivity analysisTumor typep-valueCoefficient Breast**<0.001-0.28Colorectal0.051-0.20Renal**<0.001-0.18Leukemia**<0.001-0.15Lung**<0.001-0.35NHL**<0.001-0.29Oral0.480-0.74Pancreas0.107-0.09Prostate0.005-1.85Melanoma**<0.001-0.53Gastric<0.001-0.48Thyroid0.0300.54Bladder0.0740.45Overall**<0.001-0.07Regression specifications for alternative micro-level approach using SEER dataIn the alternative micro-level approach, we conducted a similar version of the baseline analysis but used individual data from SEER. Specifically, rather than using aggregate cancer-related mortality at the population level, we used individual level data from SEER to evaluate changes in cancer-related mortality among SEER-region patients with cancer. Due to the use of individual mortality instead of aggregate rates, we used 3-year cancer-specific mortality as the outcome, which covers individuals diagnosed from 2000 to 2013. The regression equation of interest was:mortalityity=β0+β1ksy+demoi'β2+ insi'β3+y=20002013provy'β4,y+r=14stageir'?regioni,rβ5,r+u=13stagei,u'?urbani,uβ6,uwhere:mortalityity indicates whether individual i with tumor type t diagnosed in year y died from cancer within 3 years of diagnosisks is the treatment knowledge stock measuredemo is a vector of individual demographic variables: age, gender, race/ethnicity, marital status, urban/rural residence, and 4 census regionsins is a vector of insurance type indicators: uninsured, Medicaid, other. These are available after 2007 only, a separate indicator denotes unknown status prior to 2007.prov is a vector of health care provider variables at the county year/level: GPs, GP practices, radiologists, general surgeons, and radiation oncologists per capita stagei represents tumor stage (local, regional, distant) interacted with indicators for the 4 Census regions and 3 urban/rural indicators.For the regression of mortality from all tumor types on overall treatment stock, all covariates (except demographics) were additionally interacted with the tumor type to allow their impact to vary by tumor. We used OLS to keep the methodology similar to the base analysis, and clustered standard errors at the county level.The primary drawback of this approach is that controlling for patient disease stage over time allows for lead time bias, stage migration, and length biased sampling.PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Db25ub3I8L0F1dGhvcj48WWVhcj4xOTg5PC9ZZWFyPjxS

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ADDIN EN.CITE.DATA 3-5 For instance, as detection sensitivity improves over time, early stage patients in the later years of the sample would be diagnosed with cancer in SEER whereas previously they may not have been included in the data set. Thus, using individual-level SEER data could overestimate the survival improvement. This bias, however, may be mitigated by controlling for radiologists, GPs and GP practices per capita as proxies for availability of detection, while general surgeons and radiation oncologists per capita serves as a measure of variation in regional treatment intensity. ADDIN EN.CITE <EndNote><Cite><Author>Seabury</Author><Year>2016</Year><RecNum>2379</RecNum><DisplayText><style face="superscript">6</style></DisplayText><record><rec-number>2379</rec-number><foreign-keys><key app="EN" db-id="vw5sra2acxtvwheppa3pe0xre5apapzfrdre" timestamp="1582932285">2379</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Seabury, Seth A</author><author>Goldman, Dana P</author><author>Gupta, Charu N</author><author>Khan, Zeba M</author><author>Chandra, Amitabh</author><author>Philipson, Tomas J</author><author>Lakdawalla, Darius N</author></authors></contributors><titles><title>Quantifying Gains in the War on Cancer Due to Improved Treatment and Earlier Detection</title><secondary-title>Forum for Health Economics and Policy</secondary-title></titles><periodical><full-title>Forum for Health Economics and Policy</full-title></periodical><pages>141-156</pages><volume>19</volume><number>1</number><dates><year>2016</year></dates><publisher>De Gruyter</publisher><isbn>1558-9544</isbn><urls></urls></record></Cite></EndNote>6 We apply estimated changes in mortality to the full US population in order to make the results comparable to our base macro-level analysis. This approach should be considered an approximation; while SEER regions are broadly comparable to full US cancer populations, they have greater racial and ethnic diversity and greater economic deprivation. ADDIN EN.CITE <EndNote><Cite><Author>Kuo</Author><Year>2016</Year><RecNum>514</RecNum><DisplayText><style face="superscript">7</style></DisplayText><record><rec-number>514</rec-number><foreign-keys><key app="EN" db-id="0z5dssaex9wssee2wsbva224s0ssx9s22pa0" timestamp="1588447507">514</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Kuo, Tzy-Mey</author><author>Mobley, Lee R</author></authors></contributors><titles><title>How generalizable are the SEER registries to the cancer populations of the USA?