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American Journal of Epidemiology
© The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of
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Vol. 183, No. 6
DOI: 10.1093/aje/kwv234
Advance Access publication:
March 2, 2016
Practice of Epidemiology
Incorporating Transmission Into Causal Models of Infectious Diseases for
Improved Understanding of the Effect and Impact of Risk Factors
Stuart Paynter*
* Correspondence to Dr. Stuart Paynter, Level 2 Public Health Building, School of Public Health, Curtin University, Kent Street, Bentley, WA 6102,
Australia (e-mail: [email protected]).
Initially submitted March 12, 2015; accepted for publication August 26, 2015.
Conventional measures of causality (which compare risks between exposed and unexposed individuals) do not
factor in the population-scale dynamics of infectious disease transmission. We used mathematical models of 2
childhood infections (respiratory syncytial virus and rotavirus) to illustrate this problem. These models incorporated
3 causal pathways whereby malnutrition could act to increase the incidence of severe infection: increasing the proportion of infected children who develop severe infection, increasing the children’s susceptibility to infection, and
increasing infectiousness. For risk factors that increased the proportion of infected children who developed severe
infection, the population attributable fraction (PAF) calculated conventionally was the same as the PAF calculated
directly from the models. However, for risk factors that increased transmission (by either increasing susceptibility to
infection or increasing infectiousness), the PAF calculated directly from the models was much larger than that predicted by the conventional PAF calculation. The models also showed that even when conventional studies find
no association between a risk factor and an outcome, risk factors that increase transmission can still have a
large impact on disease burden. For a complete picture of infectious disease causality, transmission effects
must be incorporated into causal models.
communicable diseases; epidemiologic measurements; epidemiologic methods
Abbreviations: IR, incidence rate; PAF, population attributable fraction; RR, rate ratio; RSV, respiratory syncytial virus.
epidemiologic studies compare risks between individuals,
using the unexposed group as the reference. However, for infectious diseases that are transmitted from person to person,
the incidence in the unexposed group depends on the incidence in the exposed group (2, 3). Thus, a population-level
perspective is required to fully understand infectious disease
causality.
When considering infectious diseases, causal effects can
be divided into individual-level effects (also called direct effects), which can be detected using conventional methods
comparing individuals, and transmission effects (also called
indirect effects), which require specific methods to detect.
Risk factors that increase infectiousness will have transmission effects, leading to an increased incidence of infection
in the whole population. A risk factor that increases the probability of having an infectious contact, or that increases susceptibility to infection following contact with an infectious
case, will have both an individual-level effect (because persons
Infectious diseases remain the most important cause of
morbidity and mortality in the world’s most vulnerable populations, particularly children. Most child deaths due to infectious diseases occur in low- and middle-income settings,
where children are particularly at risk because of exposure
to environmental risk factors such as malnutrition, poor sanitation, overcrowding, and indoor smoke. (Throughout this
article, the term “exposure” refers to exposure to risk factors
such as these, as distinct from “contact,” which refers to exposure to the pathogen itself.) Maintaining the momentum of
recent gains in child survival will require renewed focus on
infectious disease control, which in turn must include interventions designed to address major risk factors (1).
For noninfectious diseases, the risk of disease is only increased in persons exposed to a risk factor. For infectious diseases, risk factors that increase the amount of transmission
in the population will also increase the risk of infection in persons who are not exposed to that risk factor. Conventional
574
Am J Epidemiol. 2016;183(6):574–582
Incorporating Transmission Into Causal Models 575
exposed to the risk factor will have an increased risk of infection) and a transmission effect (because these additional
cases will be infectious).
Halloran and Struchiner (2) have demonstrated that individual and transmission effects can be examined in isolation
by measuring the effect of a risk factor while conditioning on
contact with an infectious source. This can be done by using
data from household transmission studies, examining secondary attack rates following the occurrence of an index
case of infection in the household. Susceptibility to infection
can be assessed by focusing on secondary attack rates in family
members who are exposed or unexposed to the risk factor, and
the degree of infectiousness can be assessed by focusing on
secondary attack rates according to whether the index case is
exposed or unexposed to the risk factor. In this paper, I take
their work a step further, exploring the impact of risk factors
on infectious disease incidence at the population level, by incorporating both individual and transmission effects of a risk
factor into mathematical models. The resulting dynamic causal
models are referred to here as causal transmission models.
