Impact and effectiveness of a conjugate vaccine against invasive pneumococcal disease in Finland - a modelling approach

Figures & data

Figure 1. The proportion of vaccine-type (VT) carriage of all carriage acquisition over time since vaccine introduction. Functions $f\left(t\right)$ and $\left(1-V{E}_{col}\right)f\left(t\right)$ show the proportions of vaccine-type acquisition in the unvaccinated and vaccinated children, respectively. The scenario shown here corresponds to the observation in Finland. The initial proportion of VT carriage of all carriage among unvaccinated children at time $t=0$ is $f\left(0\right)=60\mathrm{\%}$ and decreases to $0\mathrm{\%}$ in about 70 months. The vaccine efficacy is $V{E}_{col}=50\mathrm{\%}$

Table 1. Per capita rates of carriage acquisition at time $t$ after vaccine introduction per serotype category and vaccination status. $C$ is the per capita rate of carriage acquisition, $f(t)$ is the proportion of VT carriage acquisition of all carriage, and $V{E}_{col}$ is the vaccine efficacy against carriage acquisition. Because of complete replacement in carriage, the rates of VT and NVT carriage acquisition sum up to $C$ in all three columns of the table

	Pre-vaccination period	Post-introduction period
Serotype group	Rate of acquisition	Rate of acquisition in vaccinated (proportion P)	Rate of acquisition in unvaccinated (proportion 1-P)
VT	$f\left(0\right)C$	$f\left(t\right)\left(1-V{E}_{col}\right)C$	$f\left(t\right)C$
NVT	$\left(1-f\left(0\right)\right)C$	$\left(1-f\left(t\right)\left(1-V{E}_{col}\right)\right)C$	$\left(1-f\left(t\right)\right)C$

Table 2. Per capita rates of IPD at time $t$ after vaccine introduction per serotype category and vaccination status. $IP{D}_0$ is the rate of IPD before vaccine introduction and $V{E}_{inv}$ is the vaccine efficacy against progression to disease

	Pre-vaccination period	Post-introduction period
Serotype group	Rate of IPD	Rate of IPD in vaccinated (proportion P)	Rate of IPD in unvaccinated (proportion 1-P)
VT	$IP{D}_0^{VT}$	$\frac{f\left(t\right)}{f\left(0\right)}\left(1-V{E}_{col}\right)\left(1-V{E}_{inv}\right)IP{D}_0^{VT}$	$\frac{f\left(t\right)}{f\left(0\right)}IP{D}_0^{VT}$
NVT	$IP{D}_0^{NVT}$	$\frac{1-f\left(t\right)\left(1-V{E}_{col}\right)}{1-f\left(0\right)}IP{D}_0^{NVT}$	$\frac{1-f\left(t\right)}{1-f\left(0\right)}IP{D}_0^{NVT}$

Table 3. The total and indirect impact of a vaccination program against VT, NVT, and all IPD in a before-after study setting

Serotype group	Total impact in vaccinated (proportion P)	Indirect impact in unvaccinated (proportion 1-P)
VT	$V{I}_{tot}^{VT}=1-\frac{f\left(t\right)}{f\left(0\right)}\left(1-V{E}_{col}\right)\left(1-V{E}_{inv}\right)$	$V{I}_{ind}^{VT}=\frac{f\left(t\right)}{f\left(0\right)}IP{D}_0^{VT}$
NVT	$V{I}_{tot}^{NVT}=1-\frac{1-f\left(t\right)\left(1-V{E}_{col}\right)}{1-f\left(0\right)}$	$V{I}_{ind}^{NVT}=\frac{1-f\left(t\right)}{1-f\left(0\right)}IP{D}_0^{NVT}$
All IPD	$V{I}_{tot}^{allIPD}=1-\frac{\left(1-V{I}_{tot}^{VT}\right)IP{D}_0^{VT}+\left(1-V{I}_{tot}^{NVT}\right)IP{D}_0^{NVT}}{IP{D}_0^{VT}+IP{D}_0^{NVT}}$	$V{I}_{ind}^{allIPD}=1-\frac{\left(1-V{I}_{ind}^{VT}\right)IP{D}_0^{VT}+\left(1-V{I}_{ind}^{NVT}\right)IP{D}_0^{NVT}}{IP{D}_0^{VT}+IP{D}_0^{NVT}}$

Table 4. Vaccine effectiveness against VT, NVT, and all IPD in a parallel study setting

