title: Modelling recurrent events: comparison of statistical models with continuous and discontinuous risk intervals on recurrent malaria episodes data.
abstract: BACKGROUND
  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). 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.
  
  
  METHODS
  This 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.
  
  
  RESULTS
  Using 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.
  
  
  CONCLUSIONS
  Repeated 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.
authors: Malaria Research and Training Center, Department of Epidemiology of Parasitic Diseases, Faculty of Medicine and Odonto-Stomatogy, University of Sciences, Techniques and Technologies of Bamako, BP 1805 Point G, Bamako, Mali. isagara@icermali.org.
authors: Issaka
authors: I
authors: Sagara
authors: Roch
authors: R
authors: Giorgi
authors: Ogobara K
authors: OK
authors: Doumbo
authors: Renaud
authors: R
authors: Piarroux
authors: Jean
authors: J
authors: Gaudart
mesh_terms: D000293:Adolescent; D000328:Adult; D000962:Antimalarials / Q000627:therapeutic use; D002648:Child; D002675:Child, Preschool; D003198:Computer Simulation; D006801:Humans; D007223:Infant; D007231:Infant, Newborn; D008288:Malaria / Q000188:drug therapy / Q000453:epidemiology*; D008954:Models, Biological; D015233:Models, Statistical; D012008:Recurrence; D018570:Risk Assessment; D055815:Young Adult
chemical_list: D000962:Antimalarials