Although mathematical models of infectious diseases are used
regularly to assess the impact of interventions, they have only
rarely been used to investigate the impact of environmental
risk factors on infectious disease incidence (4).
The models examined in this paper incorporate the effects
of malnutrition on the incidence of childhood infection with
respiratory syncytial virus (RSV) and rotavirus. Together
these two infections are responsible for approximately 1 in 9
infant deaths worldwide (5). Malnourished children have
poorer outcomes than well-nourished children following contact with an infectious case: Malnourished children have more
symptomatic infections and have more severe infections, with
longer duration and higher case fatality rates (6–10). Higher
rates of symptomatic infections in malnourished children, exacerbated by longer infectious periods, will act to increase the
force of infection acting on all children in the community.
METHODS
Model structure
The same model structure can be used to describe the
transmission of either RSV or rotavirus infection. Although
these infections are spread by different routes (by respiratory
droplets and fecal-oral transmission, respectively), they are
both transmitted by close person-to-person contact, as well
as by indirect contact through survival of virus on surfaces.
To more clearly illustrate the concepts examined in this
paper, I used a simplified model with only 2 categories of nutritional status—children are either well-nourished (W) or
malnourished (M). The structure of the causal transmission
model is outlined in Figure 1, which shows the model compartments for persons in the malnourished subgroup; the
compartments for the well-nourished subgroup are equivalent. Individuals are born susceptible (compartments SM and
SW) and have a risk of infectious contact of λ per day (the
force of infection, which is dependent on the number of infectious individuals). Only a proportion (αM in malnourished
children and αW in well-nourished children) of the children
who have an infectious contact will become infected (comAm J Epidemiol. 2016;183(6):574–582
EM
SM
M M
Scenario B
RM
VM
Scenario C
IM
CM
M
Scenario A
Figure 1. Structure of a causal model of childhood infection transmission. The model compartments of the malnourished subgroup
are shown; the compartments of the well-nourished subgroup are
equivalent. The parameters λα, σ, ν, and γ denote the rate of movement between model compartments. The causal mechanism of malnutrition in each scenario is shown by the open arrows. In scenario A,
the proportion of infectious children who develop severe infection is
increased among malnourished children (ρM > ρW). In scenario B, susceptibility to infection is increased among malnourished children
(αM > αW). In scenario C, malnourished children are infectious for a
longer period of time (νM < νW). Notation: C, severe infection (epidemiologic case); E, infected; I, infectious; R, recovered (temporarily immune); S, susceptible.
partments EM and EW). After the latency period (the mean
latency period is equal to 1/σ), these infected individuals become infectious (compartments IM and IW). The mean infectious period (time in compartment IM or IW) in malnourished
children is equal to 1/νM, and in well-nourished children it is
equal to 1/νW. Children in compartments RM and RW are temporarily resistant to reinfection, and they return to the susceptible state following a mean period equal to 1/γ. A proportion
of infectious children (ρM in malnourished children and ρW in
well-nourished children) progress to more severe infection and
are identified as epidemiologic cases (subsets CM and CW —
note that these are not separate model compartments but are
subsets of IM and IW). For RSV, subset C represents severe
acute lower respiratory infection, while for rotavirus, subset
C represents severe diarrhea requiring hospital admission.
For simplicity (and to better demonstrate the difference between individual and transmission effects), persons in subset
C are considered to be as infectious per day as any other individual within compartment I.
