Results

FROM FLAGGING ARCHIVE TO CASE ARCHIVE

Patients were flagged from the self help volunteering groups (97 patients of whom 74 from Alcoholics Anonymous and 23 from CAT), from the Psychiatric Ambulatory (75), from the Public Alcohology Service (36) and from hospital discharge list (173). Primary or secondary diagnoses reported on hospital discharge records were: alcoholic psychoses (8 inpatients), alcohol dependence syndrome (45), non-dependent abuse of alcohol (40), alcoholic polyneuropathy (11), alcoholic fatty liver (7), acute alcoholic hepatitis (28), alcoholic cirrhosis of the liver (39), and unspecified alcoholic liver damage (4).

Among the 381 flagged records, an archive of cases of 349 patients was constructed, with an average per patient flagging frequency of 1.09. There were 281 men and mean age was 51.7 years (SD = 15.4).

Data from prevalent cases organised according to source of flagging are shown in table 1. Among the 349 patients, 322 were flagged from one source, 23 from two sources, three from three sources and one from all the considered sources. Corresponding frequencies were 257, 21, 2 and 1 and 65, 2, 1 and 0 in men and women respectively, so that the 8.5% of men but only the 4.4% of women were flagged by more than one source. By stratifying the patients in two age classes (< 50 and ⩾ 50 years), 147, 13, 3 and 1 (younger) and 175, 10, 0 and 0 (older) were flagged by one, two, three and four sources respectively, so that the 10.4% of the younger but only the 5.4% of the older patients were flagged by more than one source.

Although men were flagged with major frequency with respect to women (80.5% v 19.5%), relevant differences among sources in the proportion of captured men were not observed (81.4%, 77.3%, 81.0% and 82.6% of men listed by F1, F2, F3 and F4, respectively). By using the capture-recapture terminology, we may therefore deduce a homogeneous catchability of sources among gender. Conversely, younger and older subjects were flagged with about the same frequency (50.4% v 49.6%). This is an effect of the design, as the age classes were chosen with the aim to obtain balanced categories. However, relevant differences among sources in the proportion of captured younger subjects were in this case observed (45.3%, 65.3%, 81.0% and 40.4% of younger patients listed by F1, F2, F3 and F4, respectively). We may therefore deduce a heterogeneous catchability of sources among the considered age classes.

TWO SAMPLE CAPTURE-RECAPTURE ESTIMATES

Table 2 shows the estimated numbers of patients with ARP by applying the two sample capture-recapture approach to all the possible combinations of two source of ascertainment. Only one of the six estimates was lower than the aggregate prevalent count (349) suggesting a positive dependence between F2 (psychiatric ambulatory list) and F3 (public alcohology service list). Conversely, the highest prevalent count (2.841) suggests a negative dependence between F1 (self help groups list) and F4 (hospital discharges list).

LOG-LINEAR MODEL BASED ESTIMATES

Table 3 shows the estimated prevalent count of subjects with ARP resulting from several log-linear models. The first model that entailed only the main effects of the four sources did not fit the data (tabulated χ² _0.05;10 = 18.3). Conversely, models 2–5 (that considered also any interaction terms) had lower residual deviance and showed significant goodness of fit (tabulated χ² _0.05;9 = 16.9; χ² _0.05;8 = 15.5; χ² _0.05;7 = 14.1). In particular, the model 3 that considered two first order interaction terms (F2*F3 and F3*F4) showed a significant improvement of the goodness of fit with respect to the model 2 that considered only one first order interaction term (LRT: D₂-D₃ = 6.38 with 1 df, p < 0.05). Adding to the model 3, one first (F1*F4: fourth model) or second (F2*F3*F4: fifty model) order interaction term, significant improvements of the goodness of fit were not obtained (D₃-D₄ = 1.51 with 1 df, p > 0.05; LRT: D₃-D₅ = 1.37 with 1 df, p > 0.05). Thus, choosing the more parsimonious model (model 3) an estimate of about 2300 patients with ARP was forecast in the target population. As this estimate is much higher with respect to that obtained from the main effects model (2297 v1492), a positive dependence between F2 (psychiatric ambulatory list) and F3 (public alcohology service list), and between F3 and F4 (hospital discharges list) may be deduced.

