The effect of statins on average survival in randomised trials, an analysis of end point postponement

Malene Lopez Kristensen; Palle Mark Christensen; Jesper Hallas

doi:10.1136/bmjopen-2014-007118

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The effect of statins on average survival in randomised trials, an analysis of end point postponement

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Re: The effect of statins on average survival in randomized trials, an analysis of end point postponement
Jodell Smith, Terry J Campbell
Published on: 25 November 2020
Do Statins only postpone death by three or four days?
Bendix Carstensen
Published on: 4 July 2016
Re:The effect of statins on average survival - revisited
Jesper Hallas
Published on: 15 March 2016
Error in median values
Jesper Hallas
Published on: 15 March 2016
The effect of statins on average survival - revisited
Shu-Ching Chang
Published on: 15 March 2016
Assessing postponement time
Roger J Marshall
Published on: 15 March 2016

Published on: 25 November 2020
Re: The effect of statins on average survival in randomized trials, an analysis of end point postponement
- Jodell Smith, student The University of the Bahamas
- Other Contributors:
  Terry J Campbell, Lecturer
Dear Editor:
This response is in relation to your article. I found this article useful in many different ways for example, the number needed to treat (NNT) systems. I also gained the knowledge of primary and secondary prevention trials. What amazed me though was that the number were so small being that the “highest value was 27 days according to the 4S study.
While I understand that patients have the right to refuse treatment, I did not expect 70% of individuals to decline. It was good to note that although the survival time was only implemented during the running time of the study, a few follow up trials were done, regardless of the mortality rate discovered. Although, according to Benner et al., (2002), “despite slightly better persistence among patients who began treatment in recent years, long-term use remains low”, the efforts made to research this drug is amazing. The idea of a hybrid model of classical NNT thinking along with a postponement model sounds interesting and effective.
The focus of your study including all-cause mortality was an unbiased study. What grasped my attention the most was that you realized your mistake, admitted your mistake, made corrections, and apologized for the inconvenienced caused. Thanks for indicating that statins are inexpensive when used in the clinical settings and I agree that if the patient has intolerance or unpleased side effects from statins, it should not be forced upon them. The use of postp...
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Dear Editor:
This response is in relation to your article. I found this article useful in many different ways for example, the number needed to treat (NNT) systems. I also gained the knowledge of primary and secondary prevention trials. What amazed me though was that the number were so small being that the “highest value was 27 days according to the 4S study.
While I understand that patients have the right to refuse treatment, I did not expect 70% of individuals to decline. It was good to note that although the survival time was only implemented during the running time of the study, a few follow up trials were done, regardless of the mortality rate discovered. Although, according to Benner et al., (2002), “despite slightly better persistence among patients who began treatment in recent years, long-term use remains low”, the efforts made to research this drug is amazing. The idea of a hybrid model of classical NNT thinking along with a postponement model sounds interesting and effective.
The focus of your study including all-cause mortality was an unbiased study. What grasped my attention the most was that you realized your mistake, admitted your mistake, made corrections, and apologized for the inconvenienced caused. Thanks for indicating that statins are inexpensive when used in the clinical settings and I agree that if the patient has intolerance or unpleased side effects from statins, it should not be forced upon them. The use of postponement measures should be given to patients whose life expectancy is short and survival rate is limited. I look forward to reading more articles from you and leaning more.

11 November 2020
Jodell C. Smith
Student
The University of the Bahamas
Nassau, Bahamas

References
Benner. J. S., Glynn. R. J., Mogun. H., Neumann. P. J., Weinstein. M. C., Avorn. J., (2002). Long-term persistence in use of statin therapy in elderly patients. JAMA. 288(4), 455–461. https://doi.org/10.1001/jama.288.4.455
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Conflict of Interest:
None declared.
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Published on: 4 July 2016
Do Statins only postpone death by three or four days?
- Bendix Carstensen, Senior Statistician
- Other Contributors:
  Marit E Jorgensen
Kristensen et al. report results from a meta-analysis of statin trials on years of life gained published in BMJ Open in 2015 (1). The authors conclude that death was postponed between -5 and 19 days in primary and between -10 and 27 days in secondary prevention trials. The paper has been widely quoted in newspapers under headlines such as "Statins are NOT a magic bullet for longer life" and "Statins may only postpone de...