The model equations and the process of model fitting are
described in detail in Web Appendix 1 and Web Tables 1–3
(available at http://aje.oxfordjournals.org/). The model parameter assumptions are summarized in Web Tables 1 and
2. The RSV model was fitted to RSV hospital admissions data
from the Philippines (11). The rotavirus model was fitted to
rotavirus infection data from Guinea-Bissau (12) and again to
rotavirus hospital admissions data from India (13). To ensure
that the models realistically reflected the actual force of infection in these settings, the models were simultaneously fitted
to estimates of the overall rate of infection and the mean force
of infection in each setting (Web Table 3).
576 Paynter
For each of the infections, 3 scenarios were modeled, each scenario making different assumptions about the mechanisms leading to an increased risk of incident acute lower respiratory infection in malnourished children. The scenarios were chosen to
highlight the difference between individual and transmission effects. In reality, these scenarios are unlikely to occur in isolation
(e.g., children with more severe disease generally have longer infectious periods).
Scenario A: In this scenario, malnutrition increases the risk of progression to more serious infection; however, malnutrition
does not alter the child’s susceptibility to infection upon contact with an infectious case or alter the infectiousness of cases. For
the RSV model, the risk of progression to severe acute lower respiratory infection in malnourished children is 1.30 times higher
than in well-nourished children (ρM = 0.065, ρW = 0.050), and for the rotavirus model the risk of progression to severe diarrhea in
malnourished children is similarly 1.33 times higher than in well-nourished children (ρM = 1/45, ρW = 1/60). Cohort monitoring
suggests that between 5% and 8% of children with RSV infection develop severe acute lower respiratory infection, while between
1/40 and 1/65 of children with rotavirus infection develop disease severe enough to be admitted to a hospital (14–17). The ratio
between ρM and ρW in the models assumes that the association between malnutrition and RSV and diarrhea incidence seen in
epidemiologic studies (8, 18–21) is due to an increase in disease progression in malnourished children (i.e., that scenario A is
true).
Scenario B: In this scenario, malnutrition increases susceptibility to infection, increasing the risk of infection in children who
have had contact with an infectious case. However, malnutrition has no effect on the infectiousness of cases or on progression to
severe infection. For the reasons described in the Introduction, it is difficult to directly measure how much malnutrition increases
susceptibility to infection (i.e., the ratio αM/αW) using conventional epidemiologic studies. Thus, the ratio αM/αW was estimated
from the model, by fitting the model while holding the incidence rate ratio (RRI) equal to 1.3 (RRI is the ratio of the incidence rate
of infection in malnourished children to the incidence rate in well-nourished children). The value of RRI in the models assumes
that the association between malnutrition and RSV and diarrhea incidence seen in epidemiologic studies (8, 18–21) is due to an
increase in susceptibility to infection in malnourished children (i.e., that scenario B is true).
Scenario C: In this scenario, malnourished children have a prolonged duration of infectiousness; however, malnutrition has no
effect on susceptibility to infection or on the progression to severe infection. For both the RSV and rotavirus models, the duration of
infectiousness is 1.3 times longer in malnourished children. For RSV, 1/νM = 6.5 days and 1/νW = 5 days. For rotavirus, 1/νM = 9 days
and 1/νW = 7 days. These parameter assumptions are consistent with available data (9, 20, 22–24).
For each of the 3 scenarios outlined above, the incidence rate (IR) of infection in the malnourished and well-nourished groups
(IRIM and IRIW) and the incidence rates of severe infection in the malnourished and well-nourished groups (IRCM and IRCW) were
calculated for the baseline situation (20% malnutrition), and then IRIW and IRCW were calculated for the counterfactual situation
(no malnutrition). Several degrees of mixing between malnourished and well-nourished children were examined, where the degree of mixing (δ) is the proportion of the malnourished subgroup “allowed” to mix with the well-nourished subgroup, and vice
versa.
Calculation of relative risks and population attributable fractions
Two incidence rate ratio measures were calculated. RRI is the incidence rate ratio for infection comparing malnourished and wellnourished children (using IRIM and IRIW from the baseline situation where 20% of children are malnourished). RRC is the equivalent
incidence rate ratio for cases of severe infection (using IRCM and IRCW from the baseline situation where 20% of children are malnourished). RRC is the incidence rate ratio that would generally be calculated from a conventional epidemiologic study.
