Vaccination Coverage

To construct the Healthcare Access and Quality (HAQ) Index, we first rescaled the log age-standardised risk-standardised death rate by cause to a scale of 0 to 100 such that the highest observed value from 1990 to 2015 was 0 and the lowest was 100. To avoid the effects of fluctuating death rates in small populations on rescaling, we excluded populations less than 1 million population from setting minimum and maximum values. Any location with a cause-specific death rate below the minimum or above the maximum from 1990 to 2015 was set to 100 or 0, respectively.
Because each included cause provided some signal on average levels of personal health-care access and quality, we explored four approaches to construct the HAQ Index: PCA, exploratory factor analysis, arithmetic mean, and geometric mean. Details on these four approaches are in the appendix (pp 7, 8, 21, 22). All four measures were highly correlated, with Spearman's rank order correlations exceeding r_s=0·98. We selected the PCA-derived HAQ Index because it provided the strongest correlations with six other currently available cross-country measures of access to care or health-system inputs (table 2). Three indicators came from the GBD Study 2015: health expenditure per capita, hospital beds per 1000, and the UHC tracer intervention index, a composite measure of 11 UHC tracer interventions (four childhood vaccinations; skilled birth attendance; coverage of at least one and four antenatal care visits; met need for family planning with modern contraception; tuberculosis case detection rates; insecticide-treated net coverage; and antiretroviral therapy coverage for populations living with HIV).⁵⁶ (link) Three indicators came from WHO (physicians, nurses, and midwives per 1000),⁵⁷ the International Labour Organization,⁴⁶ and the World Bank (coverage index based on diphtheria-pertussis-tetanus vaccine coverage, coverage of at least four antenatal care visits, and proportion of children with diarrhoea receiving appropriate treatment).⁴⁵ All indicators had correlation coefficients greater than 0·60, and three exceeded 0·80 (health expenditure per capita, the UHC tracer index, and International Labour Organization formal health coverage).Table 2

Correlations between different constructions of the HAQ Index and existing indicators of health-care access or quality

	Source and year	Geographies represented	HAQ Index construction
			PCA weighted	EFA weighted	Geometric mean	Mean
Health expenditure per capita	GBD 2015	195	0·884	0·880	0·854	0·864
Hospital beds (per 1000)	GBD 2015	195	0·700	0·683	0·625	0·650
UHC tracer index of 11 interventions	GBD 2015	188	0·826	0·820	0·812	0·818
Physicians, nurses, and midwives per 1000	WHO 2010	73	0·769	0·755	0·725	0·732
Proportion of population with formal health coverage	ILO 2010–11	93	0·808	0·798	0·773	0·781
Coverage index of three primary health-care interventions	World Bank 2015	123	0·601	0·589	0·557	0·570

The universal health coverage tracer index of 11 interventions included coverage of four childhood vaccinations (BCG, measles, three doses of diphtheria-pertussis-tetanus, and three doses of polio vaccines); skilled birth attendance; coverage of at least one and four antenatal care visits; met need for family planning with modern contraception; tuberculosis case detection rates; insecticide-treated net coverage; and antiretroviral therapy coverage for populations living with HIV. The World Bank coverage index included coverage of three interventions: three doses of diphtheria-pertussis-tetanus vaccine; at least four antenatal care visits; and children with diarrhoea receiving appropriate treatment. HAQ Index=Healthcare Access and Quality Index. PCA=principal components analysis. EFA=exploratory factor analysis. GBD=Global Burden of Disease. UHC=universal health coverage. ILO=International Labour Organization.

The appendix (pp 21, 22) provides final rescaled PCA weights derived from the first five components that collectively accounted for more than 80% of the variance in cause-specific measures. Colon and breast cancer had negative PCA weights, which implied higher death rates were associated with better access and quality of care; because this cannot be true we set these weights to zero in the final PCA-derived HAQ Index. The appendix (p 15) compares each geography's HAQ Index in 2015 with the log of its age-standardised risk-standardised mortality rates.

