More realistic Life Exp. calculations

1. More realistic Life Exp. calculations Deale Gompertz law, New Deale Malin Breast Cancer Paper I am going to talk a little more about computing discounted life expectancy, and in the second half talk about a cost-effectiveness paper where we used my method. I am going to talk a little more about computing discounted life expectancy, and in the second half talk about a cost-effectiveness paper where we used my method.

2. Key Points DEALE is easy to use, but not very accurate Life tables are the gold standard for calculating the impact of varied additive hazards on discounted LE, But Mixed DEALEs work well In Malin, CEA is used to devise a low cost breast cancer package for uninsured women-- shows tradeoffs between covering more people and generosity of care. These are my main take away points from this class. When you review, you could see if you got them.These are my main take away points from this class. When you review, you could see if you got them.

3. Survival and Life Expectancy (LE) I will start with a quick review of survival analysis and Life Expectancy. Survival analysis is the key to understanding long-term outcomes. Explain survival curve �Kaplan-Meier� : Imagine cohort of 1,000 people. Vertical S(t) axis= number of people alive at start of each subsequent year, marked on X axis= time from birth or start of treatment. What is S(t)- S(t+1)? Death, also S(t+1) = s(t) S(t). These curves come from models or data on survival e.g. of 10s of 1000s of women with various adjuvant therapies in Breast Cancer. � life expectancy � = average number of years they live = total number of years cohort lives/1,000. As shown, each vertical slice = another year. Can add them 1 year at at time to get the area under the survival curve as total years before they all die. In the graph, everyone dies on Dec 31. It is more realistic to subtract 1/2 year from each vertical slice -- Why? area of little triangle on top-- those dying might die on average halfway through the year) This is called the �half cycle correction� in Treeage. I will start with a quick review of survival analysis and Life Expectancy. Survival analysis is the key to understanding long-term outcomes. Explain survival curve �Kaplan-Meier� : Imagine cohort of 1,000 people. Vertical S(t) axis= number of people alive at start of each subsequent year, marked on X axis= time from birth or start of treatment. What is S(t)- S(t+1)? Death, also S(t+1) = s(t) S(t). These curves come from models or data on survival e.g. of 10s of 1000s of women with various adjuvant therapies in Breast Cancer. � life expectancy � = average number of years they live = total number of years cohort lives/1,000. As shown, each vertical slice = another year. Can add them 1 year at at time to get the area under the survival curve as total years before they all die. In the graph, everyone dies on Dec 31. It is more realistic to subtract 1/2 year from each vertical slice -- Why? area of little triangle on top-- those dying might die on average halfway through the year) This is called the �half cycle correction� in Treeage.

4. Life Expectancy (LE) with continuous death You can do the same thing assuming people die continually. Then instead of descending stairs, we have a smooth down-slope, and instead of a sum, we have an integral. I wont go through the calculus versions here, but if you know calculus you can check them out yourself. You can do the same thing assuming people die continually. Then instead of descending stairs, we have a smooth down-slope, and instead of a sum, we have an integral. I wont go through the calculus versions here, but if you know calculus you can check them out yourself.

5. Life Tables for males, US 2004 US life tables were used in many CEAs I have helped with. Here is an excerpt from Vital Statistics web-site: represents deaths in US for men in 2004 by a Life Table. Rows represent age intervals, I�ll go through columns: note number died = AxB, years lived is between 1000 that started and 993 that finished. Cumulative survival = area under survival curve from this age on. It is done in Excel by adding from the bottom. So at age 0, it = cum survival at age 1 + 994. Life expectancy is then cum survival/ the number alive at the start, as shown. So this table gives the life expectancy at every age. At some point, here age 100, they stop. Take a look at the handout or the NCHS website if you are interested. This is a very simple spreadsheet program to write. They should do it for you, but I am not sure they do.US life tables were used in many CEAs I have helped with. Here is an excerpt from Vital Statistics web-site: represents deaths in US for men in 2004 by a Life Table. Rows represent age intervals, I�ll go through columns: note number died = AxB, years lived is between 1000 that started and 993 that finished. Cumulative survival = area under survival curve from this age on. It is done in Excel by adding from the bottom. So at age 0, it = cum survival at age 1 + 994. Life expectancy is then cum survival/ the number alive at the start, as shown. So this table gives the life expectancy at every age. At some point, here age 100, they stop. Take a look at the handout or the NCHS website if you are interested. This is a very simple spreadsheet program to write. They should do it for you, but I am not sure they do.