RRI ¼
IRIMðbaselineÞ
:
IRIWðbaselineÞ
RRC ¼
IRCMðbaselineÞ
:
IRCWðbaselineÞ
Two variations of the population attributable fraction (PAF) of cases of severe infection due to malnutrition were calculated. The
first of these uses the conventional method of calculating the PAF using RRC and the prevalence of malnutrition (P) in the baseline
situation (25):
PAFC1 ¼
PðRRC 1Þ
:
PðRRC 1Þ þ 1
The second is an alternative PAF calculated directly from the model, using the total incidence of severe infection in the baseline
situation, and the incidence of severe infection from the counterfactual situation where no children are malnourished:
PAFC2 ¼
½P × IRCMðbaselineÞ þ ð1 PÞ × IRCWðbaselineÞ IRCWðcounterfactualÞ
:
½P × IRCMðbaselineÞ þ ð1 PÞ × IRCWðbaselineÞ Am J Epidemiol. 2016;183(6):574–582
Incorporating Transmission Into Causal Models 577
No. of Severe Cases
A)
30
25
20
15
10
5
0
Date
No. of Severe Cases
B)
40
35
30
25
20
15
10
5
0
Date
No. of Severe Cases
C)
40
35
30
25
20
15
10
5
0
Date
Figure 2. Fitted models for scenario A in 3 childhood infection settings at baseline. Circular markers show the observed number of cases each
month. A) Hospital admissions for acute lower respiratory infection associated with respiratory syncytial virus in the Philippines (11); B) rotavirus
infections in Guinea-Bissau (12); C) hospital admissions for rotavirus diarrhea in India (13). The solid lines show the monthly number of severe
infections (in malnourished and well-nourished children) calculated from the fitted models.
RESULTS
Figure 2 shows the scenario A models fitted to the observed case numbers in each setting, assuming homogenous
mixing. The fit for the scenario B and C models was similar.
Tables 1 and 2 show the results from the models assuming
Am J Epidemiol. 2016;183(6):574–582
homogenous mixing. For scenario A, there was no difference
in the incidence of infection between malnourished and wellnourished children (RRI = 1.00); however, the increased risk
of progressing to severe infection in malnourished children
meant that the incidence of cases of severe infection was
578 Paynter
Table 1. Incidence Rates (per 1,000 Child-Years) of 2 Childhood
Infections Calculated From Models Assuming Homogenous Mixinga
Scenario and
Prevalence of
Malnutrition, %
IR Measureb
IRIM
IRIW
IRCM
Table 2. Risk Measures for 2 Childhood Infections From Models
Assuming Homogenous Mixinga
RRI
IRCW
0
—
c
650
650
0
PAFC2
1.00
1.30
0.06
0.06
32.5
B
1.30
1.30
0.06
42.3
0.48
32.5
C
1.00
1.00
0.00
—
0.39
Rotavirus in Guinea-Bissau
Scenario B
20
PAFC1
A
Scenario A
650
RRC
RSV in the Philippines
RSV in the Philippines
20
Risk Measureb
Scenario
797
—
613
336
39.9
—
30.7
A
1.00
1.33
0.06
0.06
16.8
B
1.30
1.30
0.06
0.39
C
1.00
1.00
0.00
0.31
Scenario C
20
648
650
32.4
32.5
0
—
395
—
19.8
Rotavirus in Guinea-Bissau
Scenario A
20
600
600
13.3
10.0
0
—
600
—
10.0
Scenario B
20
736
566
12.3
9.4
0
—
363
—
6.1
Scenario C
20
598
600
10.0
10.0
0
—
417
—
6.9
Rotavirus in India
A
1.00
1.33
0.06
0.06
B
1.30
1.30
0.06
0.21
C
1.00
1.00
0.00
0.12
Abbreviations: PAF, population attributable fraction; RR, rate ratio;
RSV, respiratory syncytial virus.
a
The RSV model was fitted to RSV hospital admissions data from
the Philippines (11). The rotavirus model was fitted to rotavirus infection
data from Guinea-Bissau (12) and rotavirus hospital admissions data
from India (13).
b
RRI, incidence RR for infection; RRC, incidence RR for severe
infection; PAFC1, conventional PAF; PAFC2, PAF calculated from the
causal transmission models.