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Kristensen et al. report results from a meta-analysis of statin trials on years of life gained published in BMJ Open in 2015 (1). The authors conclude that death was postponed between -5 and 19 days in primary and between -10 and 27 days in secondary prevention trials. The paper has been widely quoted in newspapers under headlines such as "Statins are NOT a magic bullet for longer life" and "Statins may only postpone death by three or four days", potentially contributing to the growing skepticism against lipid-lowering treatment. But is the conclusion correct? And what are the assumptions underlying the article's conclusion? The authors use the well-known demographic fact that life extension is equal to the area between the survival curves, and refer to the paper by Wright & Weinstein (2). However they apparently overlook that this article states "A model must be constructed to extrapolate the survival curves beyond the end of the study, and the estimate of the gain in life expectancy may be very sensitive to the choice of model". Kristensen et al. implicitly use a model for extrapolation that assumes that the difference in survival between the treatment groups is 0 immediately after the close of the trial. This is not a very likely scenario, and the authors have in the limitations stated that they have only looked at lifetime gain in the studies' running time. Which makes their claims formally correct, but unfortunately also largely irrelevant. The meta-analysis in the paper calculates the overall mortality reduction in the included study populations and produces rate-ratios (RR) of 0.89, respectively 0.91 for included and excluded studies associated with statin use. In guidelines for treatment of diabetes, statins are recommended for almost all diabetes patients, so diabetes patients constitute a substantial fraction of statin treated patients. Therefore, to elucidate the effect of statin use in a more realistic way, we have calculated life expectancy for people with diabetes with or without statin treatment. We included persons registered in the Danish National Diabetes Register (3) defined as those with a diabetes diagnosis, treated with glucose lowering drugs or receiving foot care as part of their diabetes management. We modeled the mortality of persons with diabetes with age-period-cohort models for ages 0-99 for the period between 1 January 1995-31 December 2012, and used the predicted mortality rates for 2012 to calculate the remaining life expectancy with and without statin therapy at different ages, and various levels of assumed risk reduction by statin therapy.
The figure attached (http://bendixcarstensen.com/DMreg/statinYLL.pdf) shows that the gained life expectancy with statins is e.g. 1.1 years for a man aged 50 assuming a relative mortality rate of 90% which is close to the risk reduction calculated in the meta-analysis. At age 30 the years of life gained is 1.3, while at age 70 closer to 0.7 years, varying according to the risk reduction associated with statin treatment.
The simple message from the meta-analysis by Kristensen et al., that statin treatment contributes only a few days life extension, is in our view thus highly misleading since the most basic demographic assumptions have not been included in the data interpretation. For most diabetes patients the likely life extension is between 6 and 12 months, and patients currently prescribed statins for other reasons are likely to see similar average gain in life time.
A full overview of data and analysis is available at http://bendixcarstensen.com/DMreg/demoYLL.pdf
References 1 Kristensen ML, Christensen PM, Hallas J. The effect of statins on average survival in randomised trials, and analysis of end point postponement. BMJ Open 2015;5:e007118
2 Wright JC, Weinstein MC. Gains in life expectancy from medical interventions-standardizing data on outcomes. N Engl J Med 1998;339:380
3 Carstensen B, Kristensen JK, Ottosen P, Borch-Johnsen K; Steering Group of the National Diabetes Register. The Danish National Diabetes Register: trends in incidence, prevalence and mortality. Diabetologia. 2008 Dec;51(12):2187-96
Conflict of Interest:
None declared
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Conflict of Interest:
None declared.
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Published on: 15 March 2016
Re:The effect of statins on average survival - revisited
- Jesper Hallas, Professor
- Other Contributors:
  Malene Lopez Kristensen, Palle Mark Christensen
We can hardly disagree about the limitations pointed out by Dr Chang et al and by Roger Marshall. We emphasized in the discussion section that the postponements (or increment in restricted mean survival) calculated by us were restricted to the trials' running time, usually in the order of 5 years. We fully agree - and have emphasized in our paper - that they do not answer the question on what would be the benefit from a l...
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We can hardly disagree about the limitations pointed out by Dr Chang et al and by Roger Marshall. We emphasized in the discussion section that the postponements (or increment in restricted mean survival) calculated by us were restricted to the trials' running time, usually in the order of 5 years. We fully agree - and have emphasized in our paper - that they do not answer the question on what would be the benefit from a lifelong statin treatment.