Serotype group	Vaccine effectiveness in vaccinated
VT	$V{E}^{VT}=1-\left(1-V{E}_{col}\right)\left(1-V{E}_{inv}\right)$
NVT	$V{E}^{NVT}=1-\frac{1-f\left(t\right)\left(1-V{E}_{col}\right)}{1-f\left(t\right)}$
All IPD	$V{E}^{allIPD}=1-\frac{\frac{f\left(t\right)}{f\left(0\right)}\left(1-V{E}^{VT}\right)IP{D}_0^{VT}+\frac{1-f\left(t\right)}{1-f\left(0\right)}\left(1-V{E}^{NVT}\right)IP{D}_0^{NVT}}{\frac{f\left(t\right)}{f\left(0\right)}IP{D}_0^{VT}+\frac{1-f\left(t\right)}{1-f\left(0\right)}\left(1-V{E}^{NVT}\right)IP{D}_0^{NVT}}$

Figure 2. Vaccine effectiveness and total and indirect impact as function of time since vaccination onset. Parameter values: $V{E}_{col}=50\mathrm{\%}$, $V{E}_{inv}=50/90\mathrm{\%}$, $f\left(0\right)=60\mathrm{\%}$ and the initial fraction of NVT IPD out of all IPD is $20\mathrm{\%}$. VT carriage decreases to $0\mathrm{\%}$ in about 70 months. (a) Total impact (solid line) and effectiveness (dashed line) against VT; (b) total impact (solid line) and effectiveness (dashed line) against NVT; (c) total impact (solid line) and effectiveness (dashed line) against all IPD; (d) indirect impact against VT; (e) indirect impact against NVT; (f) indirect impact against all IPD

Figure 3. Overall impact against VT, NVT and all IPD as function of time since vaccination onset. Parameter values: proportion vaccinated $P=50/90\mathrm{\%}$, $V{E}_{col}=50\mathrm{\%}$, $V{E}_{inv}=90\mathrm{\%}$, $f\left(0\right)=60\mathrm{\%}$ and the initial fraction of NVT IPD out of all IPD is $20\mathrm{\%}$. VT carriage decreases to 0% in about 70 months

Figure 4. IPD cases and their vaccination status in the target cohort of PCV10 eligible children (years 2010–2016) and in the reference cohort (years 2004–2008) in Finland

Figure 5. Overall impact against PCV10, PCV10-related and serotype 19A IPD among vaccine-eligible children in Finland in years 2012–2016

Table 5. Effectiveness of PCV10 vaccination in the PCV10-eligible target cohort (2010–2016), and the impact of PCV10 vaccination based on the comparison of the target cohort with a reference cohort (2002–2008), Finland

Finland	Unvaccinated		Vaccinated		Estimate (%)	95% credible interval
Vaccine effectiveness	Cases	Follow-up years	Cases	Follow-up years
PCV10 IPD	7	69664	7	894817	92.2	(77.3, 97.3)
Non-PCV10 IPD	7	69664	65	894817	27.7	(−73.3, 64.4)
-PCV10-related IPD	5	69664	35	894817	45.5	(−58.8, 76.6)
-Non-PCV10-related IPD	2	69664	30	894817	−16.8	(−622.0, 64.7)
All IPD	14	69664	72	894817	60.0	(26.0, 76.7)
Vaccine impact	Cases in reference cohort	Follow-up years	Cases in target cohort	Follow-up years
Total impact
PCV10 IPD	342	1115954	7	894817	97.4	(94.9, 98.9)
Non-PCV10 IPD	82	1115954	65	894817	1.2	(−36.7, 28.8)
-PCV10-related IPD	61	1115954	35	894817	28.4	(−7.8, 53.1)
-Non-PCV10-related IPD	21	1115954	30	894817	−78.2	(−213.7, −2.3)
All IPD	424	1115954	72	894817	78.8	(73.0, 83.6)
Indirect impact
PCV10 IPD	342	1115954	7	69664	67.2	(34.7, 85.5)
Non-PCV10 IPD	82	1115954	7	69664	−36.7	(−179.2, 40.7)
-PCV10-related IPD	61	1115954	5	69664	−31.3	(−202.5, 51.4)
-Non-PCV10-related IPD	21	1115954	2	69664	−52.5	(−450.6, 69.7)
All IPD	424	1115954	14	69664	47.0	(12.8, 70.0)
Overall impact
PCV10 IPD	342	1115954	14	964481	95.3	(92.2, 97.3)
Non-PCV10 IPD	82	1115954	72	964481	−1.6	(−39.3, 26.1)
-PCV10-related IPD	61	1115954	40	964481	24.1	(−12.6, 49.4)
-Non-PCV10-related IPD	21	1115954	32	964481	−76.3	(−208.6, −2.5)
All IPD	424	1115954	86	964481	76.5	(70.5, 81.5)