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Foreign body injuries are a well-known threat to children due to the high risk of ingestion of small objects and choking. In order to depict the epidemiological framework of such injuries, data are mostly available for hospitalizations and partially for emergency room visits. The hidden part of the phenomenon consisting of minor self-resolved injuries is still unknown. The purpose of this paper is to provide an estimate of the overall burden of such injuries in children in Italy. Our paper proposes the use of the scale up technique to overcome most of the pitfalls of classical techniques in the estimation of the number of children aged 0–14 that suffered a foreign body injury in 2004. Our results, based on a CATI survey on 1,081 women, show that the estimated number of children under 15 years that incurred in a foreign body injury was 15,829 (95% CI: 14,376–17,282), of these 12,844 were treated in hospital or in emergency department (95% CI: 11,535–14,153). The scale-up method in conjunction with a CATI survey provides a reliable estimate of the size of hard-to-count populations as those of injured children at lower costs with respect to classical sampling schemes.

Foreign body injuries in the upper aero-digestive tract are due to the aspiration/ingestion/insertion of objects and they are one of the leading causes of injury and death in children [

In addition, we should notice that incidence estimates of such injuries usually result from the hospital discharge records and from the death certificates. However, since a large number of foreign bodies injury cases are self-resolved (e.g., parents help children to discharge the object) without accessing the health care services, underestimation of the actual incidence rates is likely to result.

To overcome these drawbacks, our approach proposes the usage of the scale-up methodology [

The estimated network size information is combined with the responses to the questions about how many people the respondents know in the population of children who experienced a foreign body injury. In order to estimate the social network size, individual responses are taken into account for a set of subpopulations with known size and then they are scaled up using the sizes of these groups to the general population.

Contrarily to the other survey techniques, scale-up methodology does not require asking people directly about problems. This presents two main advantages: first, people are more willing to answer to questions that do not touch directly their person, especially when the topic under investigation is a sensitive issue. Secondly, researchers are able to collect information about all respondents’ social network. This is relevant in particular for studying events with low prevalence, since it allows the use of samples of smaller size as compared to other survey techniques.

This work is aimed at applying the scale-up method to the estimate of the magnitude of the foreign body injury phenomenon, including in this both the known part of it (

The scale-up method was developed by Bernard and his colleagues in the 1990s [_{io}_{i}

The maximum likelihood scale-up estimator for the size _{0} of the subpopulation _{0} [

The estimator (3) requires just computing the sum of the social network’s size _{i}_{ij}_{j}_{j}_{j}

A sensitive task in the estimation of the social network size is the choice of the subpopulations of known size [

Two-thousand-four-hundred-fifty women have been contacted for the interview, and 1,081 accepted, with a response rate of 44%. Out of a total of 35,673 items, 2,039 answers were not given (5.7%) of which 1,038 referred to the political questions (2.9%). These missing values were replaced imputing the median value of each question. The 1,081 interviewed women recalled a total of 437 children that suffered a foreign body injury, out of which 351 were treated in hospital. The regression model with all the 33 subpopulations (

Subpopulation of known size used to estimate the respondents’ social network sizes.

Subpopulations of known size | Size in thousands | Subpopulations of known size | Size in thousands |
---|---|---|---|

People voted for Casa delle Libertà in 2001 elections | 18,300 | Widows younger than 60 years | 506 |

Families with 2 children | 4,436 | People sentenced for driving under the influence of alcohol in 2004 | 426 |

People volunteer in non-profit associations | 3,481 | People went in business during 2004 | 426 |

People bought a new car | 2,249 | Bought a motorcycle | 409 |

Families with only one parent living alone with children | 2,101 | Competitive basket players members of FIP | 169 |

People voted for Rifondazione Comunista in 2004 elections | 1,972 | Competitive athletes members of FIDAL | 127 |

Families with 5 or more components | 1,635 | People doing a temporary job | 119 |

People owing a car with gas or methane | 1,356 | People currently detained in prison | 57 |

People reported a robbery | 1,303 | Children adopted in 2004 | 6 |

Families with 3 or more children | 1,276 | People 100 or more years old | 6 |

Own a Mercedes car | 956 | People committed suicide in 2004 | 3 |

People working in hotels and restaurants | 859 | People reported a rape in 2004 | 2 |

Teachers | 707 | People had a kidney transplantation in 2004 | 1.7 |

People with a specialization or a PhD | 644 | People killed in 2004 | 0.7 |

People owing a BMW car | 630 | People had a heart transplantation in 2004 | 0.3 |

Women had a child in 2004 | 528 |

Regression model with all the 33 subpopulations of known size. The circles highlight the subpopulations that were eliminated with the analysis of residuals.

