Variation in pneumococcal invasiveness metrics is driven by serotype carriage duration and initial risk of disease

Abstract

Streptococcus pneumoniae is an opportunistic pathogen that, while usually carried asymptomatically, can cause severe invasive diseases like meningitis and bacteremic pneumonia. A central goal in S. pneumoniae public health management is to identify which serotypes (immunologically distinct strains) pose the most risk of invasive disease. The most common invasiveness metrics use cross-sectional data (i.e., invasive odds ratios (IOR)), or longitudinal data (i.e., attack rates (AR)). To assess the reliability of these metrics we developed an epidemiological model of carriage and invasive disease. Our mathematical analyses illustrate qualitative failures with the IOR metric (e.g., IOR can decline with increasing invasiveness parameters). Fitting the model to both longitudinal and cross-sectional data, our analysis supports previous work indicating that invasion risk is maximal at or near time of colonization. This pattern of early invasive disease risk leads to substantial (up to 5-fold) biases when estimating underlying differences in invasiveness from IOR metrics, due to the impact of carriage duration on IOR. Together, these results raise serious concerns with the IOR metric as a basis for public health decision-making and lend support for multiple alternate metrics including AR.

Keywords: Carriage duration; Compartmental model; Invasive disease; Streptococcus pneumoniae; Virulence.

Fig. 1.

Schematic diagram of the epidemiological model. Boxes represent proportions of hosts in mutually exclusive states: susceptible (S), infected asymptomatic carriers (C), invasive (I) or recovered and immune (R). Solid arrows represent flows of individuals between states, and dashed arrows represent factors influencing those flows. Equations describing the system are presented in Materials and Methods (methods Eq. 1), along with parameter definitions (Table 1). Note there are two paths from S to I, a direct path governed by the probability of initial invasion p, and an indirect path governed by 1-p (probability of initial transition to carriage state) and by the rate d of invasive disease progression from a carriage state.

Fig. 2.

Attack rate reliably captures underlying pneumococcal invasiveness parameters while invasive odds ratios fail. (A) Attack rate $(\mathrm{A}\mathrm{R}=\frac{d\tau +p}{(1-p)(d\tau +1)})$ has a positive relationship with both $p$ and d invasive parameters indicating it accurately represents pneumococcal invasiveness. (B), Invasive odds ratios $\mathrm{I}\mathrm{O}\mathrm{R}=\frac{{\tau }_0(d\tau +p)}{\tau \left(d{\tau }_0+p\right)}$ calculated with a low reference carriage duration $\left({\tau }_0=5\right.$ fails to capture increasing initial invasive progression $\left(p\right)$. (C) Alternatively, IOR fails to capture increasing constant invasive progression $\left(d\right)$ when a high carriage duration is used as a reference serotype $\left({\tau }_0=20\right)$.

Fig. 3.

Both cross-sectional and longitudinal epidemiological data support the initial risk model and highlight that IOR is confounded by carriage duration. (A) IOR data (blue dots, Brueggemann et al. (Brueggemann et al., 2004)) and model fit (orange line, ${\tau }_0/\tau$), against carriage duration $\left(\tau \right)$. (B) AR data (blue dots, Sleeman et al. (Sleeman et al., 2006)) and model fit (orange line, $p(1-p)$), against carriage duration $\left(\tau \right)$. Simultaneously fitting equations [2] to both datasets (A, B) produced parameter estimates $p=2.9\times {10}^{-4}$ and $d=0$ (i.e., invasive disease risk at point of colonization only). Serotype 14 was used as the reference for IOR calculations. IOR and AR data from serotypes 5, 1, 8, 7 F, 4, 38, 18 C, 3, 33 F, 14, 15B/C, 6 A, 23 F, 6B were used in the model fitting (Table S1).

Fig. 4.

Incorporating additional epidemiological data also provides support for the initial risk model. (A), Carriage prevalence data (blue dots, Brueggemann et al. (Brueggemann et al., 2004)) and model fit (orange line, $\frac{fh\left(b\right(p-1)\tau +1)}{b\left(h\right(f(p-1)\tau -1)-fp)}$), against carriage duration ($\tau$). (B) Incidence of acquisition data (blue dots, Sleeman et al. (Sleeman et al., 2006)) and model fit (orange line, $\frac{fh\left(b\right(p-1)\tau +1)}{b\tau \left(h\right(f(p-1)\tau -1)-fp)}$) against carriage duration ($\tau$). (C), Invasive incidence data (blue dots, Sleeman et al. (Sleeman et al., 2006)) and model fit (orange line, $\frac{fhp\left(b\right(p-1)\tau +1)}{b(p-1)\tau \left(fh\right(\tau -p\tau )+fp+h)}$), against carriage duration $\left(\tau \right)$. Simultaneously fitting endemic equilibrium equations (see SI) to data in Figs. 3A, B and 4A–C produced parameter estimates $p=2.9\times {10}^{-4},d=0,\beta =0.24$, and $f=3.1\times {10}^{-3}$ (i.e., invasive disease risk at point of colonization only). Epidemiological data from serotypes 5, 1, 8, 7 F, 4, 38, 18 C, 3, 33 F, 14, 15B/C, 6 A, 23 F, 6B were used in the model fitting (Table S1).