INTRODUCTION

One challenge in the practice of medicine lies in adequately explaining the effects of a proposed intervention to enable a patient to make an informed decision. With regard to preventive interventions, such as statin use, effect size is traditionally expressed as relative/absolute risk reductions or “number needed to treat” (NNT). However, such measures are not necessarily best for conveying intervention effect.1, 2

When contemplating preventative treatment, the additional time free of an undesirable clinical event can be considered more relevant. This average postponement of the study outcome represents an alternative to traditional effect measures for preventive treatment.3, 4 It has been shown that patients are responsive to outcome postponement, i.e., their chance of accepting the treatment changes increases when they are presented with higher values of outcome postponement.5 On the other hand, even extreme differences in the presented values of NNT do not lead to greater or lower rates of treatment acceptance.6,7,8 Moreover, NNT conveys a “lottery-like” understanding of how the treatment effect is distributed, potentially suggesting that the risk of death is influenced in only 1 in 40 treated patients. As statin treatment reduces cholesterol levels in nearly all treated patients9 and a clear correlation between LDL cholesterol lowering and mortality has been demonstrated,10 it thus seems more plausible that statins slow atherosclerotic progression to some extent and thereby potentially delay death in all persons receiving treatment.

Methodologically, the average postponement accrued during a trial’s duration can be estimated as the area between the survival curves for patients receiving the drug and placebo.4 Kristensen et al.5 recently published a systematic review of 11 randomized clinical trials of statin use, each including at least 1000 patients. They estimated that median postponement of all-cause mortality within the trial duration was 3.2 days for primary prevention and 4.1 days for secondary prevention.4 However, their approach has two important weaknesses. First, a Kaplan–Meier survival curve for the outcome in question must be available. Second, measuring the area between survival curves does not allow for calculation of the variance of outcome postponement in the single trial, and thus outcome postponement cannot be subjected to meta-analysis using this approach.

In this study, we present a method for the meta-analysis of outcome postponement based on summary statistics from RCTs. We demonstrate the application of this method to estimate the average postponement of all-cause mortality based on meta-analysis of large placebo-controlled statin trials.

METHODS

Data Sources and Searches

We searched MEDLINE (search index date: May 1, 2015) using the following MeSH terms: statins, placebo, and random*. We also searched ClinicalTrials.gov (search index date: December 1, 2015) using the following terms: “statins” AND “placebo” (interventional). We further screened the reference lists of the included papers, but identified no additional studies for inclusion.

Study Selection

Our meta-analysis included randomized controlled trials of ≥ 1000 patients, in which a statin intervention (any type) was compared with placebo using a predefined primary or secondary outcome of death by any cause and having a minimum trial follow-up of 2 years. Furthermore, we only used the original publication, i.e., we excluded sub-studies of the original trial, and we excluded trials which investigate a pediatric population (< 18 years). Lastly, we excluded trials that did not provide parameters required for postponement estimation. Initially, we screened all abstracts for eligibility. We then extracted full-texts articles, which we categorized with reasons for exclusion (Table e1-online).

Data Extraction and Quality Assessment

Two authors (MRH and KGM) independently extracted trial characteristics and outcome data from each included trial. Any discrepancies were resolved by consensus. The extracted trial characteristics included the trial’s duration; whether it represented primary, secondary, or mixed intervention; and baseline LDL cholesterol level. The effect data included hazard ratio (HR) or relative risk (RR) and 95% confidence interval (CI), and the mortality rate or cumulative mortality in the placebo group. We defined primary prevention trials as trials in which no patients had manifest cardiovascular disease at baseline, secondary prevention trials as those in which all of the patients had cardiovascular disease, and mixed prevention trials as trials including patients with and without cardiovascular disease. Two physicians independently performed trial classification.

The assessment of bias was performed using the Cochrane’s risk of bias tool.11

If the paper did not report an estimated mortality rate in the placebo group, we used the following hierarchy of alternative measures: (a) the mortality rate among patients randomized to placebo as calculated by us based on the number of randomized patients, number of outcomes, and average follow-up; (b) the cumulative mortality among patients randomized to placebo as reported in the paper; (c) the cumulative mortality among patients randomized to placebo as determined from the Kaplan–Meier survival curve; and (d) the mortality rate among patients randomized to placebo, as calculated by us based on the number of randomized patients, number of events, and median follow-up. The latter approach may overestimate or underestimate the mortality rate, depending on whether the median follow-up is higher or lower than the average.

For trials that reported relative risk (n = 6) instead of hazard ratio as the outcome measure, we used relative risk as a proxy for hazard ratio. These measures are very similar when the cumulative risk values are low, e.g., below 20%.11 None of the six trials that reported RR had a cumulative mortality risk of > 15%.

Data Analysis: Outcome Postponement

We have calculated outcome postponement of death in each trial. Postponement is described by the area between survival curves. We have used two different methods, pixel counting and our novel mathematical model to estimate this area, which equals the postponement (gain in time) achieved in the active group. For details about the methods behind estimation of postponement from the mathematical model and pixel counting, see appendixes A- and B-online.

