The study uses linked data from various national and population-level registries and datasets in Denmark. These datasets provide individual-level data on several outcomes and variables, have been used in several studies, and are known to be of high quality with low missing data rates [35]. Statistics Denmark administers the access to these datasets and ensures that security, confidentiality, and anonymity are maintained while allowing micro-level data analysis. The study investigators accessed the assembled study datasets at Statistics Denmark via a secure virtual private network (VPN) connection. The datasets provided by Statistics Denmark have no individual or organizational identifiers and are stored on servers located within Statistics Denmark. The study was approved by the by the Danish Data Protection Agency (Case No. 92/229 MC) and the University of Iowa IRB (Protocol # 200708740).

The study datasets include the Danish Facial Cleft Database, the Danish National Patient Registry, the Danish Civil Registration System, the Danish Demographic Database, and the Integrated Database for Labor Market Research. Almost all births (about 99%) with oral clefts since 1936 in Denmark have been registered in the Danish Facial Cleft Database [34]. The registry is assembled from various data sources including surgical records from the two hospitals where all oral cleft repairs surgeries are done - cleft surgeries have been centralized in Denmark since the mid 1930s. The registry also uses the records of the National Institute for Defects of Speech to which midwives and other health professionals are required to report observed cases with oral clefts. The registry includes data on presence of other malformations or syndromes. The majority of registered cases (including most of the cases born in the 1960s or later) can be linked at Statistics Denmark to the other national registries through the unique personal identification numbers.

The Danish National Patient Registry is maintained by the Danish National Board of Health and includes data from local health authorities in order to facilitate planning in the health care system. The dataset provides data on somatic hospitalizations including admission/discharge dates, diagnoses (using standard codes ICD 8 and 10), and operations. The Danish Civil Registration System includes information about marital and vital status and residence reported through local municipalities. The Danish Demographic Database is constructed by Statistics Denmark from several public administrative databases and includes data on cause of death, date and country of migration, and relationship to others sharing the same dwelling. The socioeconomic data are obtained from the Integrated Database for Labor Market Research which is based on a number of registers [36].

The cases in the study sample include 7,670 individuals born between 1936 and 2002 with oral clefts but without other major birth defects such as neural tube defects or recognized syndromes as identified from the Danish Facial Cleft Database [37]. About 9.6% of individuals in the Danish Facial Cleft Database have another major malformation besides oral clefts or a genetic syndrome [38]. As mentioned above, this sample includes virtually all individuals born with oral clefts and without other major birth defects during this period in Denmark. The controls in the study sample include 220,113 individuals without oral clefts from a randomly selected sample of about 5% of the total population of births in Denmark each year from 1936 to 2002. Both cases and controls are limited to individuals born in Denmark who were alive on or born after January 1st, 1981 (the beginning date for hospitalization data availability), lived (at least for some time) in Denmark between 1981 and 2004, and have complete information on the study variables.

We employ a panel data design where individuals have a measurement of hospitalizations for each year that they are observed in the sample. We model hospitalizations in a given year as a function of cleft status and other variables that may affect hospital use. Specifically, we use the following function:

(1)HOSPITALIZATIONSit=α0+βCLEFTi+∑d=1DλdDEMOGRAPHICdit+ ∑y=1YςyYEARyit+vit

where for individual i, the number of days hospitalized in year t (HOSPITALIZATIONS) are a function of whether the individual was born with a cleft or not (CLEFT), demographic characteristics including the individual's age, sex, and number of days spent in Denmark (DEMOGRAPHIC), and year fixed effects (YEAR). Hospitalization risks are expected to vary over age. Cleft repairs are usually completed early in life (within the first two years of life). Some follow-up surgeries may be performed during adolescence. Since cleft repair surgeries in Denmark are centralized and surgical repair costs are covered by the universal health insurance program, there is limited variation in age at repair. After adolescence, there are generally no increased hospitalizations due to cleft repair, and any additional hospitalization risks are expected to be almost entirely due to physical and mental health co-morbidities of oral clefts. In order to capture changes in hospitalization risks due to oral clefts over age, we model hospitalizations during several age groups that are feasible with the available data including 0-9, 10-19, 20-29, 30-39, 40-49, 50-59 and 60-68 years, which cover most of the life span. We do not exclude hospitalizations due to cleft repair surgeries during childhood and adolescence in order to capture the "total" effects of oral clefts on hospitalizations, and not only effects through cleft co-morbidities.