Therefore, we decided to choose the final subgroups to be used in the estimation by assessing the linear relation between the subpopulation sizes and the mean number of people recalled by respondents for each subgroup. Following Snidero

Regression model with the 20 selected subpopulations of known size chosen for the final estimates.

As shown in

Subpopulations excluded from the analysis using the algorithm based on the regression model.

Excluded subpopulations |
---|

People bought a new car |

People owing a BMW car |

People owing a car with gas or methane |

Teachers |

Teachers of primary school |

People volunteer in non-profit associations |

People with a specialization or a Ph.D |

Widows younger than 60 years |

Families with only one parent living alone with children |

Families with 2 children |

People voted for Casa delle Libertà in 2001 elections |

People voted for Rifondazione Comunista in 2004 elections |

People reported a robbery |

Using the remaining 20 subpopulations, the estimated mean social network (_{i}

The estimated number of children under 15 years that incurred in a foreign body injury (

Results of the sensitivity analysis for each subpopulation excluded from the analysis.

Excl. subpopulation | ĉ | Injury | Hospitalized |
---|---|---|---|

Bought a motorcycle | 229.0 (40.9) | 15,087.6 (706.5) | 12,242.1 (636.4) |

Own a Mercedes car | 232.5 (41.8) | 14,862.8 (696.0) | 12,059.7 (627.0) |

Competitive athletes members of FIDAL | 219.2 (39.2) | 15,759.2 (738.0) | 12,787.0 (664.8) |

Competitive basket players members of FIP | 220.1 (39.3) | 15,699.1 (735.2) | 12,738.3 (662.2) |

Families with 5 or more components | 229.8 (45.3) | 15,032.8 (704.0) | 12,197.6 (634.1) |

People went in business during 2004 | 225.8 (40.6) | 15,302.8 (716.6) | 12,416.7 (645.5) |

Families with 3 or more children | 208.7 (41.4) | 16,558.0 (775.4) | 13,435.2 (698.5) |

People 100 or more years old | 217.3 (38.6) | 15,902.9 (744.7) | 12,903.7 (670.8) |

People doing a temporary job | 207.3 (38.0) | 16,664.0 (780.4) | 13,521.2 (702.9) |

People working in hotels and restaurants | 219.0 (41.3) | 15,782.6 (739.1) | 12,806.0 (665.8) |

People sentenced for driving under the influence of alcohol in 2004 | 230.5 (41.1) | 14,990.1 (702.0) | 12,163.0 (632.3) |

Children adopted in 2004 | 211.5 (38.1) | 16,333.0 (764.9) | 13,252.7 (689.0) |

People had a heart transplantation in 2004 | 217.5 (38.6) | 15,886.9 (744.0) | 12,890.7 (670.2) |

People had a kidney transplantation in 2004 | 217.5 (38.6) | 15,887.2 (744.0) | 12,890.9 (670.2) |

Women had a child in 2004 | 211.8 (39.4) | 16,315.3 (764.0) | 13,238.3 (688.2) |

People killed in 2004 | 216.0 (38.6) | 15,996.6 (749.1) | 12,979.7 (674.8) |

People reported a rape in 2004 | 217.9 (38.7) | 15,858.8 (742.7) | 12,867.9 (669.0) |

People committed suicide in 2004 | 217.0 (38.6) | 15,924.6 (745.7) | 12,921.3 (671.7) |

People dead for a cancer in 2004 | 208.3 (38.1) | 16,587.7 (776.8) | 13,459.3 (699.7) |

People currently detained in prison | 212.3 (38.7) | 16,270.3 (762.0) | 13,201.8 (686.3) |

Notes: ĉ is the network size, Injury is the social network size estimate of the number of injuries, for ĉ; Hospitalized is the estimated number of hospitalized injuries; d is standard errors in brackets.

In _{0}) obtained omitting one at time of the subpopulations (_{j}

Our study estimated that 15,829 children suffered a foreign body injury in Italy in 2004, of which 12,844 were hospitalized or visited at the emergency department. Therefore, the estimated incidence of foreign body injuries in children in Italy is about 0.2%.