Data Analysis: Meta-analysis

We performed a meta-analysis of the postponement of all-cause death using inverse variance weighting and random effects models (STATA 14, Stata Corp., Texas) and using postponement intervals in place of confidence intervals. In order to describe effect modification by trial characteristics, we grouped trials according to (a) trial duration (> 5 years vs. < 5 years); (b) primary vs. secondary intervention; (c) reporting by HR vs. RR as effect measures for all-cause mortality; (d) high vs. low overall risk of bias; (e) trials with the highest vs. lowest reduction in LDL cholesterol after 1 year and (f) whether or not the trial was terminated earlier than originally planned; (g) according to potency of the statin (low, medium, and high); and (h) the trials with the highest mortality rate vs. the trials with the lowest mortality rate. Moreover, we added a post hoc subgroup analysis comparing trials with high vs. low degree of patient cross-over (for example, from placebo to statin). We further investigated reporting bias using a funnel plot.

To adjust for heterogeneity attributable to the varying durations of the trials, we standardized the trial duration to 5 years in the modeled postponement. Essentially, this modeled the area between survival curves for 5 years of trial duration, based on the actually observed hazard ratio and cumulative mortality among untreated patients. Appendix C-online presents the equations used for standardization. Finally, to assist with interpretation of the postponement meta-analysis, we performed a HR-based meta-analysis of all-cause mortality.

The systematic review was registered in PROSPERO [CRD42016037507].

RESULTS

Trial Retrieval

We identified 115 potentially eligible trials, 16 of which met our inclusion criteria (Fig. 1, Table e1-online). Kaplan–Meier survival curves were available for eight of the trials, and all 16 trials presented the variables required to model the area between survival curves. Table 1 presents the trial characteristics (statin type, number of patients, trial duration, and LDL status). Two (12.5%) were for primary prevention, six (37.5%) for secondary prevention, and eight (50%) for mixed prevention.

Figure 1
figure 1

Flowchart of search to identify randomized, placebo-controlled statin trials.

Full size image
Table 1 Characteristics of the Included Trials
Full size table

Outcome Postponement

Table 2 presents the estimated outcome postponement based on pixel counting and modeling. The median values were 10.6 days with the pixel counting method, and 8.9 days with the modeling method. We found strong agreement between these two methods, a slope of 0.95 with linear regression and a parametric Pearson correlation coefficient of r = 0.94. Across all trials, the summary estimate of outcome postponement was 12.6 days (PI, 7.1–18.0). The I2 value was 59.5, indicating moderate heterogeneity (P = .001). After standardization to a trial duration of 5 years, the estimated summary outcome postponement for all trials was 12.8 days (PI, 8.9–16.7), and I2 decreased to 22.3% which was no longer statistically significant (P = .179) (Fig. 2).

Table 2 Results of Outcome Postponement Calculations
Full size table
Figure 2
figure 2

Forest plots of postponement of all-cause mortality.

Full size image

Subgroups

Table 3 shows the results of subgroup analyses by trial characteristics. Briefly, the modeled outcome postponements were 10.2 days (PI, 4.1–16.3) for primary prevention, 17.4 days (PI, 6.0–28.8) for secondary prevention, and 8.5 days (PI, 1.9–15.1) for mixed prevention. HR-based meta-analyses produced a summary HR of 0.89 (CI, 0.84–0.94) for all trials, 0.78 (CI, 0.67–0.92) for primary prevention trials, 0.85 (CI, 0.75–0.96) for secondary prevention trials, and 0.92 (CI, 0.88–0.97) for mixed prevention trials (Fig. 3).

Table 3 Subgroup Meta-analyses of Postponement of All-Cause Mortality According to Trial Characteristics
Full size table
Figure 3
figure 3

Forest plot of hazard ratios in the trials.

Full size image

Risk of Bias

All included trials were large and had published or accessible protocols, concealed allocation, and blinding. All trials had a low overall risk of bias as determined using the Cochrane risk of bias tool.11 Treatment switches were a possible concern, as some trials reported that considerable proportions of patients (range, 4.8–25.4%) assigned to the placebo group switched to statin treatment or were assigned to the statin group but stopped their treatment. Outcome postponements were 11.6 days (PI, 5.1–18.1) in the ten trials with high cumulative incidence (> 4%) of treatment switches, 36.5 days (PI, 19.9–53.2) in the single trial with a low degree of switching, and 10.4 days (PI, 3.0–17.8) in the five trials with an unclear degree of switching.

DISCUSSION

Here, we investigated the effects of statin treatment on postponement of death and performed a meta-analysis. We found that statin treatment resulted in a small average increase of survival within the trials’ duration. Meta-analysis of 16 large RCTs revealed a survival gain of 12.6 days (PI, 7.1–18.0) within the trial duration. We stratified on prevention type and demonstrated the largest postponement among the trials with secondary prevention, 17 days compared to 10 and 9 days in the primary and mixed prevention groups. We expected this result, as the largest relative risk reduction has previously been found in this group.10 We examined the effect of trial duration on postponement and found a much larger postponement among the trial’s with a trial duration of 5 years and above, compared to below 5 years (19 days vs. 6 days). The difference nearly disappeared after standardization (14 days vs. 11 days), demonstrating the strong dependency of outcome postponement on trial duration. The proposed model has several important strengths. The model-derived area between survival curves showed strong agreement with the area between survival curves as measured by pixel counting. Additionally, the model does not require a Kaplan–Meier survival curve to determine the outcome postponement, increasing the applicability of this method to a wider range of trials. Lastly, the use of a confidence interval proxy for outcome postponement enabled meta-analysis.