Table 4 shows the estimates of prevalent count based on models that include interaction terms involved the adjustment of estimates for dependence among sources and/or for heterogeneity among gender or age. From the first three models, as well as from model 1 of table 3, the same estimate of prevalent count was obtained. This is explained by the absence of interaction terms in the four compared models. An improvement of the goodness of fit were obtained adding to the model 1 the term of the main effect of gender (D₁-D₂ = 139.6 with 1 df, p < 0.05). This simply indicates a significant difference between the number of flagged men and women. It should be noticed, however, that no terms involving the interaction between gender and one or more capture occasions were selected. Conversely, age did not show a main effect (D₁-D₃ = 1.3 with 1 df, p > 0.05), but a significant tendency of both, F2 and F3 to cover different age classes (D₁-D₄ = 12.3 with 2 df, p < 0.05) was observed. These results suggest, as already noticed as comment to table 1, that the considered age classes, but not gender, were responsible for heterogeneous catchability among sources. Models 1–4, however, did not fit the data (tabulated χ² _0.05;55 = 73.3; χ² _0.05;54 = 72.2; and χ² _0.05;53 = 71.0). Conversely, model 5 that entailed either main effects, dependencies and heterogeneity, showed a significant goodness of fit (tabulated χ² _0.05;49 = 66.3). On the basis of this model, an estimate of about 2500 patients with ARP was forecast in the target population.

Discussion

The results provide the first estimate of the size of ARP in a general population based on capture-recapture methodology. Although 349 persons of the target population were captured from the four local sources because they were attending or receiving care and assistance during 1997, we estimated that the number of persons with ARP was about 2500 with a prevalence of 19 every 1000 inhabitants aged more than 15 years.

It is not possible to compare these estimates with those of other studies directly. However, a 11.6 % prevalence of positive answers to one or more questions of the CAGE questionnaire has been recently reported38 in the Italian population.39Literature reports that CAGE scale, when used with one or more positive answers, achieves a sensitivity of 86% and specificity of 93% in detecting ARP.40 By applying these values at the observed prevalence of positive to the questionnaire, a true prevalence of alcohol related disorders of 5.8% is expected. These considerations suggest that the administration of a validated instrument of screening to a sample of population is an inconsistent way to size ARP in a target population.

This study shows another, but not alternative, approach to size ARP based on capture-recapture methods. Routinely collected incomplete lists are easily available and multiple lists with variable degree of completeness (hospital discharges, alcoholic and psychiatric services, self help associations, etc) can be obtained cheaply in most geographical areas. After record linkage of all available lists, the methods described in this paper can be easily applied at a very low cost by researchers and the public health administration.19

A number of methodological issues that are potential limitations to the capture-recapture methodology should be however considered.

The most important problem is the difficulty of delimiting appropriately the population under study.

Because of our strict definition of case, our estimates referred to alcoholics who seek or need treatment, so that only agencies deputed to the treatment of alcoholics were considered in this study. Agency lists include people with problems related to more severe forms of alcohol related disorders.21 This necessarily leads to underestimate the size of ARP in the target population and might explain the lower prevalence obtained by applying the capture-recapture methodology with respect to that obtained from the CAGE administration (see above).

In almost all the epidemiological applications, capture-recapture methods point out the estimate of the total population actually affected by a disease or condition. In the current application, we captured also subjects characterised by problematic use of alcohol in the past, but actually abstainers. For example, several people who have not drunk for many years attend self help groups or alcoholic services with the aim to receive assistance in maintaining abstinence. Analogously, long term alcohol related diseases (for example, alcoholic cirrhosis) may be acquired because of heavy drinking pattern in the past but with patients actually abstainers. Also for these people, however, the abstinence keeping is required to avoid the disease worsening. Thus, in the field of the ARP, it is very important to count all the subjects who need treatment and assistance to achieve or to keep abstinence from alcohol, independently by their current alcoholic behaviour.

As Hook and Regal41 discussed, a major limitation of the capture-recapture methods is that, in virtually all the epidemiological applications, you cannot formally establish whether any estimate is in fact unbiased. The unique way to take precautions against the risk of obtaining biased estimates, is the attempt to verify that the underlying assumptions of the methods are at least plausible in any particular application. This is that has been made in the current study considering the four major assumptions that must be satisfied to produce reliable counts from capture-recapture methods.