Taking into account that the official number of hospitalized children for such injury was 1,814 in 2003 [

The main limitation is that no extrapolations to any subset of the population are allowed by the method, therefore specific incidence rate such as for any foreign body type cannot be derived by this work.

With the scale-up method we obtained the target information about a number of people virtually equal to the interviewed sample size multiplied by the social network size of each respondent (about 235,000 people). The standard error was quite small (741 persons), corresponding, in relative terms, to 0.9 × 10^{−4} if we divide it by the total number of children aged 0–14 in Italy. In order to getting the same standard error magnitude using the classical probabilistic schemes, we should have planned a sample of exactly 236,254 people. Clearly, the scale up has a multiplying effect on the sample size, due to the indirect contact of a number of people. This is of course particularly appealing in view of rapidity of the CATI survey and of the lower costs associated with it. Indeed, the number of missed items was negligible, and this was obtained while the survey was conducted by interviewers not particularly experienced in the usage of the scale-up technique.

The study was designed to estimate the number of children aged 0–14 that incurred in a foreign body injury in Italy. The sample was formed randomly selecting 1,081 women aged 18–50 who answered to a CATI survey. The respondents were asked to answer to a questionnaire about:

- The number of people they know in 33 questions about populations of known size;

- The number of children they know that suffered a foreign body injury and some more details related to the injuries (target questions).

The target questions, which were referred to the 2004 year, were:

- “How many children do you know that had an injury due to the swallowing/ingestion of a foreign body?”, aimed at identifying the first target subpopulation of size _{01};

- “Of those, how many children went to the emergency service or were hospitalized?” aimed at identifying the second target subpopulation of size _{02}.

We applied a regression model with the mean number known in each subpopulation as dependent variable and the relative size of the subpopulation as independent variable to select the subpopulations of known size that meet the request of linear proportionality. Therefore, we proceeded to exclude some of the 33 subpopulations with a graphical analysis of residuals.

According to the formulas given in Equations (1) and (2) we estimated the mean social network size and the target subpopulation size along with 95% confidence interval (95% CI).

In order to understand how estimates depend on the specific choice of the subpopulations used in the analysis we carried out a sensitivity analysis. A leave-one-out strategy was adopted: one population among the selected subpopulations was picked up and excluded from the sample. This was repeated such that each population was left out once. The analysis was carried out with S-plus ver. 6.2 [

The scale-up technique has been shown to have a potential for application in the injury field. A comparison with known figures on foreign bodies injuries has shown a strong consistency with them: of course, since no data exists at the time being on the number of non-hospitalized foreign bodies injuries, the above conclusion is based on common sense and expert opinions. Further data are needed to better understand the hidden epidemiology of such injuries.

From the methodological point of view, the procedure of selecting sub-populations is still based on the empirical evaluation of the residuals. Less subjective approaches should be investigated. In this sense also the issue of missing data on recalled subpopulation sizes needs further developments; the approach based on the median which has been used in this analysis tends to underestimate standard errors, as shown in some simulation-based investigations in the field of public health research [

Injury research constitutes a terrain where most of the classical techniques can easily fail, due in particular to the high sensitiveness of some questions. In particular, a sensitive problem is how to estimate the number of children who have suffered from injuries or violence at a certain point in their life. This is important public health issue because many children who suffered from injuries often do not go to a hospital or clinic for treatment, in particular in case of facts of lower impact. In addition, children who suffered from violence in their family also find difficulty in reporting the facts. The adaptation of scale up methods to such populations could be a first step toward its use for other public health issues where some cases may be treated outside of the medical system: knowing the size of such populations is important for planning and reducing inequalities in the access of public health care systems. These considerations are emphasized when injuries are related to children and thus when the interviewed parents have to face their sense of inadequacy and guilt. In addition, such technique can successfully be used when official data are not fully recorded or when the data extraction can be costly and time inefficient. In this setting, the possibility to have a reasonable, quick and cost-effective estimation of the magnitude of the phenomenon is surely appealing.

The project has been partially financed under the project PGR00064, by the Direzione Generale per la Promozione e la Cooperazione Culturale of the Italian Ministry of Foreign Affairs (MAE) and the Secretaría de Ciencia, Tecnología e Innovación Productiva (MINCYT), Argentina and by an unrestricted grant of Prochild ONLUS.

The authors declare no conflict of interest.