Rotavirus in India
Scenario A
20
1,000
1,000
22.2
16.7
0
—
1,000
—
16.7
Scenario B
20
1,226
943
20.4
15.7
0
—
789
—
13.1
16.6
16.7
—
14.7
Scenario C
20
995
0
—
1,001
881
Abbreviations: IR, incidence rate; RSV, respiratory syncytial virus.
a
The RSV model was fitted to RSV hospital admissions data from the
Philippines (11). The rotavirus model was fitted to rotavirus infection data
from Guinea-Bissau (12) and rotavirus hospital admissions data from
India (13).
b
IRIM , IR of infection in malnourished children; IRIW, IR of infection in
well-nourished children; IRCM , IR of severe infection in malnourished
children; IRCW, IR of severe infection in well-nourished children.
c
IR could not be calculated.
higher in malnourished children than in well-nourished children (RRC = 1.30 for RSV and RRC = 1.33 for rotavirus). Removing malnutrition from the population had no impact on
the incidence of severe infection in well-nourished children;
thus, PAFC1 and PAFC2 were the same (0.06). For scenario B,
malnourished children had a higher incidence of infection
than well-nourished children (RRI was set at 1.3), which
led to a higher incidence of severe infection in malnourished
children (RRC = 1.3). Upon removing malnutrition from
the population, the incidence of severe infection in wellnourished children dropped considerably in all 3 settings.
This is because the higher incidence of infection in the
malnourished children was driving the incidence of infection
in the well-nourished children, and removing malnutrition
from the population removed this transmission effect. Thus,
PAFC2 was considerably larger than PAFC1 in all 3 settings.
For scenario C, there was no difference in the incidence of
infection or severe infection between malnourished and wellnourished children (RRI and RRC = 1.00); however, despite
this, the models found moderate-to-large values for PAFC2,
while the conventional PAF calculation predicted no impact
(PAFC1 = 0.00). In scenario C, PAFC2 was large despite there
being no difference in the incidence of severe infection between malnourished and well-nourished children, because
the higher infectiousness of the malnourished children was
driving the incidence of infection equally in both the wellnourished and malnourished children. Removing malnutrition from the population removed this transmission effect.
In both scenario B and scenario C, the discrepancy between
PAFC1 and PAFC2 was greatest in the RSV model and smallest in the India rotavirus model.
Figures 3 and 4 show the results for scenario B as the degree of mixing between malnourished and well-nourished
children decreases (as δ moves from 1 to 0). Figure 3 shows
that as the degree of mixing between the malnourished and
well-nourished subgroups decreases, PAFC1 and PAFC2 converge; however, PAFC2 remains in excess of PAFC1 until there
is no mixing between the malnourished and well-nourished
Am J Epidemiol. 2016;183(6):574–582
Incorporating Transmission Into Causal Models 579
1.6
0.5
0.4
1.4
PAF
Rate Ratio
0.3
0.2
1.2
0.1
0
1
1
0.8
0.6
0.4
0.2
0
Degree of Mixing, δ
Figure 3. Estimates of the population attributable fraction (PAF) for
scenario B in 3 childhood infection settings, according to the degree of
mixing between malnourished and well-nourished children. The solid
line shows the conventional PAF estimate (PAFC1), which is the same
for all 3 settings. The broken lines show the PAF calculated directly
from the causal transmission model (PAFC2) for each setting: respiratory syncytial virus in the Philippines (11) (dotted line), rotavirus in
Guinea-Bissau (12) (dashed line), and rotavirus in India (13) (dotteddashed line).
subgroups, at which point PAFC1 = PAFC2. Figure 4 compares
the incidence rate ratio that would be found by a conventional
epidemiologic study (RRC) with the true increase in susceptibility to infection among malnourished children (αM/αW).