6. Captions for Life Table Mild digression: period LE at birth is a measure used often in population health comparisons. It is a fictional summary statistic based on a survival curve where each drop comes from last years death rates, not from a cohort. It is a reasonable measure of population health, and my committee to measure national health recommends it. Cohort LE -- see next slide Mild digression: period LE at birth is a measure used often in population health comparisons. It is a fictional summary statistic based on a survival curve where each drop comes from last years death rates, not from a cohort. It is a reasonable measure of population health, and my committee to measure national health recommends it. Cohort LE -- see next slide

7. Cohort Life Expectancy after treatment Cohort LE after treatment comes from longitudinal studies and can be transformed to probability of survival. So if there are say 1000 in treatment cohort we followed, we divide those surviving to each period by 1000, we start with S(0) = 1, the 900 alive after a year becomes .9, and S(t) is the probability a patient is still alive at time t, and LE is the area under the survival curve/1. Cohort LE after treatment comes from longitudinal studies and can be transformed to probability of survival. So if there are say 1000 in treatment cohort we followed, we divide those surviving to each period by 1000, we start with S(0) = 1, the 900 alive after a year becomes .9, and S(t) is the probability a patient is still alive at time t, and LE is the area under the survival curve/1.

8. DEALE: If death rate is constant d, Life Expectancy = 1/d Assuming the death rate is constant is a good approximation for people with some severe diseases such as lung cancer, on dialysis for kidney failure or advanced CHF. This is the Markov assumption: With constant death rate, we get a simple formula for LE, as shown. The proof depends on formula for the sum of a geometric series. We have drawn it as continuous but its true for staircase survival also. DRAW ONE ON BOARD FOR LATER USE of DEALE STAIRCASE. Assuming the death rate is constant is a good approximation for people with some severe diseases such as lung cancer, on dialysis for kidney failure or advanced CHF. This is the Markov assumption: With constant death rate, we get a simple formula for LE, as shown. The proof depends on formula for the sum of a geometric series. We have drawn it as continuous but its true for staircase survival also. DRAW ONE ON BOARD FOR LATER USE of DEALE STAIRCASE.

9. Derivation of DEALE equation Proof of Deale: ( Algebra) with staircase survival Draw that survival on board. Sum (1+ s + s^2 + s^3 =....) = I = I s 1 = I - Is, I = 1/(1-s),Proof of Deale: ( Algebra) with staircase survival Draw that survival on board. Sum (1+ s + s^2 + s^3 =....) = I = I s 1 = I - Is, I = 1/(1-s),

10. Discounting is like death Discounting future years at rate r% is formally like assuming r% additional deaths each year. At the start of the second year, we have a proportion d who have died. When we add in years from year 2 in total years lived, each year has value 1-r So these years = S0(1-d)(1-r) = S0(1-d-r+dr) dr is the product of two small #s and so negligible If we divide year into smaller time periods, dr disappears. in the third year we have S0(1-d0-r)(1-d1-r) disc. years etc. So discounted LE = ?(1-d-r)n if death rate is constant Look at drawing, and assume no one dies but you are counting discounted years of life left, I.e. draw in top horizontal line. With people dying at rate d, take bigger chunk of each year. And what is that sum at bottom = 1/(d+r) because X in this case is d+rLook at drawing, and assume no one dies but you are counting discounted years of life left, I.e. draw in top horizontal line. With people dying at rate d, take bigger chunk of each year. And what is that sum at bottom = 1/(d+r) because X in this case is d+r

11. Example: Using the DEALE to calculate discounted life expectancy Assume a 50 year old white woman will have the average 2005 US LE of 33.3 years after cure. Assume a discount rate of 5%. What is her discounted life expectancy? Death rate = 1/33.3 = .03. So d+r =.08, so discounted life expectancy = 1/.08 = 12.5. What if we assume she will never die, I.e. L = 8. What is her discounted LE? We will do two examples: If L=infinity, d = 1/L = 0 so discounted LE = 1/(0+ .05) = 20 years. That is the most anyone can live at 5% discount rate.We will do two examples: If L=infinity, d = 1/L = 0 so discounted LE = 1/(0+ .05) = 20 years. That is the most anyone can live at 5% discount rate.

