• View in gallery
    Figure 1.

    Kaplan–Meier curves comparing time-to-parasitemia by sporozoite dose groups in human sporozoite challenge studies. (A) Tanzanian cohort via microscopy, (B) Tanzanian cohort via polymerase chain reaction (PCR), (C) combined Tanzanian and Dutch cohorts via PCR.

  • 1.

    Epstein JE, Tewari K, Lyke KE, Sim BKL, Billingsley PF, Laurens MB, Gunasekera A, Chakravarty S, James ER, Sedegah M, Richman A, Velmurugan S, Reyes S, Li M, Tucker K, Ahumada A, Ruben AJ, Li T, Stafford R, Eappen AG, Tamminga C, Bennett JW, Ockenhouse CF, Murphy JR, Komisar J, Thomas N, Loyevsky M, Birkett A, Plowe CV, Loucq C, Edelman R, Richie TL, Seder RA, Hoffman SL, 2011. Live attenuated malaria vaccine designed to protect through hepatic CD8+ t cell immunity. Science 334: 475480.

    • Search Google Scholar
    • Export Citation
  • 2.

    Seder RA, Chang L-J, Enama ME, Zephir KL, Sarwar UN, Gordon IJ, Holman LA, James ER, Billingsley PF, Gunasekera A, Richman A, Chakravarty S, Manoj A, Velmurugan S, Li M, Ruben AJ, Li T, Eappen AG, Stafford RE, Plummer SH, Hendel CS, Novik L, Costner PJM, Mendoza FH, Saunders JG, Nason MC, Richardson JH, Murphy J, Davidson SA, Richie TL, Sedegah M, Sutamihardja A, Fahle GA, Lyke KE, Laurens MB, Roederer M, Tewari K, Epstein JE, Sim BKL, Ledgerwood JE, Graham BS, Hoffman SL, 2013. Protection against malaria by intravenous immunization with a nonreplicating sporozoite vaccine. Science 341: 13591365.

    • Search Google Scholar
    • Export Citation
  • 3.

    Roestenberg M, McCall M, Hopman J, Wiersma J, Luty AJ, van Gemert GJ, van de Vegte-Bolmer M, van Schaijk B, Teelen K, Arens T, Spaarman L, de Mast Q, Snounou G, Renia L, van der Ven A, Hermsen CC, Sauerwein R, 2009. Protection against a malaria challenge by sporozoite inoculation. N Engl J Med 361: 468477.

    • Search Google Scholar
    • Export Citation
  • 4.

    Billingsley P, Sim BK, Bijker E, Roestenberg M, Lyke K, Laurens M, Mordmueller B, Gomez P, Shekalaghe S, Hodgson S, Hill A, Juma E, Ogutu B, Lell B, Alonso P, Abdullah S, Kremsner P, Tanner M, Sauerwein R, Hoffman S, 2014. Controlled human malaria infections using aseptic, purified cryopreserved Plasmodium falciparum sporozoites administered by needle and syringe. Malar J 13 (Suppl 1): 12.

    • Search Google Scholar
    • Export Citation
  • 5.

    Hodgson SH, Juma E, Salim A, Magiri C, Kimani D, Njenga D, Muia A, Cole AO, Ogwang C, Awuondo K, Lowe B, Munene M, Billingsley PF, James ER, Gunasekera A, Sim BKL, Njuguna P, Rampling TW, Richman A, Abebe Y, Kamuyu G, Muthui M, Elias SC, Molyneux S, Gerry S, Macharia A, Williams TN, Bull PC, Hill AVS, Osier FH, Draper SJ, Bejon P, Hoffman SL, Ogutu B, Marsh K, 2014. Evaluating controlled human malaria infection in Kenyan adults with varying degrees of prior exposure to Plasmodium falciparum using sporozoites administered by intramuscular injection. Infect Dis 5: 686.

    • Search Google Scholar
    • Export Citation
  • 6.

    Shekalaghe S, Rutaihwa M, Billingsley PF, Chemba M, Daubenberger CA, James E, Mpina M, Juma OA, Schindler T, Huber E, Gunasekera A, Manoj A, Simon B, Savarino E, Church LWP, Hermsen CC, Sauerwein RW, Plowe CV, Venkatesan M, Sasi P, Lweno O, Mutani P, Hamad A, Mohammed A, Urassa A, Mzee T, Padilla D, Ruben A, Sim BKL, Tanner M, Abdullah S, Hoffman SL, 2014. Controlled human malaria infection of Tanzanians by intradermal injection of aseptic, purified, cryopreserved Plasmodium falciparum sporozoites. Am J Trop Med Hyg 91: 471480.

