Network meta-analysis of (individual patient) time to event data alongside (aggregate) count data

Abstract

Background: Network meta-analysis methods extend the standard pair-wise framework to allow simultaneous comparison of multiple interventions in a single statistical model. Despite published work on network meta-analysis mainly focussing on the synthesis of aggregate data, methods have been developed that allow the use of individual patient-level data specifically when outcomes are dichotomous or continuous. This paper focuses on the synthesis of individual patient-level and summary time to event data, motivated by a real data example looking at the effectiveness of high compression treatments on the healing of venous leg ulcers.

Methods: This paper introduces a novel network meta-analysis modelling approach that allows individual patient-level (time to event with censoring) and summary-level data (event count for a given follow-up time) to be synthesised jointly by assuming an underlying, common, distribution of time to healing. Alternative model assumptions were tested within the motivating example. Model fit and adequacy measures were used to compare and select models.

Results: Due to the availability of individual patient-level data in our example we were able to use a Weibull distribution to describe time to healing; otherwise, we would have been limited to specifying a uniparametric distribution. Absolute effectiveness estimates were more sensitive than relative effectiveness estimates to a range of alternative specifications for the model.

Conclusions: The synthesis of time to event data considering individual patient-level data provides modelling flexibility, and can be particularly important when absolute effectiveness estimates, and not just relative effect estimates, are of interest.

Figure 1

Network of RCTs. In the network, a unique treatment category is indicated by a circle. Arrows between circles indicate that these treatments had been compared in a trial (trials are identified using ‘[]’, numbered as in column ‘ID’ in Table  1. (4LB, SSB, HH, Ba, Zinc Paste, BHeH, BzeaH, HV and 2LB as described in Additional file 1).

Figure 2

Graphical representation of model A results reflecting uncertainty over relative treatment effects in the probability of healing over time for the five main high compression ulcer treatments. The main figure (a) shows the expected probabilities of healing (point estimates) across time (25 months); figures (b), (c), (d) and (e) compare the expected values for four layer bandage with the healing probability (point estimates and uncertainty) of each of the other four high compression treatments. Estimates reflect the average participant in the trial data from VenUS IV (IPD study 2) (mean ulcer area at baseline of 9.4cm2 and ulcer duration at baseline of 11.5 months). (4LB, SSB, HH, Zinc Paste and 2LB as described in Additional file 1).