Abstract
BackgroundRecurrent events data analysis is common in biomedicine. Literature review indicates that most statistical models used for such data are often based on time to the first event or consider events within a subject as independent. Even when taking into account the non-independence of recurrent events within subjects, data analyses are mostly done with continuous risk interval models, which may not be appropriate for treatments with sustained effects (e.g., drug treatments of malaria patients). Furthermore, results can be biased in cases of a confounding factor implying different risk exposure, e.g. in malaria transmission: if subjects are located at zones showing different environmental factors implying different risk exposures.MethodsThis work aimed to compare four different approaches by analysing recurrent malaria episodes from a clinical trial assessing the effectiveness of three malaria treatments [artesunate + amodiaquine (AS + AQ), artesunate + sulphadoxine-pyrimethamine (AS + SP) or artemether-lumefantrine (AL)], with continuous and discontinuous risk intervals: Andersen-Gill counting process (AG-CP), Prentice-Williams-Peterson counting process (PWP-CP), a shared gamma frailty model, and Generalized Estimating Equations model (GEE) using Poisson distribution. Simulations were also made to analyse the impact of the addition of a confounding factor on malaria recurrent episodes.ResultsUsing the discontinuous interval analysis, AG-CP and Shared gamma frailty models provided similar estimations of treatment effect on malaria recurrent episodes when adjusted on age category. The patients had significant decreased risk of recurrent malaria episodes when treated with AS + AQ or AS + SP arms compared to AL arm; Relative Risks were: 0.75 (95% CI (Confidence Interval): 0.62-0.89), 0.74 (95% CI: 0.62-0.88) respectively for AG-CP model and 0.76 (95% CI: 0.64-0.89), 0.74 (95% CI: 0.62-0.87) for the Shared gamma frailty model.With both discontinuous and continuous risk intervals analysis, GEE Poisson distribution models failed to detect the effect of AS + AQ arm compared to AL arm when adjusted for age category. The discontinuous risk interval analysis was found to be the more appropriate approach.ConclusionRepeated event in infectious diseases such as malaria can be analysed with appropriate existing models that account for the correlation between multiple events within subjects with common statistical software packages, after properly setting up the data structures.
Highlights
Recurrent events data analysis is common in biomedicine
Statistical models and data analysis Four models were used for the analysis of recurrent timeto-event outcomes: i) Generalized estimating equations (GEE) model using a Poisson distribution; and three extended Cox models: ii) the Andersen-Gill counting process (AG-CP), iii) the Prentice-Williams-Peterson counting process (PWP-CP); and iv) the Shared gamma frailty model
Using the discontinuous risk interval analysis, PWP-CP, AG-CP, and the Shared gamma frailty models provided larger treatment effect on malaria episodes compared to Generalized Estimating Equations model (GEE) for the patients treated with AS + AQ or AS + SP as compared to the AL arm; risk ratio (RR) were: 0.75 (95% CI (Confidence Interval): 0.62-0.89), 0.74 respectively for AG-CP model, 0.76, 0.74 for the Shared gamma frailty model and 1.02 (0.93-1.11), 0.93 (0.87-0.99) for GEE model (Table 2)
Summary
Recurrent events data analysis is common in biomedicine. Literature review indicates that most statistical models used for such data are often based on time to the first event or consider events within a subject as independent. Even when taking into account the non-independence of recurrent events within subjects, data analyses are mostly done with continuous risk interval models, which may not be appropriate for treatments with sustained effects (e.g., drug treatments of malaria patients). Even when taking into account the non-independence of recurrent events within subjects, data analyses are mostly done with continuous risk interval models [2,3,4,5], which may not be relevant for health conditions with discontinuous risk [8]. It is quite common to encounter recurrent health conditions with such discontinuous risk intervals, e.g. in cases with persistent treatment effect Examples include infections, such as malaria, disability episodes, hospitalizations, and nursing home admissions [7,8,9,10,11,12]. Appropriate models for analysing recurrent events data include marginal models or frailty or random coefficient analysis models [8,9,10,11,12,13], which take into account the non independence assumption of events within the subject
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