    • Search Google Scholar
    • Export Citation
  • 7.

    Sheehy SH, Douglas AD, Draper SJ, 2013. Challenges of assessing the clinical efficacy of asexual blood-stage Plasmodium falciparum malaria vaccines. Hum Vaccin Immunother 9: 18311840.

    • Search Google Scholar
    • Export Citation
  • 8.

    Darton TC, Blohmke CJ, Moorthy VS, Altmann DM, Hayden FG, Clutterbuck EA, Levine MM, Hill AVS, Pollard AJ, 2015. Design, recruitment, and microbiological considerations in human challenge studies. Lancet Infect Dis 15: 840851.

    • Search Google Scholar
    • Export Citation
  • 9.

    Spring M, Polhemus M, Ockenhouse C, 2014. Controlled human malaria infection. J Infect Dis 209 (Suppl 2): S40S45.

  • 10.

    Roestenberg M, O'Hara GA, Duncan CJA, Epstein JE, Edwards NJ, Scholzen A, van der Ven AJAM, Hermsen CC, Hill AVS, Sauerwein RW, 2012. Comparison of clinical and parasitological data from controlled human malaria infection trials. PLoS One 7: e38434.

    • Search Google Scholar
    • Export Citation
  • 11.

    Arévalo-Herrera M, Forero-Peña DA, Rubiano K, Gómez-Hincapie J, Martínez NL, Lopez-Perez M, Castellanos A, Céspedes N, Palacios R, Oñate JM, Herrera S, 2014. Plasmodium vivax sporozoite challenge in malaria-naïve and semi-immune Colombian volunteers. PLoS One 9: e99754.

    • Search Google Scholar
    • Export Citation
  • 12.

    Collett D, 2003. Modelling Survival Data in Medical Research, 2nd edition. Boca Raton, FL: CRC Press.

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    Klein M, Kleinbaum DG, 2005. Survival Analysis, 2nd edition. New York, NY: Springer Science+Business Media, Inc.

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    Hosmer DW, Lemeshow S, May S, 2011. Applied Survival Analysis: Regression Modeling of Time to Event Data, 2nd edition. Hoboken, NJ: John Wiley and Sons.

    • Search Google Scholar
    • Export Citation
  • 15.

    Lover AA, Coker RJ, 2014. Re-assessing the relationship between sporozoite dose and incubation period in Plasmodium vivax malaria: a systematic re-analysis. Parasitology 141: 859868.

    • Search Google Scholar
    • Export Citation
  • 16.

    Mills M, 2011. Introducing Survival and Event History Analysis. Los Angeles, CA: SAGE Publications Ltd.

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    Mills M, 2011. The fundamentals of survival and event history analysis. Introducing Survival and Event History Analysis. Chapter 1. Los Angeles, CA: Sage Publications. Available at: http://www.sagepub.com/upm-data/39847_9781848601017_Mills.pdf.

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    White IR, Horton NJ, Carpenter J, Pocock SJ, 2011. Strategy for intention to treat analysis in randomised trials with missing outcome data. BMJ 342: d40.

    • Search Google Scholar
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    Gupta SK, 2011. Intention-to-treat concept: a review. Perspect Clin Res 2: 109112.

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    Theunissen C, Janssens P, Demulder A, Nouboussié D, Van Esbroeck M, Van Gompel A, Van den Ende J, 2009. Falciparum malaria in patient 9 years after leaving malaria-endemic area. Emerg Infect Dis 15: 115116.

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    Markus MB, 2012. Dormancy in mammalian malaria. Trends Parasitol 28: 3945.

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    Thompson FM, Porter DW, Okitsu SL, Westerfeld N, Vogel D, Todryk S, Poulton I, Correa S, Hutchings C, Berthoud T, Dunachie S, Andrews L, Williams JL, Sinden R, Gilbert SC, Pluschke G, Zurbriggen R, Hill AVS, 2008. Evidence of blood stage efficacy with a virosomal malaria vaccine in a Phase IIa clinical trial. PLoS One 3: e1493.

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    Li H, Han D, Hou Y, Chen H, Chen Z, 2015. Statistical inference methods for two crossing survival curves: a comparison of methods. PLoS One 10: e0116774.