However, the problem is that we can only know about the benefit accrued during the trial. Benefit beyond the trial has to be modelled on the basis of assumptions. Dr Marshall has kindly shared his calculations with us. They are based on extrapolations from two readings on the survival curve two years apart from each other in the LIPID trial. These extrapolations, based on the Weibull distribution, yielded an average survival of 27.1 years in the pravastatin group and 19.2 years in the placebo, for an average gain of 7.9 years. Mathematically correct as it is, it may be a stretch to extrapolate more than twenty years from two close readings. It is unclear to us whether the model takes the increase in mortality by age in to account, which would have limited the postponement achieved. We have performed a simulation, using real-life age -specific mortality rates from the Danish population in 2014. If we reduced the mortality rate by 22% from age 62 onwards as in the LIPID trial, we arrived at 1.8 years' longer survival with lifelong statin treatment. One may note that the LIPID trial is an outlier. It had the second longest postponement and the second lowest hazard ratio of all trials, only surpassed by the 4S trial. If we applied a hazard ratio of 0.89 as we found in the meta-analysis of included trials, we arrived at 0.8 years' postponement of death for lifelong statin users, starting at age 62. Stovring et al found with a model that incorporated mortality in different risk strata, postponements between 3 and 11 month for lifelong statin treatment, depending on the baseline risk and age at statin initiation (1). Chang arrived at 3.0 years for the LIPID trial. Without necessarily arguing which is correct, at least we can note that these values are highly variable and seem to be strongly dependent on assumptions.
In clinical practice, statin treatments often have a fairly limited duration, either because of non-adherence (2,3) or because users are already old when they initiate therapy. We carefully phrased our conclusions and recommendations as to reflect that the benefit in statin treatment would be limited for patients whose life-expectancy was short and that the patient or physician might reconsider the treatment if the patient had intolerance to statins.
References
1. Stovring H, Harmsen CG, Wisloff T, Jarbol DE, Nexoe J, Nielsen JB, et al. A competing risk approach for the European Heart SCORE model based on cause-specific and all-cause mortality. Eur J Prev Cardiol. 2013 Oct;20(5):827-36.
2. Monaldi B, Bologna G, Costa GG, D'Agostino C, Ferrante F, Filice M, et al. Adherence to statin treatment following a myocardial infarction: an Italian population-based survey. Clin Outcomes Res CEOR. 2015;7:273-80.
3. Shah ND, Dunlay SM, Ting HH, Montori VM, Thomas RJ, Wagie AE, et al. Long-term medication adherence after myocardial infarction: experience of a community. Am J Med. 2009 Oct;122(10):961.e7-13.
Conflict of Interest:
None declared
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Conflict of Interest:
None declared.
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Published on: 15 March 2016
Error in median values
- Jesper Hallas, Professor
- Other Contributors:
  Malene Lopez Kristensen, Palle Mark Christensen
One reader has notified us about an error in our manuscript regarding the calculated median values for postponement of death in secondary prevention trials. These errors have no implications for the conclusions or the discussion of the study.
In the abstract line 16 p.1 "and secondary prevention trials were 3.2 and 4.1 days," The correct line is "and secondary prevention trials were 5,8 and 4,1 days,"
In...
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One reader has notified us about an error in our manuscript regarding the calculated median values for postponement of death in secondary prevention trials. These errors have no implications for the conclusions or the discussion of the study.
In the abstract line 16 p.1 "and secondary prevention trials were 3.2 and 4.1 days," The correct line is "and secondary prevention trials were 5,8 and 4,1 days,"
In the results section line 17 p.2 "secondary prevention trials were 3.2 and 4.1 days," The correct line is "secondary prevention trials were 5,8 and 4.1 days,"
Please accept our apology for any inconvenience
Conflict of Interest:
None declared
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Conflict of Interest:
None declared.
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Published on: 15 March 2016
The effect of statins on average survival - revisited
- Shu-Ching Chang, Biostatistician
- Other Contributors:
  Mansen Wang, James G. Beckerman, Mark Sanz, Ty J. Gluckman, Gary L. Grunkemeier
The recent paper by Kristensen et al. [1] examined 11 randomized clinical trials (RCTs) of statins and concluded that they provide "a surprisingly small average gain in overall survival within the trials' running time", and that "The median postponement of death for primary and secondary prevention trials were 3.2 and 4.1 days, respectively."
