title: Generalizing boundaries for triangular designs, and efficacy estimation at extended follow-ups.
abstract: BACKGROUND
  Visceral leishmaniasis (VL) is a parasitic disease transmitted by sandflies and is fatal if left untreated. Phase II trials of new treatment regimens for VL are primarily carried out to evaluate safety and efficacy, while pharmacokinetic data are also important to inform future combination treatment regimens. The efficacy of VL treatments is evaluated at two time points, initial cure, when treatment is completed and definitive cure, commonly 6 months post end of treatment, to allow for slow response to treatment and detection of relapses. This paper investigates a generalization of the triangular design to impose a minimum sample size for pharmacokinetic or other analyses, and methods to estimate efficacy at extended follow-up accounting for the sequential design and changes in cure status during extended follow-up.
  
  
  METHODS
  We provided R functions that generalize the triangular design to impose a minimum sample size before allowing stopping for efficacy. For estimation of efficacy at a second, extended, follow-up time, the performance of a shrinkage estimator (SHE), a probability tree estimator (PTE) and the maximum likelihood estimator (MLE) for estimation was assessed by simulation.
  
  
  RESULTS
  The SHE and PTE are viable approaches to estimate an extended follow-up although the SHE performed better than the PTE: the bias and root mean square error were lower and coverage probabilities higher.
  
  
  CONCLUSIONS
  Generalization of the triangular design is simple to implement for adaptations to meet requirements for pharmacokinetic analyses. Using the simple MLE approach to estimate efficacy at extended follow-up will lead to biased results, generally over-estimating treatment success. The SHE is recommended in trials of two or more treatments. The PTE is an acceptable alternative for one-arm trials or where use of the SHE is not possible due to computational complexity.
  
  
  BACKGROUND
  NCT01067443 , February 2010.
authors.affiliation: Lancaster University, Lancaster, LA1 4YW, UK. a.allison@sheffield.ac.uk.|The University of Sheffield, Western Bank, Sheffield, S10 2TN, UK. a.allison@sheffield.ac.uk.
authors.forename: Annabel
authors.initials: A
authors.lastname: Allison
authors.affiliation: MRC Tropical Epidemiology Group, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT, UK. tansy.edwards@lshtm.ac.uk.
authors.forename: Tansy
authors.initials: T
authors.lastname: Edwards
authors.affiliation: Drugs for Neglected Diseases initiative (DNDi) Africa, Centre for Clinical Research, Kenya Medical Research Institute, Nairobi, Kenya. romollo@dndi.org.|Maseno University, Private Bag, Maseno, Kenya. romollo@dndi.org.
authors.forename: Raymond
authors.initials: R
authors.lastname: Omollo
authors.affiliation: DNDi, Geneva, Switzerland. falves@dndi.org.
authors.forename: Fabiana
authors.initials: F
authors.lastname: Alves
authors.affiliation: Lancaster University, Lancaster, LA1 4YW, UK. dominic.magirr@meduniwien.ac.at.|Centre for Medical Statistics, Medical University of Vienna, Spitalgasse 23, Vienna, 1090, Austria. dominic.magirr@meduniwien.ac.at.
authors.forename: Dominic
authors.initials: D
authors.lastname: Magirr
authors.affiliation: MRC Tropical Epidemiology Group, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT, UK. neal.alexander@lshtm.ac.uk.
authors.forename: Neal D
authors.initials: ND
authors.lastname: E Alexander
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D007630:Kenya; D007898:Leishmaniasis, Visceral / Q000175:diagnosis / Q000188:drug therapy* / Q000469:parasitology; D016013:Likelihood Functions; D015233:Models, Statistical; D011336:Probability; D012008:Recurrence; D012074:Remission Induction; D012107:Research Design / Q000706:statistics & numerical data*; D018401:Sample Size; D013397:Sudan; D016896:Treatment Outcome; D014344:Trypanocidal Agents / Q000008:administration & dosage / Q000493:pharmacokinetics*
chemical_list: D014344:Trypanocidal Agents