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    Royston P, Parmar MK, 2013. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Med Res Methodol 13: 152.

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    Andersen PK, Perme MP, 2010. Pseudo-observations in survival analysis. Stat Methods Med Res 19: 7199.

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    Nakagawa S, Cuthill IC, 2007. Effect size, confidence interval and statistical significance: a practical guide for biologists. Biol Rev Camb Philos Soc 82: 591605.

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    Parner ET, Andersen PK, 2010. Regression analysis of censored data using pseudo-observations. Stata J 10: 408422.

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    Moorthy VS, Reed Z, Smith PG, 2009. MALVAC 2008: measures of efficacy of malaria vaccines in Phase 2b and Phase 3 trials—scientific, regulatory and public health perspectives. Vaccine 27: 624628.

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Considerations for Comprehensive Analyses of Sporozoite-Based Controlled Human Malaria Infection Studies

Andrew A. LoverMalaria Elimination Initiative, University of California, San Francisco, San Francisco, California

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There has been renewed interest in the use of sporozoite-based approaches for controlled human malaria infections (CHMIs), and several sets of human challenge studies have recently completed. A study undertaken in Tanzania and published in 2014 found dose dependence between 10,000 and 25,000 sporozoite doses, as well as divergent times-to-parasitemia relative to earlier studies in European volunteers, with important implications for planning future studies. Analysis of time-to-event data has had extensive development in recent years, but these methods have had limited exposure outside biostatistics. Expansion of the published analyses to include recent methodological approaches optimized for the types of data used could provide a richer analysis of these studies and may result in alternative findings. Specifically, in a re-analysis of these data using survival analysis techniques, the differences recorded in prepatent periods between the two dosing regimens do not reach statistical significance, and there is no evidence for statistically significant differences in prepatent periods between the Dutch and Tanzanian study sites. Although these findings do not impact the reported safety and tolerability of challange with cryopreserved Plasmodium falciparum sporozoites (PfSPZ), or invalidate the authors' hypotheses regarding naturally acquired immunity and its effect on parasite growth rates and prepatent periods, they highlight important opportunities to more fully use datasets from these trials and related CHMI experiments in the planning of future challenge studies.

Experimental injection of infective malaria parasites as sporozoites is currently undergoing a re-evaluation as a viable strategy for prevention of malaria infections in humans (using radiation-attenuated sporozoites)1,2 and for controlled human malaria infection (CHMI) (using non-attenuated sporozoites).35 Recently published work reports on the use of cryopreserved Plasmodium falciparum sporozoites (PfSPZ Challenge; Sanaria Inc., Rockville, MD) for challenge experiments in human volunteers in Tanzania.6

I applaud the authors' efforts to bring these critically important studies to malaria-endemic settings in sub-Saharan Africa, and agree that this is truly a milestone in global efforts toward development of platforms for CHMIs.

Although ethical and experimental aspects of human challenge experiments have received detailed consideration,79 the associated analytical issues have not. In this perspective, I suggest that expansion of Shekalaghe and others' analysis to include newer complementary approaches specifically optimized for time-to-event data provides a richer and more comprehensive view of these important results. Moreover, these suggestions are general, and could also be considered in other related CHMI studies with similar analytical strategies, for example.2,10,11

Time-to-event data (also called “survival” data, although the endpoint point may be any outcome) have several important characteristics. These data are generally skewed (non-normally distributed) and usually include censoring—that is, cases where the outcome is not known.12 Both of these issues present special obstacles in analysis, and the field has seen extensive growth with an increasingly large choice of analytical strategies and models. Many of these methods have the potential to augment and to complement existing approaches, and applying these methods to data from the PfSPZ studies suggests that contrary to the reported results, within the limited sample sizes, there is no evidence for statistically significant differences in dose response within the tested range of sporozoites, nor evidence for statistically significant differences in responses between the Dutch and Tanzanian cohorts to sporozoite exposure.