Figure 4 demonstrates that at higher levels of mixing, conventional studies will underestimate the true effect, while at lower
levels of mixing, conventional studies will overestimate the
true effect. The degree of underestimation of the true effect is
largest in the India rotavirus model and smallest in the RSV
model.
Figures 5 and 6 show the results for scenario C as the degree
of mixing between malnourished and well-nourished children
decreases. Figure 5 shows that (as with scenario B) in scenario
C, PAFC1 and PAFC2 converge as the degree of mixing decreases, until PAFC1 = PAFC2, when there is no mixing between
malnourished and well-nourished children. Figure 6 demonstrates that for scenario C, RRC remains close to 1 until there are
low levels of mixing between malnourished and well-nourished
children, at which point RRC increases rapidly.
DISCUSSION
These causal transmission models have demonstrated that
conventional epidemiologic methods are unable to detect the
impact of the transmission effects of risk factors. Scenario A
incorporated purely individual-level effects (malnourished
children were neither more susceptible to infection nor more
Am J Epidemiol. 2016;183(6):574–582
1
0.8
0.6
0.4
0.2
0
Degree of Mixing, δ
Figure 4. Comparison of the conventional rate ratio (RRC) with the actual increase in susceptibility to infection among malnourished children
(αM /αW) for scenario B in 3 childhood infection settings, according to the
degree of mixing between malnourished and well-nourished children.
The solid line shows the RRC, which is the same for all 3 settings.
The broken lines show αM /αW for each setting: respiratory syncytial
virus in the Philippines (11) (dotted line), rotavirus in Guinea-Bissau
(12) (dashed line), and rotavirus in India (13) (dotted-dashed line).
infectious). Thus, in this scenario the relative risk from a
conventional epidemiologic study (RRC) could be used to accurately predict the PAF using the conventional formula.
Scenario B incorporated both individual and transmission
effects, and scenario C incorporated purely transmission effects. Thus, in both of these latter scenarios, the total amount
of transmission in the population was increased when malnutrition was present in the population, and removing malnutrition from the population resulted in a larger benefit than
would be predicted by the conventional PAF calculation.
This difference remained substantial even with low degrees
of mixing between the malnourished and well-nourished
subgroups.
While transmission effects occurred in scenarios B and C
in all 3 settings, the impact of these effects differed between
settings. Two factors appear to determine the impact of the
transmission effects: the overall force of infection and the duration of immunity following infection. The mean force of infection was 0.0021 per day in the RSV model, 0.0022 per day
in the Guinea-Bissau rotavirus model, and 0.0044 per day in
the India rotavirus model. In the RSV model the mean duration of immunity following infection was 63 days, while in
the rotavirus models this was 102 days. Settings with a higher
force of infection have a higher incidence of infection, but
they also have a higher prevalence of immune persons; thus,
additional infectiousness has a progressively smaller impact on incidence, and conversely, there is reduced benefit in
580 Paynter
PAF
A)
3
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
PAF
B)
Rate Ratio
Degree of Mixing, δ
0.4
0.2
2
0
1
0.8
0.6
0.4
0.2
0
Degree of Mixing, δ
C)
PAF
0.4
1
0.2
1
0.8
0.6
0.4
0.2
0
Degree of Mixing, δ
0
1
0.8
0.6
0.4
0.2
0
Degree of Mixing, δ
Figure 5. Estimates of the population attributable fraction (PAF) for
scenario C in 3 childhood infection settings, according to the degree of
mixing between malnourished and well-nourished children. The solid
lines denote the conventional PAF estimate (PAFC1) for each setting.
The broken lines denote the PAF calculated directly from the causal
transmission model (PAFC2) for each setting. A) Respiratory syncytial
virus in the Philippines (11); B) rotavirus in Guinea-Bissau (12); C) rotavirus in India (13).
reducing the amount of infectiousness from very high levels.
This mechanism will be exacerbated if the duration of
immunity is longer following infection. The RSV model has
the lowest force of infection (however, in absolute terms this
is still high—most children have been infected by RSV by
their second birthday) and the shorter duration of immunity
following infection, so the impact of transmission effects is
largest in this model (Table 2, Figures 3 and 5).