This appears to question the value of statins, yet the information a...
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The recent paper by Kristensen et al. [1] examined 11 randomized clinical trials (RCTs) of statins and concluded that they provide "a surprisingly small average gain in overall survival within the trials' running time", and that "The median postponement of death for primary and secondary prevention trials were 3.2 and 4.1 days, respectively."
This appears to question the value of statins, yet the information as presented in this paper should not dissuade their use. Because the study restricted its analysis to, "... within the trials' running time", it reflects a shortsighted view. This is compounded by the fact that many of these trials were stopped early. Importantly, patients on statins enjoy a much greater lifetime extension benefit than that noted within the limited timeframe of these trials, as we will show using a re-analysis of the Kristensen et al. data.
It's also important to note that one of the larger included trials lacking a mortality benefit, ALLHAT-LLA, had a between difference reduction in LDL-cholesterol of only 17% [2]. This largely reflected the high rate of statin use in the usual care arm.
The authors used pixel count to estimate the area between the Kaplan-Meier curves for survival. This area equals the difference in mean survival between the two patient cohorts. But, the authors used only the initial part of the survival curves, during the trials' relatively short run-times, ranging from 2.0 to 6.1 years.
The true gain in mean survival should be based on the patients' entire lifetime. We attempted to estimate this quantity using the following method, which we demonstrate using the series [3] that the authors used for demonstration in their online Appendix [4]. Figures are available from the authors upon request (ShuChing.Chang@providence.org).
1. 1. The original Kaplan-Meier curves from Figure 2A in the NEJM paper [3], were digitized using the Engauge Digitizer program [5] to convert the published curve segments into x and y coordinates.
2. 2. Gompertz distributions were fit to the digitized points using the optim function in the statistical package R [6]. The Gompertz distribution [7] is widely used to model survival, fits especially well for older populations [8] and fit these curves very well, as measured by the Kolmogorov-Smirnov tests (p ~ 1.00 for both Pravastatin and Placebo curves).
3. Once we had the model parameters for the Gompertz distribution, we extrapolated the curves out to the end of the patients' lifetimes. The median survival times for the fitted curves of Pravastatin and Placebo were 16.4 years and 13.3 years, respectively, and the difference of median survival times between these two groups was 3.1 years.
4. Finally, we computed the areas between the curves, using the Gompertz formulas. The extension of life out to the end of the RCT (6.1 years) was 22 days, which agrees with what the authors found using their pixel-counting method. But, the total savings in mean lifetime, shown in green, is 3.0 years.
Conclusion
To base clinical decision-making on the extended survival achieved during the relatively short time period of an RCT runtime is misleading; "extra lifetime during the RCT" is only one measure of efficacy. More pertinent to an informed discussion between physician and patient are the lifetime benefits of statins. In this example, the extension of life went from 22 days during the trial period only to 3.0 years for the patient's expected lifespan.
Just we were ready to submit our letter, we found the letter by Professor Marshall [9]. We agree with all he said, and he even foretold the approach that we were taking: "It may be possible to improve on these estimates, scanning and digitizing the published survival curves and fitting the Weibull survival to the digital curves".
References
1. Kristensen, M. L., Christensen, P. M., & Hallas, J. The effect of statins on average survival in randomised trials, an analysis of end point postponement. BMJ open 2015; 5(9): e007118
2. ALLHAT Collaborative Research Group. JAMA 2002;288:2998-3007
3. [No authors listed]. Prevention of cardiovascular events and death with pravastatin in patients with coronary heart disease and a broad range of initial cholesterol levels. The Long-Term Intervention with Pravastatin in Ischaemic Disease (LIPID) Study Group. N Engl J Med 1998;339:1349-57.