Analysis of the prepatent periods (time from sporozoite exposure to detectable parasites) in the original study was limited to a comparison of geometric means (GMs) via a nonparametric Wilcoxon rank-sum test. Although this strategy and related nonparametric methods are in common use in some fields, there exist several alternative methods for the analysis of time-to-event data,13 and a large body of literature exists with approaches that allow comprehensive analyses of these types of data.14 In earlier work with Plasmodium vivax, it was shown that application of non-survival analytical methods may lead to biased conclusions regarding dose dependence in sporozoite inoculations.15 In addition, although transforming the event times as GMs may address problems related to differences in dispersion, there is still the potential for biased estimates.16,17

A second issue that has received extensive attention in the epidemiological and clinical trial literature is one of potential biases from exclusion in the analysis of any patients originally randomized.18 The authors of the Sanaria study were unable to include all patients in their analysis as some had no recorded parasitemia, and therefore no analyzable time points; consequently, three patients were removed from the analysis. Inclusion of all patients randomized in an ‘intent-to-treat’ analysis has several advantages.19 First, it has the potential to avoid biased conclusions, and second, it allows use of all captured patient data, which maximizes the results of individual trials. Inclusion of all accrued patient-time from these trials is an especially important consideration in light of the inherently limited sample sizes.

Finally, the “failed” infections that were removed from the analysis may have been delayed incubation periods—although this phenomenon is better documented in P. vivax infections, it has also been reported in both naturally acquired P. falciparum infections20,21 and in other P. falciparum CHMI trials.22 While extended follow-up is neither feasible nor ethical in these challenge studies, these patients' follow-up time can still contribute to the study results using survival analysis.

There are other important challenges in analysis of these data: several of the Kaplan–Meier survival curves cross one another (see Figure 1), and the polymerase chain reaction (PCR)-based outcomes show evidence for proportional hazard violations. In these instances, assumptions underlying standard methods for survival analyses are violated (log-rank tests and Cox proportional hazard models, respectively). Although alternates for both situations have been developed (including Renyi log-rank tests23 and multivariate models24,25), these methods have had limited use outside of biostatistics.

Figure 1.
Figure 1.

Kaplan–Meier curves comparing time-to-parasitemia by sporozoite dose groups in human sporozoite challenge studies. (A) Tanzanian cohort via microscopy, (B) Tanzanian cohort via polymerase chain reaction (PCR), (C) combined Tanzanian and Dutch cohorts via PCR.

Citation: The American Society of Tropical Medicine and Hygiene 93, 6; 10.4269/ajtmh.15-0327

Multivariate models, in general, also provide two advantages over rank-sum-type tests; they allow for adjustment for any differences in baseline covariates, and more importantly provide an estimate of effect size. This last issue is especially important, as statistical significance does not always imply a clinically or biologically important effect.26 Notably, two types of well-validated models that avoid limitations of the Cox model (flexible parametric survival models and regression methods using pseudovalues) are both readily implemented in many standard statistical software packages including Stata (College Station, TX), SAS (Cary, NC), and R (Foundation for Statistical Computing, Vienna, Austria).25,2729

To illustrate the potential impact of complementary approaches, data from the original studies have been reanalyzed using these alternative approaches (see Figure 1 and Tables 13). These survival analyses consisted of 1) unadjusted comparisons using log-rank tests (or alternatives where the survival curves cross) followed by 2) multivariate models.

Table 1

Nonparametric survival analysis comparisons between time-to-parasitemia in the 10,000 vs. 25,000 sporozoite dose groups; full data and truncated data (Tanzania study)

Source of estimates End point Comparison Statistical test Full data (N = 24) P value Reduced data (N = 21) P value
Original publication Parasitemia (via microscopy) 10,000 vs. 25,000 dose Wilcoxon sign-rank 0.023
This work Parasitemia (via microscopy) 10,000 vs. 25,000 dose Log-rank 0.179 0.050*
This work Parasitemia (via PCR) 10,000 vs. 25,000 dose Renyi log-rank 0.266 0.102*

PCR = polymerase chain reaction.

This is an inappropriate use of survival methods as censoring has been ignored, but is shown for completeness.

Table 2

Multivariate Cox model for time-to-parasitemia via microscopy in human sporozoite challenge trials, comparing dose and study cohorts (N = 42)

Outcome Risk factor HR HR 95% CI P value
Parasitemia (via microscopy) 2,500 sporozoite dose Reference
10,000 sporozoite dose 0.86 0.22–3.27 0.821
25,000 sporozoite dose 1.15 0.32–4.21 0.830
Study cohort Tanzania Reference
Netherlands 1.21 0.52–2.81 0.655

CI = confidence interval; HR = hazard ratio.

