Dynamics of Pertussis Transmission in the United States

F. M. G. Magpantay; P. Rohani


Am J Epidemiol. 2015;181(12):921-931. 

In This Article


Pertussis Incidence Data

Weekly pertussis notifications from the 49 continental states (including Washington, DC) were obtained from the Project Tycho (University of Pittsburgh; http://www.tycho.pitt.edu/) level I database.[19] We used data from the early vaccine era, starting from 1938 and extending to 1955 when available. Missing data near the end of this period resulted in shorter time series for some states (see Web Table 1 http://aje.oxfordjournals.org/content/181/12/921/suppl/DC1, available at http://aje.oxfordjournals.org/). Mississippi, Nevada, North Dakota, South Dakota, and Wyoming were omitted from our analyses due to overrepresentation of missing data in these states, as explained in Web Appendices1–3 http://aje.oxfordjournals.org/content/181/12/921/suppl/DC1. We also obtained monthly pertussis incidence data spanning the years 1951–2010 from the National Notifiable Diseases Surveillance System (NNDSS).

Periodicity Analysis and Classification Into Groups

We characterized the interepidemic period in each state from 1938 to 1955. The dominant period at each time step was determined using the biwavelet package,[25] which computes the bias-corrected wavelet power spectrum.[26] Additional description of the wavelet analysis method is provided in Web Appendix 2 http://aje.oxfordjournals.org/content/181/12/921/suppl/DC1. We noted the state-specific interepidemic period corresponding to the dominant signal in the wavelet decomposition and examined its evolution over time. We detected 4 distinct patterns, which formed the basis for the grouping of states. The estimated timing of any transitions is given in Web Table 2 http://aje.oxfordjournals.org/content/181/12/921/suppl/DC1.

All time-series preprocessing involved 1) square-root transformation of incidence data to stabilize the variance and 2) imputation of missing data using linear interpolation. Linear trends were removed, and each time series was normalized to have a mean value of 0 and a variance of 1. To reduce edge effects, we padded the time series with zeros prior to wavelet decomposition, and the signals from the first and last 3 years of the time period were discarded.

Contrasting Demographic and Epidemiologic Features Across Groups

To provide a mechanistic underpinning for the observed variation in state-specific periodicity, we compiled a set of potentially explanatory characteristics in each state, described in Table 2. Group 4 was not included in this comparison since it contained only 2 states. Many attributes were unavailable for Washington, DC, during the early vaccine era, so it was omitted from the analyses for these characteristics (indicated in Table 2).

We chose possible predictors of periodicity based on epidemiologic theory regarding childhood infectious diseases that are subject to seasonally varying transmission,[27–32] such as pertussis. It has been shown that the periodicity of epidemics is determined by a combination of factors, including the baseline transmission rate, the magnitude of the seasonal variation in transmission, and the birth rate, which modulates the rate of susceptible-pool replenishment.[4,31,33] High transmission and birth rates are predicted to lead to annual epidemics, while lower rates lead to multiennial cycles.[33,34] Seasonality generates annual cycles when its magnitude is small, with these cycles giving way to multiennial oscillations with increasing large-amplitude seasonality.[27,34]

Consequently, we selected household crowding and the fraction of people living in urban environments as potential determinants of transmission. In the absence of information on vaccine uptake during this era, the per capita birth rate remained our only indicator of the rate of recruitment of susceptible persons (susceptibles). The number of children per family was assumed to serve as an indicator of both susceptible recruitment and transmission within households. In states where multiennial epidemics, rather than annual outbreaks, were observed, we expected the fraction of families with no children to be higher and conversely the fraction with more than 1 child to be lower. Additionally, school attendance was considered as a potential indicator of both transmission between children and the amplitude of seasonality.

Historical per capita health spending was selected as a possible correlate for vaccine uptake during the early vaccine era. The other demographic characteristics that we considered were the mean population size, variation in population size, and variation in the birth rate. We also considered the latitude of the population centroid of each state and epidemiologic quantities such as the mean incidence and timing of seasonal peaks, quantified by the residual phase. The residual phase was calculated by extracting the phase from the wavelet decomposition and then subtracting the mean phase over all of the time series.[35] This reflects the relative timing of the peak in each state as compared with the average timing of the peaks across the country.

In order to examine whether historical patterns may have influenced recent pertussis epidemiology, we compiled summary features of pertussis incidence using the 1951–2010 NNDSS records. To characterize pertussis resurgence, we carried out segmented or piecewise linear regression analysis, wherein the independent variable (time) was partitioned into intervals joined at an unknown but estimated breakpoint, with independent slopes fitted to each interval (further details are available in Web Appendix 4 and Web Figure 1 http://aje.oxfordjournals.org/content/181/12/921/suppl/DC1). Therefore, for each state, pertussis incidence could be separated into 2 intervals separated by a state-specific turning point, or breakpoint. This breakpoint was used as an indicator of the onset of resurgence in a given state and the associated slope of the subsequent linear regression as an indicator of its speed. We also calculated mean monthly incidence of pertussis per 100,000 people for each state from 2001 to 2010.

Analysis of variance (ANOVA) and the Kruskal-Wallis test were used to compare the values of the characteristics across groups. The differences in the underlying assumptions and implications of these 2 tests are discussed further in Web Appendix 5 http://aje.oxfordjournals.org/content/181/12/921/suppl/DC1. To compare the residual phases of the annual outbreak periods, we used the circular versions of these tests. The mean values for each characteristic in each group are presented in Web Tables 3 and 4 http://aje.oxfordjournals.org/content/181/12/921/suppl/DC1.