A Simple Method of Measuring Vaccine Effects on Infectiousness and Contagion

Yasutaka Chiba

Division of Biostatistics, Clinical Research Center, Kinki University School of Medicine, Osaka, Japan.

DOI: 10.4236/ojs.2013.34A002                

Abstract

The vaccination of one person may prevent another from becoming infected, either because the vaccine may prevent the first person from acquiring the infection and thereby reduce the probability of transmission to the second, or because, if the first person is infected, the vaccine may impair the ability of the infectious agent to initiate new infections. The former mechanism is referred as a contagion effect and the latter is referred as an infectiousness effect. By applying a principal stratification approach, the conditional infectiousness effect has been defined, but the contagion effect is not defined using this approach. Recently, new definitions of unconditional infectiousness and contagion effects were provided by applying a mediation analysis approach. In addition, a simple relationship between conditional and unconditional infectiousness effects was found under a number of assumptions. These two infectiousness effects can be assessed by very simple estimation and sensitivity analysis methods under the assumptions. Nevertheless, such simple methods to assess the contagion effect have not been discussed. In this paper, we review the methods of assessing infectiousness effects, and apply them to the inference of the contagion effect. The methods provided here are illustrated with hypothetical vaccine trial data.

Keywords

Indirect Effect; Interference; Mediation Analysis; Potential Outcome; Principal Stratification