Given that parental socioeconomic and demographic factors may affect the child's cleft risks and hospitalization outcomes, we also adjust in (Equation 1) models for age groups 0-9 and 10-19 years for maternal and paternal education, employment and income in year t-1 (PARENT_SOCIOECONOMIC), maternal and paternal ages in year t (PARENT_DEMOGRAPHIC), maternal marital status in year t-1 (PARENT_MARITAL), and area-level characteristics in year t-1 including maternal county of residence and county's population density (AREA) as follows:

(2)HOSPITALIZATIONS=α0′+β′CLEFTi+ ∑s=1SδsPARENT_SOCIOECONOMICsi(t-1)+ ∑d=1Dλd′DEMOGRAPHICdit+ ∑p=1PκpPARENT_DEMOGRAPHICpit+ ∑r=1RπrPARENT_MARITALri(t-1)+∑a=1AγaAREAai(t-1)+ ∑y=1Yςy′YEARyit+uit

We use (') to indicate that the coefficients vary between (Equation 1) and (Equation 2). We include the socioeconomic, marital status and area variables at time t-1 given that child hospitalizations may have reverse effects on parental income, employment, marital status, and residential location.

We do not include parental socioeconomic and demographic characteristics for ages older than 19 years as these are not available for a large proportion of these age groups (links between parent and children are available beginning for the 1953 birth cohort and are nearly complete from 1960) [39]. Furthermore, we do not include in the main model for age groups older than 19 individual-level socioeconomic characteristics because, as mentioned above, cleft status may have negative impacts on the individual's educational attainment, wealth, employment, and marriage status, which in turn may affect hospitalizations. Therefore, estimating the "total" effects of cleft status on hospitalizations requires omitting these variables from the model. However, we also evaluate the "direct" effects of oral clefts on hospitalizations separately from the indirect effects on psychosocial and economic performance by estimating an additional specification of (Equation 1) for ages 20 years and older that controls for individual-level education, income, marital status, employment, and marital status (SOCIOECONOMIC) as well as county of residence and county's population density (AREA) given that oral cleft status may affect the individual's social mobility and residential location. All these additional socioeconomic and area controls are measured at year t-1 in order to account for the potential reverse effects of hospitalizations on these variables.

(3)HOSPITALIZATIONSit=α″0+β″CLEFTi+ ∑s=1Sδ″sSOCIOECONOMICsi(t-1)+ ∑d=1Dλ″dDEMOGRAPHICdit+ ∑a=1Aγ″aAREAai(t-1)+ ∑y=1Yς″yYEARyit+eit

We use (") to indicate that the coefficients are different from the above two equations. In addition to estimating the effects of any cleft, we estimate the effects of cleft types (cleft lip alone, cleft palate alone, and cleft lip with palate) on hospitalizations given that oral cleft status effects may vary by cleft type/severity. Tables 1 and 2 list the distribution of all model variables for ages 19 years or younger and older than 19 years, respectively.

The number of days hospitalized per year includes a high proportion of zero values (zero-inflated measure) and is skewed to the right due to the small proportion of lengthy hospitalizations. Two-part models [40], commonly referred to as Hurdle models in the case of count dependent variables, are typically used for outcomes with such a distribution [41,42]. The first part estimates the probability of hospital admission, and the second part estimates the function of hospitalization days for those who were hospitalized. In addition to accommodating the zero-inflated and right-skewed dependent variable, the two-part model evaluates if oral clefts have different effects on hospitalization propensity and on length of stay after admission. For example, individuals with clefts may have a higher propensity of being admitted to the hospital due to potentially facing higher risks for certain chronic conditions (such as mental health issues or cancer). However, once admitted, they may or may not have a different length of stay.

We use a two-part model with logistic regression to estimate the probability function for hospital admission and zero-truncated Poisson regression to fit the function of length of stay for admitted individuals. We evaluate the effects of oral clefts in both functions and estimate the overall combined incremental effect on hospitalization days from both models. We estimate the standard error of the overall incremental effect using bootstrap with 500 replications. In order to account for the multiple yearly observations of the same individual over the entire age group when evaluating the oral cleft effects on hospitalization probability and length of stay for those hospitalized, we estimate the variance-covariance matrix for the regression coefficients using a robust Huber-type estimator [43]. This estimator accounts for the repeated observations of the same individual over time in the used panel data design. Given that the logistic regression and zero-truncated Poisson regression models are expected to provide consistent estimates of the regression coefficients, adjusting the standard error estimates is appropriate in this case for accounting for repeated measurements.

Figure 1 shows the hospital admission rates and length of stay by age for the cleft and control groups. Individuals with oral clefts have higher hospital admission rates than individuals without clefts at all age groups but the differences decrease significantly with age. Also, hospitalized individuals with clefts have on average a longer length of stay for most age groups except at 60-68 years of age, with the differences significantly decreasing with age. The average annual hospital admission rates among the individuals with oral clefts range from 27% during ages 0-9 years to 13% during ages 60-68 years. The lowest hospital admission rate for affected individuals is 10% for ages 40-49 years. The average annual hospital admission rate for individuals without clefts ranges from 9% for ages 0-9 years to 13% for ages 60-68, with a lowest admission rate of 6% for ages 11-19 years.

