The bridge coding method is used when there is a major change in the coding process (ICD version change or switch from a manual to an automatic coding system). The method consists of coding a large set of death certificates twice, applying the rules prevailing before and after the change. The ratios of numbers of death calculated by cause category before and after the change, called "comparability ratios," generate information for trend analyses and characterization of "jumps" in mortality time series. However, analyses of long-period time series do not necessarily use comparability ratios 1 6 .

Bridge coding analyses have been carried out in the United States and England and Wales for each ICD change since the eighth version of the ICD (ICD-8) 7 8 9 10 11 12 . Bridge coding analysis was also used and generated detailed results for the change from ICD-9 to ICD-10 in some countries (Scotland, Sweden, Italy, Spain, France, and Canada) 13 14 15 16 17 18 . However, to the authors' knowledge, most European countries have not implemented bridge coding to assess ICD changes. Comparability ratios are heterogeneous between country, most likely because of variations in intra-group composition of causes of death, reporting practices, and ICD coding interpretation. Therefore, it is unlikely that a comparability ratio for one country can be inferred from the results of other countries.

The concordance table and cause recombination approach consists of determining the most consistent cause categories, under medical consideration, for two successive ICD revisions. Analysis of mortality using the resulting categories is then theoretically influenced little by coding changes. This approach typically only works well when considering the coding of any particular cause reported on the death certificate. It is often not effective when considering changes in the rules for selecting the underlying cause of death, especially when such rule changes favor the selection of one cause over another. It is often impossible to recombine codes to fully account for these changes.

The method was used on French, Dutch, and Swedish data 19 20 21 . This approach, complex and time-consuming when it is applied to a single country, is even more difficult to use in the context of an international study 22 .

The time series analysis method consists of looking for sustainable jumps, evaluating their statistical significance and amplitude, and possibly smoothing the time series by adjusting the data with correction factors. The method is easy to document, even when the volume of data considered is large (many countries, many causes of death, etc.). Furthermore, the method is necessary when the time of the change in the data production process is unknown 23 . To the authors' knowledge, the detection of jumps in mortality data has rarely been undertaken 22 24 , but, in particular for Janssen et al's work 22 , has given rise to fruitful international public health studies 25 26 27 28 . However, the methods used in these studies did not take advantage of the recent development of automated jump detection methods in indexed data analysis (by time or other variables) 29 30 31 . Interest in the automatic jump detection method resides in its ability to avoid the subjectivity of visual detection or a priori selection of jump positions.

The aim of this paper is to propose a complement to a time series analysis method that was previously developed by Janssen et al. 22 , allowing detection of sustainable jumps attributable to changes in data production and development of correction factors by age and gender in order to enable subsequent epidemiological analyses. The method is then applied to a wide range of different mortality time series: 13 causes of death for each of six European countries participating in the AMIEHS (Avoidable Mortality in the European Union, toward better Indicators for the Effectiveness of Health Systems) project http://amiehs.lshtm.ac.uk/.

The following step-by-step approach was adopted:

1. Given a list of selected causes of death, the ICD codes to be considered were determined by nosologists based on the correspondence table method, while maintaining the medical consistency of the list of codes for the various ICD revisions.

2. An automated jump detection method was applied to the mortality rate time series for each of the selected causes of death.

3. For documented jumps (e.g., ICD changes), the available comparability ratios were compared to the amplitude of the estimated jumps. For nondocumented jumps, general information feedback was requested from the national data producers.

4. For documented or plausible jump positions, the statistical significance of the between-age and between-gender jump amplitude heterogeneity was evaluated by means of a regression model, and correction factors were deduced from the results.

The mortality data were derived from the AMIEHS project dataset. Six countries were included in the analysis: Spain, France, the Netherlands, Germany, Sweden, and England and Wales (considered together). In order to simplify presentation, Estonia, which is participating in the AMIEHS project, has not been considered in this paper because Estonia used a specific coding system until 1994. The study period is 1970 to 2005. While causes of death are usually coded with four-digit ICD codes, the AMIEHS dataset only contains three-digit codes for practical reasons. Some precision in the characterization of causes has thus been lost.