12. Mortality and age But, overall death rates increases steadily with age (Gompertz ,1826). Death rate doubles every 8.5 years 30 - 85; women�s rate = 60% that of men the same age similarly for incidence of heart disease So, crude death rate is smaller than 1/L Especially in countries with young populations. crude rate a poor measure of current health On average, the hazard of dying in the whole population is not constant, and death rates increase geometrically with age, doubling every 8 years , with men almost double women. Heart disease goes up at about the same rate. Crude death rates are heavily influenced by the age of the population -- young countries will necessarily grow a lot, and crude death rates will rise. In my committee to measure national health we recommend LE as a measure of current health, not the crude death rate. On average, the hazard of dying in the whole population is not constant, and death rates increase geometrically with age, doubling every 8 years , with men almost double women. Heart disease goes up at about the same rate. Crude death rates are heavily influenced by the age of the population -- young countries will necessarily grow a lot, and crude death rates will rise. In my committee to measure national health we recommend LE as a measure of current health, not the crude death rate.

13. What is impact of added hazards on LE? Need some model to fit data, and then to do calculations. We often assume a baseline or �normal� death rate and model death from additional risks as added to that. So if the death rate from disease B is b, then the death rate for a 40 year old with B is modeled as d40 +b. This ignores the fact that d40 includes some b. b may change predictably in years from incidence. �Additive hazard model� is used for both estimating b, and then in using it in other models. If you don�t have or believe cause of death, reference disease population is young, may assume all cause mortality is essentially disease mortality. The Framingham model we looked at earlier did not have this form -- the risk factors multiplied. But the form we have here is more common for the impact of �independent� diseases or of a dread disease on LE. It probably doesn�t work for little kids in Africa either, as any of the diseases takes out the same kids. may or may not want to take out that risk from regular death rates. Often it is negligible. pattern of death: crisis, remission etc.�Additive hazard model� is used for both estimating b, and then in using it in other models. If you don�t have or believe cause of death, reference disease population is young, may assume all cause mortality is essentially disease mortality. The Framingham model we looked at earlier did not have this form -- the risk factors multiplied. But the form we have here is more common for the impact of �independent� diseases or of a dread disease on LE. It probably doesn�t work for little kids in Africa either, as any of the diseases takes out the same kids. may or may not want to take out that risk from regular death rates. Often it is negligible. pattern of death: crisis, remission etc.

14. Using the DEALE to calculate impact of dread disease Consider a 50 year old white woman with the average US 2005 LE of 33.33 years. She gets breast cancer and after treatment is assumed to have a 7% chance of dying from it each year. Assume hazard of �normal� and breast cancer deaths add. �Normal� death hazard = 1/33.33 = .03. Combined hazard = .07+.03 = 0.1, so new life expectancy is 1/.01 = 10 years. What is her Discounted LE, with a 5% discount rate? Keep using d = 1/L and vice versa. normal + b + r = .3 +.7 +.5 = .15 1/.15 = 6.67 discounted years.Keep using d = 1/L and vice versa. normal + b + r = .3 +.7 +.5 = .15 1/.15 = 6.67 discounted years.

15. Effect of added hazard in Fixed Lifetime LE model Assume without disease, death rate is 0 for L years, and then the person dies. what does the survival curve look like? What if there is an added hazard of 5% per year? Staircase: new LE = 1+s+s2 +�sL-1 = (1-sL)/(1-s) = 16.4 half-cycle correction 16.4(1-d/2) = 15.96 Or new Life expect. = ? 0 to L : exp(-.0513t)dt = [1-exp(-.0513L)]/.0513. If L = 33.3, this is 15.96 Death rate without disease is assumed to be 0 in early stage of fixed lifetime model. Draw fixed life time and also additional hazard. This model works surprisingly well, as you can see in my paper.Death rate without disease is assumed to be 0 in early stage of fixed lifetime model. Draw fixed life time and also additional hazard. This model works surprisingly well, as you can see in my paper.

