Statistical Methods for Infectious Diseases Lecture 1 M. Elizabeth - PowerPoint PPT Presentation

Outline Framework Concepts Simple SIR Models Statistical Methods for Infectious Diseases Lecture 1 M. Elizabeth Halloran Hutchinson Research Center and University of Washington Seattle, WA, USA January 6, 2009

Outline Framework Concepts Simple SIR Models Framework Transmission and Dependent Happenings Direct and Indirect Effects Vaccine efficacy and effectiveness Concepts Transmission probability Time Lines of Infection Basic Reproductive Number, R 0 Contact Structures; Mixing Patterns Simple SIR Models Endemic versus Epidemic Models

Outline Framework Concepts Simple SIR Models Framework Transmission and Dependent Happenings Direct and Indirect Effects Vaccine efficacy and effectiveness Concepts Transmission probability Time Lines of Infection Basic Reproductive Number, R 0 Contact Structures; Mixing Patterns Simple SIR Models Endemic versus Epidemic Models

Outline Framework Concepts Simple SIR Models Transmission ❼ Transmission from one host to another is fundamental to the survival strategy of most infectious agents. ❼ Each infectious agent has its own life cycle, modes of transmission, population dynamics, evolutionary pressures, and molecular and immunological interaction with the host. ❼ Transmission may involve an insect or other vector, and its ecology. ❼ Our focus is on underlying principles of dynamics and study design common to many infectious diseases.

Outline Framework Concepts Simple SIR Models Dependent versus Independent Happenings ❼ Sir Ronald Ross 1916 ❼ 2nd Nobel Prize in Medicine : elucidation of mosquitos as malaria transmitters ❼ Transmission models of malaria ❼ Theory of happenings ❼ In dependent happenings, the number of individuals becoming affected depends on the number of individuals already affected.

Outline Framework Concepts Simple SIR Models Dependent Happenings and Vaccine Effects ❼ Due to the dependent happenings in infectious diseases (Ross 1916), vaccination can produce several different kinds of effects ❼ At the individual level ❼ And at the population level.

Outline Framework Concepts Simple SIR Models Direct and Indirect Effects of Interventions ❼ Direct effects of interventions on those receiving the intervention, such as a protective vaccine ❼ Indirect effects of interventions, say in reducing infectiousness of breakthrough infections or reducing the number of infectious people exposing others. ❼ Develop an appropriate terminology to describe different effects ❼ Interaction in assumptions about transmission dynamics and choice of study design to evaluate the effect of interest

Outline Framework Concepts Simple SIR Models

Outline Framework Concepts Simple SIR Models Vaccine efficacy and effectiveness ❼ generally estimated as one minus some measure of relative risk, RR , in the vaccinated group compared to the unvaccinated group: VE = 1 − RR . ❼ The groups being compared could be composed of individuals or of populations or communities.

Outline Framework Concepts Simple SIR Models Historical Example: Typhoid inoculation efficacy ❼ Karl Pearson versus immunologist A.E. Wright BMJ (1904) ❼ compared correlation coefficient for typhoid inoculation (about 0.1) with that of smallpox vaccination (0.578 to 0.769) ❼ claimed antityphoid inoculation should be stopped.

Outline Framework Concepts Simple SIR Models Vaccine efficacy: typhoid and cholera ❼ Greenwood and Yule (1915) (Proc Roy Soc Med) ❼ Thoughts on the statistics of evaluating vaccines in the field ❼ Pre-dates person-time analysis ❼ Discussion of “confounding” ❼ Problem of people being inoculated during epidemic

Outline Framework Concepts Simple SIR Models

Outline Framework Concepts Simple SIR Models Pertussis vaccine efficacy ❼ Kendrick and Eldering (1939) ❼ Person-time analysis versus conditional on exposure to infection

Outline Framework Concepts Simple SIR Models

Outline Framework Concepts Simple SIR Models

Outline Framework Concepts Simple SIR Models Polio vaccine trials ❼ Francis et al (1955) ❼ Observed Control Study, “to administer vaccine to children in the second grade of school; the corresponding first and third graders would not be inoculated, but would be kept under observation for the occurrence of poliomyelitis in comparison with the inoculated second graders.” ❼ Placebo Control Study, “children of the first, second, and third grades would be combined. One half would receive vaccine; the other matching half, serving as strict controls, would receive a solution of similar appearance....”

Outline Framework Concepts Simple SIR Models Transmission probability, p ❼ p = probability that, given a contact between an infective source (host) and susceptible host, successful transfer of the infectious agent will occur so that the susceptible host becomes infected (or a carrier).

• Susceptible host • Infectious host • Infectious agent • Type and definition of contact Outline Framework Concepts Simple SIR Models infectious agent Infectious Susceptible host host contact Transmission probability depends on:

Outline Framework Concepts Simple SIR Models Time Lines of Infection Dynamics of Disease Appearance Resolution Time of of symptoms of infection infection Non diseased - immune Incubation - carrier Symptomatic Susceptible - dead period period - recovered Dynamics of Infectiousness Infection not Time of Infection transmitable infection transmittable Non infectious - removed Latent Infectious - dead Susceptible period period - recovered Time

Outline Framework Concepts Simple SIR Models Ordinary Smallpox Mean: 11.48 days Fig. 1 Distribution of Incubation Period (Onset of Fever) Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Infected Second period: All cases recognized Onset of vesicles (day 4 of on day 3 of rash (day 6 of fever) rash). In first period, all cases Onset of papules recognized; contacts of Disease Recognition Onset of macular (day 3 of rash, recognized cases & household Onset of fever rash (day 4 of day 6 of fever) contacts of contacts fever) vaccinated, observed 12 days for fever. 30% die on days 7-14 Incubation Period of fever (uniform dist.) Day of -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 fever Infected One day before rash Infectiousness 4x One day after onset of fever 2x 2x 1x Latent period 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Day of fever Infected At the end of the 1 st day of fever: At the end of the 3rd day of fever (beginning of 4 th ): Behavior 47.5% withdraw to the home 5% go to the hospital + those who withdrew to the home 47.5% go to the hospital 1 st recognized case in hospital � vacc. hosp. workers Day of 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 fever Infected

Outline Framework Concepts Simple SIR Models Modified Smallpox Mean: 11.48 days Fig. 2 50% of those born before 1971 Distribution of Incubation Period (Onset of Fever) Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Infected Second period: All cases recognized Onset of vesicles (day 4 of rash). on day 3 of rash (day 6 of fever) In first period, 75% of cases recognized (remaining 25% on Onset of papules day 10 of fever); contacts of Disease Recognition Onset of macular (day 3 of rash, Onset of fever recognized cases & household rash (day 4 of day 6 of fever) contacts of contacts vaccinated, fever) observed 12 days for fever. 10% die on days 7-14 of fever Incubation Period (uniform dist.) Day of -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 fever Infected One day before rash Infectiousness 0.33(4x) One day after onset of fever 0.33(2x) 0.33(2x) 0.33x Latent period Day of 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 fever Infected At the end of the first day of fever: At the end of the 3rd day (beginning of 4 th day) of fever: Behavior 25% withdraw to the home 50% go to the hospital + those who withdrew to the home 25% go to the hospital 1 st recognized case in hospital → vacc. Hosp. workers Day of 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 fever Infected