Similar to the previous serum banks, a two-stage cluster sampling technique was used to draw a national sample (NS) in NL [1 (link), 2 (link)]. Forty municipalities were sampled within five regions proportional to size (Fig. 1). Within each of these municipalities, an age-stratified sample was drawn from the population register. As life expectancy is increasing, the maximum age in this study was extended from 79 (in the previous surveys) to 89 years, resulting in age strata 0, 1–4, 5–9, …, up to 75–79, 80–89 years of age. A detailed description of the sample size calculations and total number of invitees per study sample can be found in Additional file 1: Table S1. In total, we aimed for 158 participants per municipality, resulting in 6320 participants. Therefore, initially, a sample of in principal 494 individuals per municipality was drawn in the first 11 municipalities, however during the study this was adjusted for the age strata 0–54 years because of lower response rate than expected, which resulted in a total of 818 persons invited in the next 13 municipalities. Finally, in the last 16 municipalities 193 extra men (in total 1011 persons) were invited in the age range of 20–54 year since women responded predominantly. In total 32,244 individuals were planned to receive an invitation in the Dutch national sample.Fig. 1

Overview of the selected municipalities. Municipalities depicted in black are included in the national sample and municipalities in grey are low vaccination coverage areas. * indicate a municipality with oversampling of non-Western migrants, ▲ indicate a municipality with oversampling of non-Western migrants and oversampling of people with migration background from Suriname, Aruba and the former Dutch Antilles. The Caribbean Netherlands sample, taken from the Dutch Caribbean islands Bonaire, St. Eustatius and Saba, are shown at the bottom left

To evaluate whether the predicted level of vaccination coverage required to control rabies (P_crit = 1 – 1/R₀) was sufficient in practice [20 ], we plotted the size of village-level outbreaks (an outbreak was defined as at least two cases not interrupted by an interval of more than one month) against vaccination coverage in that village at the time of the case that initiated the outbreak.
Vaccination coverage was modeled by susceptible reconstruction using demographic parameters described above (we show the results from using the largest estimate of r_dogs (0.10 dogs/y) because this gives the most conservative predictions of the impacts of vaccination, but results are very similar using the lower r_dogs estimates). We assumed coverage was approximately 20% in January 2002 and that the duration of vaccine-induced immunity (1/ν) was approximately 3 y (http://www.intervet.co.uk/Products_Public/Nobivac_Rabies/090_Product_Datasheet.asp). Numbers of vaccinated and susceptible animals within a village were adjusted according to the doses of vaccine used at village vaccination stations on each campaign date (sufficient vaccine was provided such that all animals brought to the station could be vaccinated). A time series of cases in a village and the associated susceptible reconstruction are shown in the inset of Figure 4A.
To predict the expected size of outbreaks given the observed variability in transmission, we simulated outbreaks in a starting population of 500 dogs (similar to the domestic dog population size in an average village); this choice had little effect on our results. We used our parameter estimates (Table 1) to randomly assign secondary cases and corresponding generation intervals. Each realization was seeded by a single animal and the starting population was initialized with vaccination coverage generated from a binomial distribution. For comparison with the outbreak data we conditioned each realization upon >1 secondary case (Figure 4A). Demographic parameters were incorporated, and 10,000 runs were completed for each starting condition. We also calculated the probability of an outbreak of a particular size or larger being seeded by one infectious case to evaluate the coverage needed to prevent outbreaks with different degrees of certainty (Figure 4C and Figure S4).
If V and N denote numbers of vaccinated individuals and the total population size respectively, then vaccination coverage can be expressed as a proportion P = V/N. The number of vaccinated dogs declines following a campaign as individuals die and as vaccine-induced immunity wanes (V_t = V₀e^–(d+ν)t, where d is the death rate and 1/ν is the duration of vaccine-induced immunity), whereas the total population grows at the rate of population increase (N_t = N₀e^rt). To prevent sustained endemic transmission, vaccination coverage must be maintained above P_crit (such that R is held below 1). From our estimates of demographic parameters and R₀, we calculated the proportion of the population that needs to be vaccinated, P_target, to prevent vaccination coverage falling below P_crit during the interval, T, between campaigns: P_target = e^(ν+d+r)TP_crit. This formulation for estimating the coverage needed to interrupt endemic transmission given turnover in the domestic dog population assumes that immunity from vaccination lasts an average of 1/ν time units and declines exponentially. In reality, vaccine-induced immunity is likely to be closer to a fixed duration, and thus fewer dogs would be expected to lose immunity during the 1-y interval between campaigns than under the exponential model. This indicates that our estimate of P_target may be slightly overestimated, although this is an important area for further investigation.