</title><secondary-title>Cancer causes &amp; control</secondary-title></titles><periodical><full-title>Cancer causes &amp; control</full-title></periodical><pages>1117-1126</pages><volume>27</volume><number>9</number><dates><year>2016</year></dates><isbn>0957-5243</isbn><urls></urls></record></Cite></EndNote>7As shown in Table S2 below, the results between our main macro-level analysis and the individual-level approach are comparable. The key changes are that pancreatic cancer has increased magnitude and becomes statistically significant at p=0.022, while renal, thyroid, and bladder cancers are no longer statistically significant. Table S3. Results of individual-level SEER analysisMicro-level approach: Individual-level SEER analysisBase analysis (macro-level)Tumor typeChange in deathsp-valueChange in deathsp-valueBreast-109,228<0.001-127,874<0.001Colorectal-84,519<0.001-46,7050.004Renal-7,588.067-5,365<0.001Leukemia-115,463<0.001-38,586<0.001Lung -370,453<0.001-375,256<0.001NHL-45,170<0.001-48,836<0.001Oral-12,379<0.001-2,0590.189Pancreas-21,3940.022-3,1400.054Prostate-14,0980.519-476,2100.075Melanoma-16,9370.002-6,615<0.001Gastric-7,5480.002-4,0240.019Thyroid2080.9608250.028Bladder-2,3060.8857,7680.002All tumors-839,490<0.001-1,291,769<0.001* Estimate not available due to 0 treatment stock in 2000–2013. Note: Sensitivity analysis included individuals diagnosed through 2013 to allow for 3-year mortality. Changes in deaths in 2014–2016 were projected based on parameter estimates to increase comparability with the base analysis.Table S4. SEER region healthcare providers per 10,000 populationYearRadiologistsGeneral surgeonsRadiation oncologistsGPs20000.981.160.132.8220011.011.220.132.8620031.021.190.142.9120041.011.180.132.8720061.021.170.142.8620071.021.160.142.8720081.031.160.142.8520091.041.140.142.8520101.041.120.142.8620131.081.170.152.9420141.071.140.152.9420151.071.140.152.9520161.071.120.152.97Note: GP = general practitioners. AHRF data for the given variables is unavailable for 2002, 2005, 2011, and 2012. It was interpolated for the purposes of the individual-level analysis.Regression specification for the falsification testWe performed a falsification test examining whether future approvals affected past mortality rates. The specification was the same as equation 4, above, with the addition of the variable nda_post4, which contained the sum of the four future years of approvals. For example, when t=2007, nda_post4 is the sum of approvals for that tumor type in 2008–2011. Equation 6 below displays the regression equation, which was estimated with weighted least squares, similar to equation 4. Note that this specification excludes the final four years of data, therefore the maximum year in equation 6 is 2012.morti,t=βi,0+βi,1incidi,t+βi,2incidi,t-1+β3Ki,t+β4nda_post4i,t+εi,tIn contrast to the treatment stock measure, we did not impose a weighting scheme as there is no theoretical structure for a future approval to affect the past. The coefficient on nda_post4 was small and statistically insignificant. Table S5 shows the estimated treatment stock coefficient for equation 4 compared to the treatment stock and nda_post4 coefficients estimated from equation 6.Table S5. Comparison of results from original fixed effects estimation and falsification testEquation 4(original)Equation 6 (falsification)VariableEstimated coefficientp-valueEstimated coefficientp-valueKi,t-5.31<.001-5.88<.001nda_post4i,t--0.010.887References ADDIN EN.REFLIST 1.National Cancer Institute. Milestones in Cancer Research and Discovery. 2015; . Accessed February 26, 2020.2.Driscoll JC, Kraay AC. Consistent covariance matrix estimation with spatially dependent panel data. Review of economics and statistics. 1998;80(4):549-560.3.Hoechle D. Robust standard errors for panel regressions with cross-sectional dependence. The stata journal. 2007;7(3):281-312.4.Ferrari S, Cribari-Neto F. Beta Regression for Modelling Rates and Proportions. Journal of Applied Statistics. 2004;31(7):799-815.5.StataCorp. betareg — Beta regression. 2020; . Accessed February 26, 2020.6.StataCorp. margins — Marginal means, predictive margins, and marginal effects. 2020; . Accessed February 26, 2020. ................
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