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. E. Halloran and M. G. Hudgens, “Causal Inference for Vaccine Effects on Infectiousness,” International Journal of Biostatistics, Vol. 8, No. 2, 2012, Article 6. doi:10.2202/1557-4679.1354
[2]	P. R. Rosenbaum, “Interference between Units in Randomized Experiments,” Journal of the American Statistical Association, Vol. 102, No. 477, 2007, pp. 191-200. doi:10.1198/016214506000001112
[3]	M. G. Hudgens and M. E. Halloran, “Towards Causal Inference with Interference,” Journal of the American Statistical Association, Vol. 103, No. 482, 2008, pp. 832-842. doi:10.1198/016214508000000292
[4]	T. J. VanderWeele, E. J. Tchetgen Tchetgen and M. E. Halloran, “Components of the Indirect Effect in Vaccine Trials: Identification of Contagion and Infectiousness Effects,” Epidemiology, Vol. 23, No. 5, 2012, pp. 751-761. doi:10.1097/EDE.0b013e31825fb7a0
[5]	S. Datta, M. E. Halloran and I. M. Longini, “Efficiency of Estimating Vaccine Efficacy for Susceptibility and Infectiousness: Randomization by Individual Versus Household,” Biometrics, Vol. 55, No. 3, 1999, pp. 792-798. doi:10.1111/j.0006-341X.1999.00792.x
[6]	M. G. Hudgens and M. E. Halloran, “Causal Vaccine Effects on Binary Post-Infection Outcomes,” Journal of the American Statistical Association, Vol. 101, No. 473, 2006, pp. 51-64. doi:10.1198/016214505000000970
[7]	Y. Chiba and M. Taguri, “Conditional and Unconditional Infectiousness Effects in Vaccine Trials,” Epidemiology, Vol. 24, No. 2, 2013, pp. 336-337. doi:10.1097/EDE.0b013e31828261f5
[8]	M. M. Glymour and S. Greenland, “Causal Diagrams,” In: K. J. Rothman, S. Greenland and T. L. Lash, Eds., Modern Epidemiology, 3rd Edition, Lippincott Williams and Wilkins, Philadelphia, 2008, pp. 183-209.
[9]	J. Pearl, “Causality: Models, Reasoning, and Inference,” 2nd Edition, Cambridge University Press, Cambridge, 2009.
[10]	M. E. Sobel, “What Do Randomized Studies of Housing Mobility Demonstrate? Causal Inference in the Face of Interference,” Journal of the American Statistical Association, Vol. 101, No. 476, 2006, pp. 1398-1407. doi:10.1198/016214506000000636
[11]	T. J. VanderWeele, “Concerning the Consistency Assumption in Causal Inference,” Epidemiology, Vol. 20, No. 6, 2009, pp. 880-883. doi:10.1097/EDE.0b013e3181bd5638
[12]	M. E. Halloran, M. P. Préziosi and H. Chu, “Estimating Vaccine Efficacy from Secondary Attack Rates,” Journal of the American Statistical Association, Vol. 98, No. 461, 2003, pp. 38-46. doi:10.1198/016214503388619076
[13]	S. Greenland, J. Pearl and J. M. Robins, “Causal Diagrams for Epidemiologic Research,” Epidemiology, Vol. 10, No. 1, 1999, pp. 37-48.
[14]	M. G. Hudgens and M. E. Halloran, “Causal Vaccine Effects on Binary Post-Infection Outcomes,” Journal of the American Statistical Association, Vol. 101, No. 473, 2006, pp. 51-64. doi:10.1198/016214505000000970
[15]	C. E. Frangakis and D. B. Rubin, “Principal Stratification in Causal Inference,” Biometrics, Vol. 58, No. 1, 2002, pp. 21-29. doi:10.1111/j.0006-341X.2002.00021.x
[16]	J. M. Robins and S. Greenland, “Identifiability and Exchangeability for Direct and Indirect Effects,” Epidemiology, Vol. 3, No. 2, 1992, pp. 143-155.
[17]	J. Pearl, “Direct and Indirect Effects,” Proceedings of the Seventeenth Conference on Uncertainty and Artificial Intelligence, San Francisco, 2-5 August 2001, pp. 411-420.
[18]	Y. Chiba and M. Taguri, “Assessing the Causal Infectiousness Effect in Vaccine Trials,” In: iConcept Press, Ed., Vaccines—Benefits and Risks, iConcept Press, Hong Kong, 2013, in press.
[19]	K. Hirano, G. W. Imbens and G. Ridder, “Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score,” Econometrica, Vol. 71, No. 4, 2003, pp. 1161-1189.
[20]	S. Greenland, “Estimating Standardized Parameters from Generalized Linear Models,” Statistics in Medicine, Vol. 10, No. 7, 1991, pp. 1069-1074. doi:10.1002/sim.4780100707
[21]	M. Taguri, Y. Matsuyama, Y. Ohashi, A. Harada and H. Ueshima, “Doubly Robust Estimation of the Generalized Impact Fraction,” Biostatistics, Vol. 13, No. 3, 2012, pp. 455-467. doi:10.1093/biostatistics/kxr038
[22]	T. Sato and Y. Matsuyama, “Marginal Structural Models as a Tool for Standardization,” Epidemiology, Vol. 14, No. 6, 2003, pp. 680-686. doi:10.1097/01.EDE.0000081989.82616.7d
[23]	J. M. Robins, “Association, Causation, and Marginal Structural Models,” Synthese, Vol. 121, No. 1-2, 1999, pp. 151-179. doi:10.1023/A:1005285815569
[24]	J. M. Robins, M. A. Hernán and B. A. Brumback, “Marginal Structural Models and Causal Inference in Epidemiology,” Epidemiology, Vol. 11, No. 5, 2000, pp. 550-560.
[25]	Y. Chiba and T. J. VanderWeele, “A Simple Method for Principal Strata Effects When the Outcome Has Been Truncated Due to Death,” American Journal of Epidemiology, Vol. 173, No. 7, 2011, pp. 745-751. doi:10.1093/aje/kwq418
[26]	J. L. Zhang and D. B. Rubin, “Estimation of Causal Effects via Principal Stratification When Some Outcomes Are Truncated by Death,” Journal of Educational and Behavioral Statistics, Vol. 28, No. 4, 2003, pp. 353-368. doi:10.3102/10769986028004353
[27]	J. L. Zhang, D. B. Rubin and F. Mealli, “Evaluating the Effects of Job Training Programs on Wages through Principal Stratification,” In: D. Millimet, J. Smith and E. Vytlacil, Eds., Advances in Econometrics: Modeling and Evaluating Treatment Effects in Econometrics, Elsevier Science, New York, 2008, pp. 117-145.
[28]	Y. Chiba, “The Large Sample Bounds on the Principal Strata Effect with Application to a Prostate Cancer Prevention Trial,” International Journal of Biostatistics, Vol. 8, No. 1, 2012, Article 12. doi:10.1515/1557-4679.1365
[29]	T. J. VanderWeele and E. J. Tchetgen Tchetgen, “Bounding the Infectiousness Effect in Vaccine Trials,” Epidemiology, Vol. 22, No. 5, 2011, pp. 686-693. doi:10.1097/EDE.0b013e31822708d5
[30]	Sjolander, “Bounds on Natural Direct Effects in the Presence of Confounded Intermediate Variables,” Statistics in Medicine, Vol. 28, No. 4, 2009, pp. 558-571. doi:10.1002/sim.3493
[31]	T. Lange, S. Vansteelandt and M. Bekaert, “A Simple Unified Approach for Estimating Natural Direct and Indirect Effects,” American Journal of Epidemiology, Vol. 176, No. 3, 2012, pp. 190-195. doi:10.1093/aje/kwr525
[32]	L. Valeri and T. J. VanderWeele, “Mediation Analysis Allowing for Exposure-Mediator Interactions and Causal Interpretation: Theoretical Assumptions and Implementation with SAS and SPSS Macros,” Psychological Methods, Vol. 18, No. 2, 2013, pp. 137-150. doi:10.1037/a0031034
[33]	Y. Chiba and M. Taguri, “Alternative Monotonicity Assumptions for Improving Bounds on Natural Direct Effects,” International Journal of Biostatistics, in press. doi:10.1515/ijb-2012-0022