Generally, deaths are coded using the same ICD revision in each calendar year. The dates of the ICD revisions used by each European country are presented in table 1.

For 13 causes of death selected in the AMIEHS project, the method of allocating the ICD-8, ICD-9, and ICD-10 codes was as follows:

• When the cause was included in the Eurostat 65 causes shortlist 32 , the codes defined by Eurostat were retained.

• For other causes, two nosologists independently selected the optimal three-digit codes. Then, a final choice was made in order to minimize the coding-related jumps in cause of death-specific time series analysis. Table 2 shows the related codes.

The Polydect method 33 was applied to yearly log mortality rate time series for each country and cause of death.

Given that mortality analyses are often based on multiplicative assumptions, log-linear generalized models were used. Thus, the time series jump detection method was applied to the log mortality rates.

Let O_t, be the number of deaths during year t, p_t be the number of person-years, and L t = log O t p t be the log mortality rate time series. The occurrence of jumps in the log mortality rate time series may be expressed as follows:

log E ( O t ) = log ( p t ) + g ( t ) + ∑ t’ ∈ S d t’ ⋅ 1 ( t > t’ ) ,

In which g is a continuous function, S is the set of jump locations, and {d_t,t ∈ S} are the corresponding jump magnitudes.

In this model, g, S, and {d_t, t ∈ S} are all assumed unknown.

The method consists of three main steps:

1. A left and right limit of E(L_t) were estimated for each point t using two local polynomial smoothers, denoted P_l(t) and P_r(t), fitted on [t - h, t) and (t, t + h], respectively, where h is the bandwidth for the estimation to be estimated in further steps. If t ∉ S, and the jumps location are distant from at least h, then, given that g is continuous, we expect E(P₁(t)) = E(P_r(t)) = g(t). Else, if t ∈ S, we expect E(P₁(t)) = g(t) and E(P_r(t)) = g(t)+d_t.

The noise σof the L_t process is estimated as:

σ ^ = ∑ t min L t - P l ( t ) 2 , L t - P r ( t ) 2 T - 1

The polynomial kernel of the smoothers could, a priori, be constant, linear, or quadratic, depending on the number of observations and the curvature level of the time series. Since, in the present case, the number of observations was not greater than 40, and the time series was expected to be quite stable, a linear kernel was selected.

2. Considering M(t) = P_r(t)-P₁(t), jump points were defined as points where the signal-to-noise ratio M ( t ) σ ^ was higher than a threshold C _α.

C _α was chosen such that, if t is not a jump point, P M ( t ) σ ^ > C α ≤ α . The analytic calculation of C _α is given elsewhere 33 . In the following steps, α was set to 10^-5, a low value, in order to avoid as many as possible false positive jumps.

Then, S = t : M ( t ) σ ^ > C α and d ^ t = M ( t ) , t ∈ S ^ were directly estimated. When several jumps were detected in a time range less than the bandwidth, only the jump that maximized M(t) was retained.

3. The bandwidth h was estimated by minimizing the Hausdorff distance 29 , defined as:

d H ( S , S ^ ; h ) = max sup t 1 ∈ S ^   inf t 2 ∈ S ^ t 1 - t 2 , inf t 1 ∈ S ^   sup t 2 ∈ S ^ t 1 - t 2 ,

in which d H ( S , S ^ ; h ) was calculated through a bootstrap procedure, setting B, the number of batches used, equal to 1000. A full description of this method is given elsewhere 33 .

For a given jump i, the multiplicative factor MF_i between before and after the jump period was calculated as:

M F i = exp d i ,

in which d_i is the amplitude of the jump.

Age categories were defined as the tertile of the cause-specific death counts.

Generally, when considering J different population groups (age and gender), a generalized additive model (GAM) with an overdispersed Poisson distribution is used 34 35 . The model has the following form:

log E O t,j = log p t,j + g j ( t ) + ∑ t’ ∈ S d t’,j ⋅ 1 ( t > t’ ) ,

in which j is one of the J groups, g_j are continuous functions fitted by a thin plate penalized regression spline, S is the set of jump locations, and {d_t,j, t ∉ S} are the corresponding jump magnitudes for group j.