The postponement of death from other interventions varies greatly. One recent review on medical interventions for cancer, approved by the EMA from 2009 to 2013, showed that only 51% of the drugs postponed death at all. The median follow-up was 5.4 years.28 A different study evaluated the effects of regular exercise and a calorie restricted diet in healthy males, demonstrating a postponement of death by 6.2 months. Lastly, smoking cessation in a high-risk population postponed death by around 31 months.4

As a tool for conveying treatment effects to patients, the concept of outcome postponement has important advantages over the number needed to treat (NNT). Most importantly, outcome postponement achieves greater responsiveness from patients. Surveys demonstrate that patients have the same likelihood of accepting a hypothetical treatment across NNT values ranging from 10 to 400.6, 29 On the other hand, patients presented with benefits conveyed in terms of outcome postponement clearly discriminate between efficient and less-efficient treatments. Additionally, an NNT value may be criticized for conveying a “lottery-like” understanding of how treatment effect is distributed—for example, an NNT value of 40 could be wrongfully interpreted as meaning that 1 in 40 patients will experience all of the benefits treatment, while the remaining 39 experience no effect.

The most important clinical limitation of our model is that it does not capture the outcome postponement accrued after trial termination. Estimation of such benefits is difficult and heavily relies on untestable assumptions. For example, Marshall used extrapolations from the LIPID trial to estimate the gain in life expectancy from lifelong statin treatment (i.e., for the rest of their lives) and arrived at a gain of 7.9 years. However, Chang et al. used the same data in a different model and estimated a gain of 3.0 years.30 Using a model that incorporated mortality in different risk strata, Støvring et al.31 estimated that lifelong statin treatment was associated with survival gains ranging from 3 to 11 months. Franco et al.32 used life-table techniques and reported outcome postponements of 2.0 and 2.4 years for lifelong statin use starting from 40 and 60 years of age, respectively. Some of these models apply the strong assumption that HR remains constant throughout the subject’s lifetime, and most assume that all subjects can maintain lifelong statin treatment, which has been established as unrealistic in nearly all drug utilization studies.33, 34 Using our presently described method, we modeled the mortality outcome postponement in a recent study that provides Kaplan–Meier curves for 20 years of follow-up of the WOSCOPS trial, estimating an outcome postponement of 152 days (PI, 70–236 days).35 Given the uncertainties of estimating survival gain after trial termination, it is important to emphasize that our calculated outcome postponement is that achieved within the trial’s duration and should be considered an underestimate of the full outcome postponement including all post-trial follow-up. There is also a possibility of error by assuming that the survival curves would conform to an exponential decay function within the trial’s running time or that this assumption is violated by the standardization to 5 years. However, the fact that there is good agreement between modeled postponement and postponement measured by pixel counting suggests that such violations are insignificant.

Other models have been proposed for estimating and presenting outcome postponement during a trial’s duration. Lytsy36 described a “delay of events” model that essentially estimates the average outcome postponement among patients who experienced the outcome, rather than among all patients randomized to receive treatment as in our model. The estimated outcome postponement in the 4S study16 which they used as motivating case was 1.0 year, which was larger than our estimate of 36.5 days. Notably, the “delay of event” measure seems to have little clinical utility, as it only applies to patients who die during the course of the trial, e.g., a population that cannot be identified at baseline. Additionally, Royston and Parmar37, 38 developed the concept of restricted mean survival time (RMST), which generalizes outcome postponement. The RMST approach is fully developed from a theoretical and practical point of view, and it is the method of choice if data are available at the individual level.

From a clinical viewpoint, it would be a cautious and pragmatic approach to offer statins in accordance with the prevailing guidelines, i.e., as secondary prevention for all patients with manifest atherosclerotic disease and as primary prevention for certain high-risk patients. Statins are inexpensive, usually well tolerated,39 and show a favorable cost-utility.40 Based on the present evidence that statins do not have a large effect on postponement of all-cause mortality within a trial’s duration, physicians and patients may be more inclined to discontinue treatment in patients showing intolerance to statins or having a short life expectancy.

In summary, we have developed a simple method for estimating outcome postponement based on summary measures that are almost universally available. This method is amenable to meta-analyses, and we believe that it may be a useful approach to presenting the benefits of preventive interventions to patients. We envisioned outcome postponement used as complementary to the prevailing measures. With regard to the subject matter in our present meta-analysis, statin treatment resulted in a small gain in average survival within the trials’ duration. However, statins reduce the risk of cardiovascular outcomes, which could add value to the drug, from the patient’s perspective, irrespective of the effect on all-cause mortality.