Table 3

Multivariate flexible parametric survival model for time-to-parasitemia via PCR in human sporozoite challenge trials, comparing dose and study cohorts (N = 42)

Outcome Risk factor HR HR 95% CI P value
Parasitemia (via PCR) 2,500 sporozoite dose Reference
10,000 sporozoite dose 0.71 0.16–3.21 0.653
25,000 sporozoite dose 1.29 0.33–5.10 0.714
Study cohort Tanzania Reference
Netherlands 1.44 0.52–3.95 0.474

CI = confidence interval; HR = hazard ratio; PCR = polymerase chain reaction.

Although the original authors' analysis of microscopy-based outcomes suggests that “Volunteers in the 10,000 PfSPZ group had a significantly different prepatent period than in the 25,000 PfSPZ group GM of 15.4 and 13.5 days, Wilcoxon, P = 0.023),”6 a survival analysis does not provide evidence of differences using a log-rank test (P = 0.179). Analysis of the qPCR-based end point also shows no statistically significant differences in event times (Renyi log-rank P = 0.266), which is consistent with the difference in GM times (11.1 and 12.6 days [P = 0.073], not reported in the original publication). Kaplan–Meier plots of these data are shown in Figure 1A and B. Moreover, the potential additional information from a fuller consideration of patient censoring can be seen in the differences between the full and reduced datasets (Table 1).

In addition, the original analysis found that “…the GM pre-patent period for the Tanzanians who received the 10,000 PfSPZ dosage regimen was 15.4 days, and the GM pre-patent period for the Dutch was 12.6 days (P = 0.0192, Wilcoxon 2-tailed).” However, in a complementary survival analysis, the unadjusted comparisons of these times (N = 18) with analysis as time-to-event data do not provide any evidence of statistically significant differences (log-rank P = 0.288; Renyi log-rank = 0.110).

Finally, to illustrate a comprehensive assessment of the overall impacts of sporozoite dosage and study site, multivariate models were used to provide covariate adjustment, and show no evidence for statistically significant differences in times-to-positivity by microscopy (Table 3) or PCR (Figure 1C, Table 2) between any of the dose categories or between the two study sites in a direct comparison of the combined cohorts (N = 42). Results by microscopy were modeled using a Cox proportional hazard model, whereas the PCR-based end points were examined using flexible parametric survival models due to evidence for nonproportional hazards.

Importantly, although the results from this complementary analysis do not impact the reported safety or tolerability of PfSPZ Challenge, they highlight some areas that could be considered in further analyses. It should be highlighted that these two types of analyses address subtly different questions: the original authors' analysis allows for a more ready interpretation that may be most useful for policy makers and the general public, whereas the time-to-event analysis offers a more nuanced and comprehensive, but harder to convey, set of results. Related issues have had detailed consideration in the evaluation of malaria vaccine efficacy.30

Secondly, these results should partially allay the authors' concerns regarding any potential differences in response to challenge between Dutch and Tanzania subjects in future work; and suggest that the Tanzanian cohort with potentially low lifetime P. falciparum exposure had similar responses to the malaria-naïve Dutch volunteers. However, there are likely important questions of delayed patency due to prior exposures in other populations with higher lifetime P. falciparum exposure that could have important implications for future work, and sample sizes should be expanded to more fully investigate these issues.

In summary, a wider selection of analytical approaches drawing on survival analysis methods could provide additional important insights to inform future work using these technically demanding and critically important experiments toward global malaria elimination.

Note: Supplemental Appendix 1 contains statistical methods; Supplemental Appendix 2 contains the dataset for this analysis.

ACKNOWLEDGMENT

I am grateful for the comments of an anonymous reviewer, which greatly strengthened this work.

  • 1.

    Epstein JE, Tewari K, Lyke KE, Sim BKL, Billingsley PF, Laurens MB, Gunasekera A, Chakravarty S, James ER, Sedegah M, Richman A, Velmurugan S, Reyes S, Li M, Tucker K, Ahumada A, Ruben AJ, Li T, Stafford R, Eappen AG, Tamminga C, Bennett JW, Ockenhouse CF, Murphy JR, Komisar J, Thomas N, Loyevsky M, Birkett A, Plowe CV, Loucq C, Edelman R, Richie TL, Seder RA, Hoffman SL, 2011. Live attenuated malaria vaccine designed to protect through hepatic CD8+ t cell immunity. Science 334: 475480.

    • Search Google Scholar
    • Export Citation
  • 2.

