A novel method for interpreting survival analysis data: description and test on three major clinical trials on cardiovascular prevention

Abstract

Background: Major results of randomized clinical trials on cardiovascular prevention are currently provided in terms of relative or absolute risk reductions, including also the number needed to treat (NNT), incorrectly implying that a treatment might prevent the occurrence of the outcome/s under investigation. Provided that these results are based on survival analysis, the primary measure of which is time-to-the outcome and not the outcome itself, we sought an alternative method to describe, analyse and interpret clinical trial results consistent with this assumption, so as to better define qualitative and quantitative heterogeneity of various therapeutic strategies in terms of their effects and costs.

Methods: The original Kaplan-Meier graphs of three major positive cardiovascular prevention trials (PROVE-IT, LIFE and HOPE) were captured from the PDF images of the article and then digitalized. We calculated the difference between the placebo and active treatment curves and plotted it as a function of time to describe the event-free time gain (Time-Gain) produced by the active treatment. By calculating the exposure to the active treatment in terms of months (MoT) as a function of time and dividing it for the corresponding time-dependent number of event-free years gained (i.e. months/12), we described the kinetics of the pharmaco-economic index MoT/y+. The same procedure was repeated replacing MoT with the actual number of patients being treated at each time point as a function of time to obtain the NNT to gain 1 event-free year (NNT/y+) curve.

Results: The Time-Gain curves depict the kinetics of the treatment-related effect over time and possess the peculiar feature of being smooth and accurately fitted by second-order polynomial functions (a*time2 + b*time); similarly, also the MoT/y+ and NNT/y+ curves can be accurately fitted by power functions (a*timeb). These curves and indices allow to fully appreciate the quantitative and qualitative heterogeneity, both in terms of effects and costs, of the different therapeutic strategies adopted in the three trials.

Conclusions: With our novel method, by exploiting original Kaplan-Meier curves from three major clinical trials on cardiovascular prevention, we generate new information on the actual consequences of choosing a therapeutic strategy vs another, thus ultimately providing the clinical gain in terms of time-dependent functions. Accurately assessing clinically and economic meaningful results from any intervention trial reporting positive results through this approach, facilitates objective comparisons and increases reliability in predicting survival among the various therapeutic options provided.

Trial registration: PROVE-IT (Pravastatin or Atorvastatin Evaluation and Infection Therapy (TIMI22), Clinical trial registration number: NCT00382460, date of registration: September 29, 2006, study start date: November 2000). LIFE (Losartan Intervention For Endpoint Reduction in Hypertension (LIFE) Study, Clinical trial registration number: NCT00338260, date of registration: June 20, 2006, study start date: June 1995). HOPE (Heart Outcomes Prevention Evaluation; we could not find Clinical trial registration number and date of registration).

Keywords: Clinical trials; Hazard ratio; Kaplan-Meier; Non-parametric; Survival analysis.

Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Fig. 1

Graphic illustration of the PISA method. Original inverse Kaplan-Meier graphs were first captured from the PDF of the article as high-definition images (.png) and then converted into data using the UN-SCAN-IT Graph Digitalizer software. Digitalized data were visualized and misplaced points (x-axis) spacing was then forced to 0.25 months, and when missing the incidence (y-axis), data was automatically interpolated with the linear method using the two closest points. The integral function of the inverse KM curves (Time-Lost) was obtained by applying piecewise integration using the trapezoid rule with equal x segments. Then, the Time-Gain curve was obtained from the difference between the integrals of placebo and active treatment, plotted as a function of time. Finally, we performed curve fitting on data up to the time when 50% of the total population was still being followed up

Fig. 2

Incidence plots and Time-Gain curves for PROVE-IT (4p-MACE), LIFE (3p-MACE) and HOPE (3p-MACE) trials. 4p-MACE* outcome: death from any cause, myocardial infarction, documented unstable angina requiring rehospitalization, revascularization with either percutaneous coronary intervention or coronary-artery bypass grafting—if these procedures were performed at least 30 days after randomization—and stroke; 3p-MACE outcome: cardiovascular death, non-fatal stroke and non-fatal myocardial infarction), a Incidence plots in the PROVE-IT (blue line: pravastatin 40 mg, red line: atorvastatin 80 mg), LIFE (blue line: atenolol, red line: losartan) and HOPE (blue line: placebo, red line: ramipril) studies. b Observed Time-Gain curves (continuous line) throughout the duration of the three studies and fitted Time-Gain curves (f50%; dotted lines) with the extrapolation beyond time at which less than 50% of the cohort was in follow-up (indicated by arrows) for PROVE-IT and LIFE trials. For the HOPE trial (due to the absence of data of population in follow-up), the fit and the extrapolation were performed beyond half the duration of the trial (indicated by arrows)

Fig. 3

Pharmaco-economic indices MoT/y+ and NNT/y+ for PROVE-IT (4p-MACE*), LIFE (3p-MACE) and HOPE (3p-MACE) trials. a Observed (continuous green lines) Months of treatment per 1 year gained (MoT/y+) curves throughout the three trial and estimated MoT/y+(eMoT/y+; dotted green lines) up to time 72 months. The arrows show the time at which the 50% of the cohort was in follow-up for PROVE-IT and LIFE trial and the 50% of the duration of the study for the HOPE trial. b Observed (continuous red lines) number needed to treat per 1 year gained (NNT/y+) curves throughout the three trial and estimated NNT/y+ (eNNT/y+; dotted red lines) curves up to time 72 months. The arrows show the time at which the 50% of the cohort was in follow-up for PROVE-IT and LIFE trial and the 50% of the duration of the study for the HOPE trial