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Design and Evaluation of Prophylactic

Interventions Using Infectious Disease

Incidence Data from Close Contact Groups

Yang Yang1, Ira M. Longini, Jr.1, M. Elizabeth Halloran1

Technical Report 04-09

July 22, 2004

Department of Biostatistics

Rollins School of Public Health

Emory University

Atlanta, Georgia 30322

Department of Biostatistics, Rollins School of Public Health,

Emory University, 1518 Clifton Road NE, Atlanta, GA 30322 USA

Telephone: (404)727-9169FAX: (404)727-1370

e-mail: yyang3@sph.emory.edu

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Summary. Prophylaxis of contacts of infectious cases such as household

members and treatment of infectious cases are methods to prevent spread

of infectious diseases. We develop study designs and statistical methods for

estimating the efficacy of such interventions in reducing susceptibility and

infectiousness as well as for estimating the transmission probabilities. We

consider both the design with prospective follow up of close contact groups

and the design with ascertainment of close contact groups by an index case.

Randomization by groups and by individuals are compared. We develop two

methods for estimating the efficacy and transmission probabilities for each

design. The first uses maximum likelihood, and the second uses a generalized

linear models framework estimated by iteratively re-weighted least squares

with the EM algorithm. We develop a method to deal with the left truncation

of the case-ascertained follow up design. We use these methods to compare

the designs using simulations and to analyze data from a trial of an antiviral

agent in preventing influenza in household contacts.

Key words: Infectious disease; Intervention efficacy; Community trial;

Antiviral agent; Left truncation; Linear model

1.Introduction

Transmission of many infectious diseases takes place mainly through close

contacts in mixing groups such as households, daycare centers, schools, and

the workplace, and to a lesser extent through casual contacts in the commu-

nity at large. Data from clinical studies based on close contact groups offer a

basis for estimating person-to-person and community-to-person transmission

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probabilities and, more importantly, for evaluating the effectiveness of pro-

phylactic interventions such as vaccination and antiviral agents. Estimation

of the person-to-person transmission probabilities within the close contact

groups is conditioned on exposure to infection and, thus, can be used to es-

timate the effect of the intervention on both reducing susceptibility to infec-

tion and reducing transmission to others (Halloran, Longini and Struchiner,

1999). A good study design improves the quality of the information as well

as reduces both the length of the observation period and the number of close

contact groups needed to assess effectiveness of the intervention. Key study

design elements include randomization scheme and ascertainment method.

Typically, in infectious disease studies, the intervention product and placebo

are randomized either at the individual level within the close contact groups,

where each person is randomized independently, or at the group level, where

participants in the same groups receive either the intervention product or

placebo (Hayes et al., 1995; Donner, 1998). The two randomization schemes

may result in substantially different precision of the parameter estimates

(Datta, Halloran and Longini, 1999). Unlike the randomization issue, the

method to recruit and to follow close contact groups is intuitively related

to the size of a clinical trial. For example, a prospective trial generally has

complete observations in the sense that groups free of disease are enrolled

at the beginning of an epidemic season and then followed to some predeter-

mined end point. For a case-ascertained follow-up trial, close contact groups

are enrolled for observation if and only if an index case is ascertained. The

case-ascertained trial size would be much smaller than that of a prospective

follow-up study with the same number of cases, but at the price of poten-

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tial bias due to left truncation of the infection status of the non-index cases.

These later cases could already be infected at the time of ascertainment of

the close contact group, but not yet showing symptoms. If this left trunca-

tion can be dealt with, then the case-ascertained trials may be preferable to

the larger prospective trials.

Many methods are available for analyzing clinical trial data of acute in-

fectious diseases based on close contact groups (Becker, 1989). Longini and

Koopman (1982), Longini et al. (1988), Addy, Longini and Haber (1991)

and Magder and Brookmeyer (1993) developed methods that use only final

infection status of individuals within each close contact group. Rampey et al.

(1992) developed a method for time of onset data for prospective trials, but

not for case-ascertained trials.

In this paper, we develop two estimation procedures for both prospective

and case-ascertained clinical trials in close contact groups using likelihood-

based methods and generalized linear models fitted by iteratively re-weighted

least squares in combination with the EM algorithm. Individual- and group-

level randomization schemes as well as prospective and case-ascertained de-

signs are compared using simulations. The approaches are generalized to

stratified populations that include discrete covariates. We use these new

methods to estimate the prophylactic and treatment effectiveness of an in-

fluenza antiviral agent in two household trials.

2. Methods

Suppose, without loss of generality, that influenza is the infectious disease of

interest and that the close contact groups are households. In addition, the in-

tervention of interest is the prophylactic use of influenza antiviral agents. We

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define two types of potentially infectious contact: (1) being in the household

with another infected person, and (2) making contact with possibly infected

people outside of the household. We define p as the daily transmission prob-

ability per contact within the household between a susceptible person and an

infective person if both have not received antiviral agents. Similarly, define

b as the daily probability that a susceptible and untreated person is infected

by a source of infection from the community. The antiviral efficacy for sus-

ceptibility to infection and illness (AVES) measures how much an antiviral

agent will relatively reduce the probability that an uninfected person will be

infected and ill, when exposed to infection, compared to an uninfected person

not using an antiviral agent. Then AVES= 1 − θ, where θp is the reduced

transmission probability if the susceptible person is taking an antiviral agent

and exposed to an untreated infected person in the household. For simplicity,

we assume that efficacy is the same for contacts outside the household, i.e.,

the reduced transmission probability for a person taking an antiviral agent is

θb. The antiviral efficacy for infectiousness (AVEI) is how much an antiviral

agent will relatively reduce the probability that an infected person will trans-

mit influenza to others compared to an infected person who is not using an

antiviral agent. Then, AVEI= 1 − φ, where φp is the reduced transmission

probability if the infective person is treated. If both people of a transmission

pair are treated, we assume independence and multiplicativity of θ and φ

so that the transmission probability reduces to θφp. We make the following

assumptions about influenza: 1. The latent period (i.e., time from infection

to being infectious) is the same as the incubation period (i.e., time from in-

fection to the onset of illness symptoms). 2. The probability distributions of

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