The first assumption is that the target population is closed. In reality, no population is closed, thus this assumption can only be satisfied to a reasonable degree. If the alcoholic population is very dynamic, with members entering and leaving with great frequency, the recapture will be less likely to include people identified in the first capture. This leads to an overestimate of the population of alcoholics.42 To allow for the assumption that the alcoholic population was reasonably stable during the study period, we limited the duration of the observation to one year.

The second assumption is that false-positive subjects should not be present on any list.43 In our study, it is assumed that all the listed people have ARP. In the current application, people who attended self help groups to be supportive of others with ARP (for example, friends or family of alcoholics), patients who received care and assistance from the psychiatric ambulatory or the public alcoholic service with diagnosis different from alcohol dependence and/or abuse (for example, dependence from other substances), and patients discharged with a diagnosis not directly indicating the alcohol aetiology (for example, liver cirrhosis without mention of alcohol), were not included in the lists.

The third assumption is that the capture sources are independent. In reality, this assumption is not required if more than two captures are used and an algorithm is used to account for dependence among captures.29 31 Despite this, you should be aware that not all the possible interactions are appreciable by any algorithm, especially when sample size is small. In the current application, although the two sample capture-recapture estimates suggested a negative dependence between F1 (self help groups lists) and F4 (hospital discharges list), the corresponding interaction term did not significantly improve the goodness of fit of the log-linear model accepted. This might lead to an overestimate of the prevalent count of subjects with ARP.

The fourth assumption is that for any single source each case in the population has the same probability of ascertainment, although any two sources may differ in this probability.14 In contrast, we can reasonably hypothesise that each list tends to preferentially cover different subsets of the population. It is very difficult, in an epidemiological observational framework, to control every putative source of heterogeneity among people. For example, we observed that considering age as a heterogeneity source in the log-linear model, improvements of the goodness of fit of the model were obtained. In particular, the psychiatric ambulatory and the public alcoholic service tended to cover preferentially younger subjects. Although an analysis stratified by gender and age has permitted us to correct the estimate, we cannot exclude that other important strata remain unidentified and may contribute to a biased estimate. Confidence intervals of our counts, already very wide when only dependence among sources was considered (1524, 3794), were even wider when also gender and age effects were taken into account (1623, 4627).

From a health service point of view, it is very important to know the proportion of the total estimated population who have attended different services. Our data suggest that of every 1000 subjects who seek treatment for alcohol related disorders resident in Voghera, only 14 attended the Public Alcohology Service, 30 the Psychiatric Ambulatory, 38 the self help volunteering groups and 68 were discharged with a primary or secondary alcohol related diagnosis. Moreover, only 7.7% of the cases were flagged by more than one source, suggesting a scarce collaboration among services and groups in the management of alcoholics. These data may change over time and space depending on the type and availability of treatment, on the ability of physicians to identify patients with ARP and on the management of patients discharged with an alcohol related diagnosis.

It might be speculated that, in the specific issue of the treatment of alcoholics, overlapping among sources might be considered as a proxy indicator of the functioning of the network among public services and self help volunteering groups supporting care and assistance of alcoholics and facilitating their abstinence from alcohol.44 Two main positive dependencies among sources were observed in our application. Firstly, people flagged by the Psychiatric Ambulatory (F2) were more pobably also flagged by the Alcohology Service (F3). Secondly, people discharged for alcohol related diseases (F4) were more probably flagged by the Alcohology Service. These findings suggest a good functioning of the network between the public services of the area involved in the treatment of alcoholics. On the other hand, as the two sample estimate considering intersection between hospital and self help groups was much higher with respect to the other two sample estimates, then the patients discharged for alcohol related diseases were not preferentially sent to the self help groups of the area. These findings suggest that the proposed method, involving the comparison between multiple information sources, is potentially useful for the health planners to verify the functioning of the network among the public services and self help volunteering groups.

Our study suggests that capture-recapture is an appropriate approach for estimating the prevalence of ARP when different lists of alcoholics can be obtained from different types of agencies involved with problematic use of alcohol. However, the use of this method requires careful attention to the underlying assumptions discussed above and cautious interpretations.