title: Sample size determination for estimating antibody seroconversion rate under stable malaria transmission intensity.
abstract: BACKGROUND
  In the last decade, several epidemiological studies have demonstrated the potential of using seroprevalence (SP) and seroconversion rate (SCR) as informative indicators of malaria burden in low transmission settings or in populations on the cusp of elimination. However, most of studies are designed to control ensuing statistical inference over parasite rates and not on these alternative malaria burden measures. SP is in essence a proportion and, thus, many methods exist for the respective sample size determination. In contrast, designing a study where SCR is the primary endpoint, is not an easy task because precision and statistical power are affected by the age distribution of a given population.
  
  
  METHODS
  Two sample size calculators for SCR estimation are proposed. The first one consists of transforming the confidence interval for SP into the corresponding one for SCR given a known seroreversion rate (SRR). The second calculator extends the previous one to the most common situation where SRR is unknown. In this situation, data simulation was used together with linear regression in order to study the expected relationship between sample size and precision.
  
  
  RESULTS
  The performance of the first sample size calculator was studied in terms of the coverage of the confidence intervals for SCR. The results pointed out to eventual problems of under or over coverage for sample sizes ≤250 in very low and high malaria transmission settings (SCR ≤ 0.0036 and SCR ≥ 0.29, respectively). The correct coverage was obtained for the remaining transmission intensities with sample sizes ≥ 50. Sample size determination was then carried out for cross-sectional surveys using realistic SCRs from past sero-epidemiological studies and typical age distributions from African and non-African populations. For SCR < 0.058, African studies require a larger sample size than their non-African counterparts in order to obtain the same precision. The opposite happens for the remaining transmission intensities. With respect to the second sample size calculator, simulation unravelled the likelihood of not having enough information to estimate SRR in low transmission settings (SCR ≤ 0.0108). In that case, the respective estimates tend to underestimate the true SCR. This problem is minimized by sample sizes of no less than 500 individuals. The sample sizes determined by this second method highlighted the prior expectation that, when SRR is not known, sample sizes are increased in relation to the situation of a known SRR. In contrast to the first sample size calculation, African studies would now require lesser individuals than their counterparts conducted elsewhere, irrespective of the transmission intensity.
  
  
  CONCLUSIONS
  Although the proposed sample size calculators can be instrumental to design future cross-sectional surveys, the choice of a particular sample size must be seen as a much broader exercise that involves weighting statistical precision with ethical issues, available human and economic resources, and possible time constraints. Moreover, if the sample size determination is carried out on varying transmission intensities, as done here, the respective sample sizes can also be used in studies comparing sites with different malaria transmission intensities. In conclusion, the proposed sample size calculators are a step towards the design of better sero-epidemiological studies. Their basic ideas show promise to be applied to the planning of alternative sampling schemes that may target or oversample specific age groups.
authors.affiliation: London School of Hygiene and Tropical Medicine, Keppel Street, WC1E 7HT, London, UK. nuno.sepulveda@lshtm.ac.uk.|Center of Statistics and Applications of University of Lisbon, Faculdade de Ciências da Universidade de Lisboa, Bloco C6 - Piso 4, 1749-1016, Lisboa, Portugal. nuno.sepulveda@lshtm.ac.uk.
authors.forename: Nuno
authors.initials: N
authors.lastname: Sepúlveda
authors.affiliation: London School of Hygiene and Tropical Medicine, Keppel Street, WC1E 7HT, London, UK. chris.drakeley@lshtm.ac.uk.
authors.forename: Chris
authors.initials: C
authors.lastname: Drakeley
mesh_terms: D000913:Antibodies, Protozoan / Q000097:blood*; D056808:Biostatistics / Q000379:methods*; D004812:Epidemiologic Methods; D006801:Humans; D008288:Malaria / Q000453:epidemiology*; D018401:Sample Size; D000069078:Seroconversion
chemical_list: D000913:Antibodies, Protozoan