    Seder RA, Chang L-J, Enama ME, Zephir KL, Sarwar UN, Gordon IJ, Holman LA, James ER, Billingsley PF, Gunasekera A, Richman A, Chakravarty S, Manoj A, Velmurugan S, Li M, Ruben AJ, Li T, Eappen AG, Stafford RE, Plummer SH, Hendel CS, Novik L, Costner PJM, Mendoza FH, Saunders JG, Nason MC, Richardson JH, Murphy J, Davidson SA, Richie TL, Sedegah M, Sutamihardja A, Fahle GA, Lyke KE, Laurens MB, Roederer M, Tewari K, Epstein JE, Sim BKL, Ledgerwood JE, Graham BS, Hoffman SL, 2013. Protection against malaria by intravenous immunization with a nonreplicating sporozoite vaccine. Science 341: 13591365.

    • Search Google Scholar
    • Export Citation
  • 3.

    Roestenberg M, McCall M, Hopman J, Wiersma J, Luty AJ, van Gemert GJ, van de Vegte-Bolmer M, van Schaijk B, Teelen K, Arens T, Spaarman L, de Mast Q, Snounou G, Renia L, van der Ven A, Hermsen CC, Sauerwein R, 2009. Protection against a malaria challenge by sporozoite inoculation. N Engl J Med 361: 468477.

    • Search Google Scholar
    • Export Citation
  • 4.

    Billingsley P, Sim BK, Bijker E, Roestenberg M, Lyke K, Laurens M, Mordmueller B, Gomez P, Shekalaghe S, Hodgson S, Hill A, Juma E, Ogutu B, Lell B, Alonso P, Abdullah S, Kremsner P, Tanner M, Sauerwein R, Hoffman S, 2014. Controlled human malaria infections using aseptic, purified cryopreserved Plasmodium falciparum sporozoites administered by needle and syringe. Malar J 13 (Suppl 1): 12.

    • Search Google Scholar
    • Export Citation
  • 5.

    Hodgson SH, Juma E, Salim A, Magiri C, Kimani D, Njenga D, Muia A, Cole AO, Ogwang C, Awuondo K, Lowe B, Munene M, Billingsley PF, James ER, Gunasekera A, Sim BKL, Njuguna P, Rampling TW, Richman A, Abebe Y, Kamuyu G, Muthui M, Elias SC, Molyneux S, Gerry S, Macharia A, Williams TN, Bull PC, Hill AVS, Osier FH, Draper SJ, Bejon P, Hoffman SL, Ogutu B, Marsh K, 2014. Evaluating controlled human malaria infection in Kenyan adults with varying degrees of prior exposure to Plasmodium falciparum using sporozoites administered by intramuscular injection. Infect Dis 5: 686.

    • Search Google Scholar
    • Export Citation
  • 6.

    Shekalaghe S, Rutaihwa M, Billingsley PF, Chemba M, Daubenberger CA, James E, Mpina M, Juma OA, Schindler T, Huber E, Gunasekera A, Manoj A, Simon B, Savarino E, Church LWP, Hermsen CC, Sauerwein RW, Plowe CV, Venkatesan M, Sasi P, Lweno O, Mutani P, Hamad A, Mohammed A, Urassa A, Mzee T, Padilla D, Ruben A, Sim BKL, Tanner M, Abdullah S, Hoffman SL, 2014. Controlled human malaria infection of Tanzanians by intradermal injection of aseptic, purified, cryopreserved Plasmodium falciparum sporozoites. Am J Trop Med Hyg 91: 471480.

    • Search Google Scholar
    • Export Citation
  • 7.

    Sheehy SH, Douglas AD, Draper SJ, 2013. Challenges of assessing the clinical efficacy of asexual blood-stage Plasmodium falciparum malaria vaccines. Hum Vaccin Immunother 9: 18311840.

    • Search Google Scholar
    • Export Citation
  • 8.

    Darton TC, Blohmke CJ, Moorthy VS, Altmann DM, Hayden FG, Clutterbuck EA, Levine MM, Hill AVS, Pollard AJ, 2015. Design, recruitment, and microbiological considerations in human challenge studies. Lancet Infect Dis 15: 840851.

    • Search Google Scholar
    • Export Citation
  • 9.

    Spring M, Polhemus M, Ockenhouse C, 2014. Controlled human malaria infection. J Infect Dis 209 (Suppl 2): S40S45.