The causal transmission models have also demonstrated
that conventional epidemiologic methods give biased effect
estimates for risk factors that act at least partially through
transmission effects. Figure 4 shows that in scenario B, conventional studies will tend to underestimate the true effect
(i.e., RRC < αM /αW) when the degree of mixing is high
(because the transmission effects are shared between the malnourished and well-nourished children, reducing the difference in incidence between these groups), and they will tend
to overestimate the true effect (i.e., RRC > αM /αW) when the
degree of mixing is low (because the transmission effects
are confined to the malnourished children, increasing the
difference in incidence between the malnourished and wellnourished groups). The difference between the India rotavirus
model and the Guinea-Bissau rotavirus model in Figure 4
also indicates that if the force of infection is higher, conventional studies will tend to underestimate the true effect more.
Figure 6. Variation in the conventional rate ratio (RRC) in scenario C
in 3 childhood infection settings, according to the degree of mixing between malnourished and well-nourished children. The mean duration
of infection is 1.3 times longer in malnourished children than in wellnourished children in all 3 settings. The broken lines show RRC for
each setting: respiratory syncytial virus in the Philippines (11) (dotted
line), rotavirus in Guinea-Bissau (12) (dashed line), and rotavirus in
India (13) (dotted-dashed line).
Conventional studies examining the RRC for malnutrition
have found inconsistent results (6, 8, 24). One possible explanation for at least part of this inconsistency may be the variation
in the force of infection and the degree of mixing between
study settings. Mathematical modeling may provide a way
of comparing these study results to gain a better estimate of
the underlying true effect, αM /αW (although accurate parameter values for the force of infection and the degree of mixing
would be required).
Figure 6 shows that for moderate-to-high degrees of mixing, the RRC in scenario C was too small to be detected by anything other than the largest of conventional epidemiologic
studies, despite the fact that the increased infectiousness in
malnourished children had a large impact on the risk of infection in the entire population, as seen by the high values of
PAFC2 in Figure 5. The concern here is that risk factors that
act predominantly via increasing infectiousness may be
missed by conventional studies comparing incidence between exposed and unexposed subjects. An example of this
phenomenon could be the effect of vitamin C deficiency/
insufficiency on acute respiratory infections. In a recent
Cochrane review (26), vitamin C supplementation did not appear to reduce the incidence of colds among persons taking
supplements compared with persons not taking them (relative
risk = 0.97, 95%confidenceinterval: 0.94,1.00).However, the
review also found that vitamin C supplementation reduced
the duration of colds in supplemented children by 14%
Am J Epidemiol. 2016;183(6):574–582
Incorporating Transmission Into Causal Models 581
(95% confidence interval: 7, 21). The review’s authors, Hemila
and Chalker, concluded that vitamin C supplementation fails
to reduce the incidence of colds in the general population (26);
however, if we consider the impact of transmission effects as
illustrated in scenario C, it is likely that vitamin C insufficiency,
even in only a subgroup of the population, will influence the
total incidence of colds at the population level, by increasing
the amount of transmission from persons with vitamin C
insufficiency.
The models showed that the impact of transmission effects
is dependent on the level of mixing between exposed and
unexposed children. It is reasonable to assume that there
will be some degree of associative mixing within the different
exposure groups, because children sharing a common environmental exposure are more likely to share socioeconomic
circumstances. Previous studies have demonstrated that social contact patterns can be quantified and incorporated into
transmission models (27, 28). The use of similar methods to
quantify the level of mixing between exposed and unexposed
groups would enable a more accurate interpretation of conventional epidemiologic measures.
The findings from the RSV and rotavirus models may not
necessarily be applicable to all infections. In particular, for infections with a large environmental reservoir (including zoonoses), the infectiousness of humans will have a relatively smaller
impact on ongoing transmission. In addition, the source of infection in both the RSV and rotavirus models is cases with
acute infection (be this symptomatic or asymptomatic). In contrast, many infections (including streptococcal infections, typhoid, and hepatitis B) are spread by chronic carriers. For
these infections, risk factors that increase the acquisition or duration of carriage, or increase pathogen shedding from persons
with carriage, will have an important impact on transmission.