16. A better formula for LE with dread disease Weighted average of DEALE and Fixed Lifetime model of LE Suppose in someone over 50, normal LE = L, hazard from dread disease = d LE = p(1- exp(-dL))/d +(1-p)/(d + 1/L), with p = .5 to .75 works well over a wide range of d and L. Easier to implement in EXCEL than a life table. for the 50 year old woman, with p = .75 L =33.3, d =.05, we have LE = .75 * 16 + .25 * 12.5 = 15.1 Keeler E, Bell R. New Deales: other approximations of Life Expectancy, Med Dec Making (12) 307-311,1992. This approach used by numerous graduate students to avoid the effort of a life table. Draw some charts on board? BreakThis approach used by numerous graduate students to avoid the effort of a life table. Draw some charts on board? Break

17. Malin paper Context In 1999, California paid for mammographic screening of uninsured women, but not subsequent treatment. California was considering giving up to $15 million for their treatment. Wanted advice on what to cover. I helped Jennifer Malin with quick project. Screening bills of uninsured were paid out of tobacco settlement. Some private foundations provided some treatment, but state was considering doing more. How could they stretch their limited funds for supporting treatment? They asked Jennifer Malin, a self-confident young doctor, and she asked me to help. How would you have done it?Screening bills of uninsured were paid out of tobacco settlement. Some private foundations provided some treatment, but state was considering doing more. How could they stretch their limited funds for supporting treatment? They asked Jennifer Malin, a self-confident young doctor, and she asked me to help. How would you have done it?

18. Framing Use cost-effectiveness analysis to rate different treatments -- costs from CA government perspective = direct medical, but health benefits to women. For budget, need estimates of �incidence.� actual: cases expected from current screening levels potential: if screens = uninsured x incident cancer <65 Early (curable) breast cancer in women under 65. Studied 8 representative women. 45 or 60 ER+ (can use tamoxifen) or ER- lymph node involved (40%) or not (20% 10 year survival) Budget goes to medical costs, want maximum health benefit for that. good setup for CEA. This incidence is the incidence of breast cancer found in positive mammographies, not of breast cancer per se. So again we have issue of current people getting screened, vs what would happen if treatment were also covered. We did both. Curable because that is way more efficient and luckily incurable are eligible for Medicaid, under 65 because most women get insurance at that age. Outcomes and best treatment depends on pateint characteristics, we picked 8 types to study - reasonable data on breakdown to these typesBudget goes to medical costs, want maximum health benefit for that. good setup for CEA. This incidence is the incidence of breast cancer found in positive mammographies, not of breast cancer per se. So again we have issue of current people getting screened, vs what would happen if treatment were also covered. We did both. Curable because that is way more efficient and luckily incurable are eligible for Medicaid, under 65 because most women get insurance at that age. Outcomes and best treatment depends on pateint characteristics, we picked 8 types to study - reasonable data on breakdown to these types

19. Treatments Diagnostic evaluation always given Therapy for DCIS always given Surgery: mastectomy or BCS post-op radiation Adjuvant therapy tamoxifen for ER+ and chemo reconstruction after mastectomy BMT: expensive risky last chance procedure Follow-up: regular always given intensive shown to have no benefit in trials Things that are always given are not part of decision, but have to be included because they use up the budget. Choices involve what kind of surgery, and subsequent radiation and adjuvant therapy are given to whom.Things that are always given are not part of decision, but have to be included because they use up the budget. Choices involve what kind of surgery, and subsequent radiation and adjuvant therapy are given to whom.