4. http://bmjopen.bmj.com/content/suppl/2015/09/24/bmjopen-2014- 007118.DC1/bmjopen-2014-007118supp_appendix.pdf
5. Mitchell, M. (2002). Engauge digitizer 4.1. URL http://digitizer.sourceforge.net
6. R Core Team, R (2015). R: A language and environment for statistical computing. Vienna, Austria; 2014. URL http://www. R-project.org
7. Gompertz, B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical transactions of the Royal Society of London 1825, 513-583
8. Kiche, J., Aduda, J., Athiany, K. H. O., BO, A., & Wanjoya, A. Comparison Of Survival Models And Estimation Of Their Parameters With Respect To Mortality in a Given Population. Mathematical Theory and Modeling 2014; 4(7): 164-176
9. http://bmjopen.bmj.com/content/5/9/e007118.full/reply#bmjopen_el_9394
Conflict of Interest:
None declared
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Conflict of Interest:
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Published on: 15 March 2016
Assessing postponement time
- Roger J Marshall, Associate Professor
Kristensen et al [1] have estimated "postponement" of death in trials due to statins. Their finding is that postponement is measured in days - median pooled 3 to 4 days - which suggests statins have scarcely any benefit. It may well be that their benefits are, indeed, minimal, but the point of this note is not to question efficacy of statins, rather it is to suggest that the statistical analysis presented in this study...
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Kristensen et al [1] have estimated "postponement" of death in trials due to statins. Their finding is that postponement is measured in days - median pooled 3 to 4 days - which suggests statins have scarcely any benefit. It may well be that their benefits are, indeed, minimal, but the point of this note is not to question efficacy of statins, rather it is to suggest that the statistical analysis presented in this study is somewhat misleading.
The method is based on estimating the difference in the area between survival curves of statin and placebo up to a cutoff in time. However, although the area under a survival curve equals average survival time when taken over the whole time span, its interpretation when taken up to a cutoff cannot be viewed in this way. Royston and Parmar [2] have referred to the area under a survival curve up to a cutoff as "restricted mean survival time" (rmst). In effect, rmst replaces survival times that occur after the cutoff with the cutoff value itself. For example in the authors' LIPID case study (Appendix B of [1]), which has a 6.1 year cutoff, it is tantamount to assuming that everyone who survived beyond 6.1 years actually "died" at 6.1 years. Since about 90% of people in the statin group and 85% in the placebo groups survived beyond 6.1 years, and are all regarded as having died at that same time, it is no surprise the mean difference is very small (22 days).
It seems more meaningful to consider postponement of death as the area between placebo and statin groups taken over the full time span. Without raw data and complete follow-up, this cannot be done. However an attempt can be made to model survival from the reported Kaplan-Meier plots to extrapolate the full survival. For example, in Appendix B of [1], a model which allows an increasing hazard may be appropriate (given the apparent increasing slopes). A Weibull model could be considered [3]. It has two parameters and a relatively simple mathematical form for its survival function. The model can be fitted from any two points on a survival curve, and solving for the two parameters. For the LIPID study I took time points at t=6.1 and t=4 years and estimated the survival, S(t), as best I could from the published graphic, for each of the two curves, giving S(6.1)=0.888 and S(4)=0.935 for the statin group, and 0.854 and 0.919 for placebo. The fitted models give mean survival 27.1 and 19.2 years, with mean difference 7.9 years (calculation details available from me).
This analysis, which assumes that the benefit of the drug continues beyond the duration of the trial, is admittedly rather crude. First, it assumes a Weibull model with parameters estimated, rather inefficiently, from two points on a survival curve and read off presumably with some inaccuracy from the ordinates of a zoomed printed graphic. It may be possible to improve on these estimates, scanning and digitizing the published survival curves and fitting the Weibull survival to the digital curves.
However, the difference is unlikely to be appreciable; the main point is that postponement of death is more realistically measured in years if survival curves are extrapolated rather than a few days (7.9 years for the LIPID trial against 22 days as reported in [1]). Further, given that there is a different cutoff for each of the trials analysed in [1] (ranging from 2 to 6.1 years), the reported postponements are not comparable so that pooling them, as the authors have done, is questionable. It would be interesting to analyse each of the trials, as suggested here for the LIPID trial, to obtain a more constructive overall measure.
References
1. Kristensen ML, Christensen PM, and Hallas J. The effect of statins on average survival in randomized trials: an analysis of end point postponement. BMJ Open 2015;5:e007118.doi:10.1136/bmjopen-2014-00718
2. Royston P, Parmar MKB. Restricted mean survival time: an alternative to the hazard ratio for design and analysis of randomized trials with a time-to-event outcome. BMC Medical Research Methodology 2013,13:152 http://www.biomedcentral.com/1471-2288/13/152)
3. https://en.wikipedia.org/wiki/Weibull_distribution
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