The models presented here have a number of potential limitations. First, the models only incorporate a single risk factor. In reality, a number of risk factors will be present in the
population, and each risk factor that increases transmission
will be responsible for a proportion of the force of infection
acting on the population at baseline (or alternatively, each
risk factor that increases transmission is responsible for a
proportion of the basic reproductive number (R0) in that population). The interplay between these risk factors at the population level will depend on the interaction of multiple risk
factors in the same individual. Second, malnutrition is modeled as a binary variable. In reality, the effect of malnutrition
progressively increases as malnutrition worsens (29). Methods have been developed to include both multiple risk factors
and continuous exposure variables in conventional PAF calculations (30), and similar solutions can be incorporated into
causal transmission models. A third potential limitation is the
simplified model structure. For example, resistance to infection with both RSV and rotavirus increases with age during
early childhood, a phenomenon that has not been incorporated into the model structure (an acceptable simplification,
as the models are not being fitted to age-specific data). In addition, modeling the 3 separate scenarios is somewhat artificial, and in reality all 3 scenarios may occur to some degree.
A fourth limitation is that other mechanisms, not modeled
here, may also contribute to increased transmission in children
with malnutrition. Children with more severe respiratory
Am J Epidemiol. 2016;183(6):574–582
infection may excrete more virus, although this has not
been examined specifically for malnutrition. Conversely,
children with more severe disease may have fewer contacts
than those with milder illness. It is also plausible that malnourished children have shorter incubation periods, which
would also affect transmission. A final limitation is the
requirement to determine parameters from the literature.
While some parameters, such as the duration of infectiousness, are relatively straightforward to estimate from existing
studies, others, such the rate of loss of immunity following
infection (γ), are more difficult to estimate (the method
used to estimate the value of γ for each infection is described
in Web Appendix 1). Inaccuracy in this latter parameter is
particularly problematic, because the model results suggest
that the impact of transmission effects is dependent on the duration of immunity following infection, as well as the force of
infection.
Because of these limitations, the estimates presented here
are best considered approximations of the impact of transmission effects, showing the direction and approximate magnitude
of the biases inherent in using conventional epidemiologic
methods to investigate the causality of infectious disease. More
accurate estimates will require models incorporating new data
from studies directly examining transmission effects and population mixing levels. For the present, however, several practical points of advice can be taken from the model findings (see
text Appendix).
To fully understand infectious disease causality, we need
to understand the dynamics of causality at the population
level. Infectious diseases remain the biggest killer of children
globally, and new infectious threats are emerging or reemerging regularly. Increased efforts are warranted to refine epidemiologic methods to more accurately assess the causality of
infectious diseases and to more accurately measure the disease burden attributable to infectious disease risk factors.
ACKNOWLEDGMENTS
Author affiliations: School of Public Health, University of
Queensland, Brisbane, Queensland, Australia (Stuart Paynter);
and School of Public Health, Curtin University, Perth, Western
Australia, Australia (Stuart Paynter).
Conflict of interest: none declared.
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APPENDIX
Practical Advice From the Model Findings
1. Accurate estimation of the effect and impact of a risk factor on infectious disease incidence requires an understanding of the underlying mechanism of action of the risk
factor and the resulting transmission dynamics.
2. Risk factors that act at least partially through transmission
effects will be responsible for a larger proportion of the
total disease burden than would be estimated using conventional epidemiologic methods.
3. The effect of risk factors that act predominantly via increasing the infectiousness of exposed persons may be
missed by conventional studies comparing incidence between exposed and unexposed subjects.
4. Conventional measures of effect for the same risk factor
can vary from setting to setting, depending on the underlying risk of infection and the degree of mixing between
exposed and unexposed individuals.
Am J Epidemiol. 2016;183(6):574–582