20. Data on benefits and costs EBCTCG had great data on treatment of early breast cancer: surgery, radiation and chemo. We also looked at reconstruction and BMT where data was not as good. Had expert opinion from earlier papers. Costs from Medicare allowed charges for services, AWP for drugs (with PHS discounts in sens. analysis) EBCTCG trialists collaborative group = trials with 10s of thousands of women randomized to all these treatments. JM also searched recent abstracts etc. for effects of new technologies. BMT was a bad example of technological diffusion -- a lot of people were winging this expensive, risky therapy without being required to be in trials, and without any evidence it worked. Problem of charges -- what would this government program for poor women pay? We assumed standard allowed charges and looked at some discounts in sensitivity analysis.EBCTCG trialists collaborative group = trials with 10s of thousands of women randomized to all these treatments. JM also searched recent abstracts etc. for effects of new technologies. BMT was a bad example of technological diffusion -- a lot of people were winging this expensive, risky therapy without being required to be in trials, and without any evidence it worked. Problem of charges -- what would this government program for poor women pay? We assumed standard allowed charges and looked at some discounts in sensitivity analysis.

21. Issues Utility of life during and after treatment disutility of treatment x length of treatment? later life disutility? Evidence vs. Standard of care radiation after surgery does not improve survival BCS dominates mastectomy + reconstruction. if it is possible. but law mandates private insurers cover reconstruction No evidence on BMT effectiveness we calculated how good it would have to be to be cost-effective. BC treatment very onerous -- people suffer now so they will live longer. some studies and opinions on how low QOL is during therapy -- we multiplied time in therapy x (1-QOL) to get the health cost of treatment. A few weeks that were subtracted from much larger LE gains. after treatment, global QOL of survivors was reported to be very high. -- no change for BCS vs mastectomy, but some other satisfaction measures were higher with BCS. A standard trick if you don�t know how good something is a calculation of how good it would have to be to be worthwhile -- BMT would have to reduce mortality to 20% BC treatment very onerous -- people suffer now so they will live longer. some studies and opinions on how low QOL is during therapy -- we multiplied time in therapy x (1-QOL) to get the health cost of treatment. A few weeks that were subtracted from much larger LE gains. after treatment, global QOL of survivors was reported to be very high. -- no change for BCS vs mastectomy, but some other satisfaction measures were higher with BCS. A standard trick if you don�t know how good something is a calculation of how good it would have to be to be worthwhile -- BMT would have to reduce mortality to 20%

22. Calculating Life expectancy gains Studied 8 types of women age 45, 60 node - and + = 20, 40% 10 year survival, ER+ (can use tamoxifen), ER- breast cancer. Used reported odds from EBCTCG for survival to 10 years, then constant added BC risk over normal women for rest of life. constant added hazard fit well for first 10 years Lots of calculations to get discounted LE, so used mixed Deale, EXCEL Validated results against Life Tables for one treatment always within .03 years. ER+ women can use Tamoxifen a cheap treatment that works well on them. Odds of survival to 10 years for various treatments -- see paper. Why odds? that�s what the trial reports because they analyze with logistic or cox. These 8 cases x treatment packages x various discount rates � lots of calculations.ER+ women can use Tamoxifen a cheap treatment that works well on them. Odds of survival to 10 years for various treatments -- see paper. Why odds? that�s what the trial reports because they analyze with logistic or cox. These 8 cases x treatment packages x various discount rates � lots of calculations.

23. Life tables for women with breast cancer Start with standard life table for population of interest Add in another column for hazard of dying if you have breast cancer by age this column depends on age of onset type of disease and treatment Use combined hazard = sum of these columns Just need to add two more columns -- one with the breast cancer risk, and one combined. Maybe draw on board.Just need to add two more columns -- one with the breast cancer risk, and one combined. Maybe draw on board.

24. Presenting Results For all recommendations, we talked about number of lives saved, not QALYs gained. Put together a minimum package of very cost-effective treatments Costed some more expensive treatments: more radiation, breast reconstruction Compared this to giving the minimum package to more uninsured women with cancer. Briefed the foundation that was trying to get a sensible measure passed. They liked lives rather than discounted QALYs, as who would not. Women were of comparable ages, so lives made sense, particularly in this within disease context. We generally like the efficient care for more, but once you touch someone it is hard to deny them any standard care. Briefed the foundation that was trying to get a sensible measure passed. They liked lives rather than discounted QALYs, as who would not. Women were of comparable ages, so lives made sense, particularly in this within disease context. We generally like the efficient care for more, but once you touch someone it is hard to deny them any standard care.