  • 10.

    Roestenberg M, O'Hara GA, Duncan CJA, Epstein JE, Edwards NJ, Scholzen A, van der Ven AJAM, Hermsen CC, Hill AVS, Sauerwein RW, 2012. Comparison of clinical and parasitological data from controlled human malaria infection trials. PLoS One 7: e38434.

    • Search Google Scholar
    • Export Citation
  • 11.

    Arévalo-Herrera M, Forero-Peña DA, Rubiano K, Gómez-Hincapie J, Martínez NL, Lopez-Perez M, Castellanos A, Céspedes N, Palacios R, Oñate JM, Herrera S, 2014. Plasmodium vivax sporozoite challenge in malaria-naïve and semi-immune Colombian volunteers. PLoS One 9: e99754.

    • Search Google Scholar
    • Export Citation
  • 12.

    Collett D, 2003. Modelling Survival Data in Medical Research, 2nd edition. Boca Raton, FL: CRC Press.

  • 13.

    Klein M, Kleinbaum DG, 2005. Survival Analysis, 2nd edition. New York, NY: Springer Science+Business Media, Inc.

  • 14.

    Hosmer DW, Lemeshow S, May S, 2011. Applied Survival Analysis: Regression Modeling of Time to Event Data, 2nd edition. Hoboken, NJ: John Wiley and Sons.

    • Search Google Scholar
    • Export Citation
  • 15.

    Lover AA, Coker RJ, 2014. Re-assessing the relationship between sporozoite dose and incubation period in Plasmodium vivax malaria: a systematic re-analysis. Parasitology 141: 859868.

    • Search Google Scholar
    • Export Citation
  • 16.

    Mills M, 2011. Introducing Survival and Event History Analysis. Los Angeles, CA: SAGE Publications Ltd.

  • 17.

    Mills M, 2011. The fundamentals of survival and event history analysis. Introducing Survival and Event History Analysis. Chapter 1. Los Angeles, CA: Sage Publications. Available at: http://www.sagepub.com/upm-data/39847_9781848601017_Mills.pdf.

    • Search Google Scholar
    • Export Citation
  • 18.

    White IR, Horton NJ, Carpenter J, Pocock SJ, 2011. Strategy for intention to treat analysis in randomised trials with missing outcome data. BMJ 342: d40.

    • Search Google Scholar
    • Export Citation
  • 19.

    Gupta SK, 2011. Intention-to-treat concept: a review. Perspect Clin Res 2: 109112.

  • 20.

    Theunissen C, Janssens P, Demulder A, Nouboussié D, Van Esbroeck M, Van Gompel A, Van den Ende J, 2009. Falciparum malaria in patient 9 years after leaving malaria-endemic area. Emerg Infect Dis 15: 115116.

    • Search Google Scholar
    • Export Citation
  • 21.

    Markus MB, 2012. Dormancy in mammalian malaria. Trends Parasitol 28: 3945.

  • 22.

    Thompson FM, Porter DW, Okitsu SL, Westerfeld N, Vogel D, Todryk S, Poulton I, Correa S, Hutchings C, Berthoud T, Dunachie S, Andrews L, Williams JL, Sinden R, Gilbert SC, Pluschke G, Zurbriggen R, Hill AVS, 2008. Evidence of blood stage efficacy with a virosomal malaria vaccine in a Phase IIa clinical trial. PLoS One 3: e1493.

    • Search Google Scholar
    • Export Citation
  • 23.

    Li H, Han D, Hou Y, Chen H, Chen Z, 2015. Statistical inference methods for two crossing survival curves: a comparison of methods. PLoS One 10: e0116774.

    • Search Google Scholar
    • Export Citation
  • 24.

    Royston P, Parmar MK, 2013. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Med Res Methodol 13: 152.

    • Search Google Scholar
    • Export Citation
  • 25.

    Andersen PK, Perme MP, 2010. Pseudo-observations in survival analysis. Stat Methods Med Res 19: 7199.

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Author Notes

* Address correspondence to Andrew A. Lover, Malaria Elimination Initiative, University of California, 550 16th Street, 3F, San Francisco, CA 94158. E-mails: andrew.lover@ucsf.edu or Andrew.A.Lover@gmail.com

Author's address: Andrew A. Lover, Malaria Elimination Initiative, University of California, San Francisco, CA, E-mail: andrew.lover@ucsf.edu.

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