S is supposed known, and the aim is to test for each t ∈ S:

H0: d t , 1 = ⋯ = d t,J

Backward variable selection was used to suppress, successively, age and gender from the model if their respective effects on the jump amplitude were not statistically significant at the 5% level, using Wald's test.

The MGCV (Multiple smoothing parameter estimation by Generalized Cross Validation) R package was used for this purpose 36 .

Correction factors were calculated for all confirmed jumps.

The correction factors were calculated for use in subsequent analyses, not discussed in this article, with a log-linear model of general form:

log E ( O t ) = log ( p t ) + c t + f ( X t ) ,

in which t is the year between T₁ and T₂ (respectively equal to 1970 and 2005 in this study); c_t is the correction factor and f(X_t) could be any function of independent variables to be estimated.

The correction factors were set so that the last values of the corrected mortality rates were equal to the exact mortality rates, i.e., c T 2 = 0 . This choice was based on the supposed superior quality and between-country comparability of the most recent year's data.

The foregoing results in the following definition of the correction factors c_t:

For t ∈ [T₁, T₂],

c t = ∑ t’ ∈ S , t’ < t d t’ - ∑ t’ ∈ S d t’ = - ∑ t’ ∈ S , t’ ≥ t d t’ .

The estimate of c_t was then directly obtained from the estimates of S and d_t detailed earlier.

A corrected version of the log mortality rate was then obtained as:

L t cor = L t - c t

By applying the jump detection method to all of the time series, a set of jumps was obtained (table 3). Most of the jumps detected were concomitant with a known coding change (ICD updates or change from a manual to an automatic coding system). Some of the jumps (e.g., for heart failure and rheumatic heart disease) were of great amplitude and almost systematically observed in each country. For the former East Germany, most of the changes were concomitant with the reunification of Germany.

The answers from data producers, contacted to determine whether the jump was related to a data production issue, were consistent between countries. Most (excluding the "No answer," 42 out of 44) of the detected jumps were confirmed to be related to a coding change. The three-digit coding constraint was given as an explanation for some jumps (rheumatic heart disease in France, ischemic heart disease in Spain, etc.), especially when countries chose specific codes (as in Spain for malignant colorectal neoplasm). The 1990 and 1991 jumps in East Germany were related to a complete change of coding staff. However, most of the coding changes are not documented by a literature reference.

Given the large proportion of confirmed jumps, we decided to exclude from subsequent treatment the jumps for which we received a negative answer from data producers.

It was possible to compare a few of the multiplicative factors with the comparative ratios generated by bridge coding studies corresponding to ICD-9 to ICD-10 changes (table 4). In particular, the large multiplicative factors (e.g., for rheumatic heart disease) had no related comparative ratios. Some coding changes were not detected by the jump detection method (Hodgkin's disease in England and Wales and Sweden and renal failure in England and Wales). However, none of the detected jumps were found unrelated to a coding change.

Considering some of the most clear-cut time series, the profile of the corrected time series is quite different from that of the uncorrected series (Figure 1). It is noteworthy that the corrected curves do not reduce the general trends at the jump positions, which would have been the case if constant rather than linear kernel smoothing was chosen. Rather, they prolong the trends, even if the jump is in the opposite direction of the general trend.

Concerning hypertension in the Netherlands, we observe a trend shift between the periods before and after the corrected jumps. Such trend shift is not taken into account by the current method.

With regard to the jump amplitude heterogeneity test by age and gender, only 19 out of 47 jumps were not statistically significantly heterogeneous (table 5). Five of the jumps were heterogeneous by gender, 15 by age, and eight by age and gender simultaneously. While the jump amplitudes are of the same order by gender, even when statistically heterogeneous, they are of different orders when considered by age group. This was particularly marked for rheumatic heart disease and heart failure.