The changes in hospital admission rates by age vary between the cleft and control groups. Among individuals with oral clefts, admission rates continuously decrease with age until age 40-49 years and increase thereafter. Among individuals without clefts, admission rates increase markedly from ages 11-19 to 20-29 years by about two times, decrease slightly after that until age 40-49 years, and increase thereafter. Unlike differences between individuals with and without clefts in admission rate changes over age, there is no difference between the two groups in the direction of changes in hospital length of stay over age.

Table 3 reports the effects of oral cleft status and cleft type on the probability of hospital admission, hospitalization days among those admitted, and the total combined effects on hospitalization days from the two-part model for each of the study age groups. Additional file 1: Tables S1, Additional file 2: Table S2, Additional file 3: Table S3, Additional file 4: Table S4, Additional file 5: Table S5, Additional file 6: Table S6, Additional file 7: Table S7, report detailed regression results. Also reported in Table 3 is the percentage change in hospitalizations with oral clefts relative to the control group without clefts, which are also depicted in Figures 2 and 3 for the overall cleft status and cleft type effects, respectively. Oral clefts significantly increase hospitalizations in most age groups below 60 years, with generally decreasing effects by age. Oral clefts have insignificant effects on hospitalizations between 60 and 68 years of age.

Oral clefts increase the probability of hospital admission in all age groups below 60 years and increase the length of stay among those hospitalized for age groups below 50 years. The increase in admission probability ranges from 0.17 for age group 0-10 years to 0.013 for age group 50-59 years. This is equivalent to a 195% to 13% increase in hospital admission probability relative to the control individuals without oral clefts. The effects on hospitalization days per year among those admitted range from 2.5 days for age group 0-10 years to 0.8 days for age group 40-49 years, which represent 48% to 10% increase in length of stay relative to controls. The total effect of oral clefts on hospitalization days from the two-part model (which combines effects on probability of admission and hospitalization days conditional on use) ranges from 1 day per year for age group 0-10 years to 0.16 days per year for age group 50-59 years. These represent 233% to 16% increases in hospitalization days relative to the controls. The total absolute oral cleft effect in the 0-10 age group is twice as large as that in the 11-19 age group and four times as large as that in the 20-29 age group. However, the percentage increase in hospitalization days relative to the controls is still very high in the 11-19 age group at 202%.

Among the cleft types, cleft lip with palate has the largest total effects on hospitalizations for all age groups below 60 except for age group 40-49 years for which cleft palate alone has the largest total effect. Cleft lip alone has the smallest effect compared to the other cleft types. Cleft lip with palate significantly increases hospital admission probability per year by increments ranging from 0.25 for the 0-10 age group to 0.024 for age 50-59 years. These represent 285% to 26% increases in admission probability, respectively, relative to the controls. The largest increase in hospitalization probability with cleft lip with palate relative to the controls is 362% for the 11-19 age group. Cleft lip with palate significantly increases length of stay among those hospitalized only up to age 29 years, with the increases ranging between 3.4 days per year for the 0-10 age group to 0.4 days per year for the 20-29 age group, which represent 64% to 8% increases in hospital length of stay relative to controls, respectively. The total effects of cleft lip with palate on hospitalization days range from 1.5 days per year for the 0-10 age group to 0.3 days per year for the 50-59 age group, which represent 335% to 30% increase relative to controls, respectively. The largest increase in total hospitalizations with cleft lip with palate relative to controls is 386% for the 11-19 age group.

In contrast, cleft palate alone significantly increases length of stay among those hospitalized for all age groups below 50 years except for the 30-39. The largest effects are for the 0-10 and 40-49 age groups, for which length of stay is increased by more than 2 days per year (about 46% and 32% increase relative to controls, respectively). The total effects of cleft palate alone on hospitalization days range from 1 day per year for the 0-10 age group to 0.3 days per year for ages 40-49 years, which exceed the effects for the intermediate age groups and represent hospitalization increases of 219% and 54% relative to the controls, respectively.

Cleft lip alone generally has no significant effects on hospitalizations beyond 29 years of age (only a very small and marginally significant effect for the 30-39 age group). The total effects of cleft lip alone on increasing hospitalizations range from 0.6 days per year for the 0-10 age group to 0.1 day per year for the 20-29 year old group, which are equivalent to 133% to 17% increase relative to the controls, respectively. Cleft lip alone decreases hospitalization days for ages 60-68 years by half a day per year (37% decrease relative to the controls).

Table 4 reports the effects of oral clefts on hospital admission and length of stay among those hospitalized for age groups older than 19 years adjusting for individual-level socioeconomic and area characteristics (Equation 3). Additional file 3: Table S3, Additional file 4: Table S4, Additional file 5: Table S5, Additional file 6: Table S6 and Additional file 7: Table S7 report detailed regression results. The goal is to evaluate the extent to which the total cleft effects on hospitalizations described above are mediated by these characteristics which may also be affected by oral clefts. Adjusting for individual-level socioeconomic and area characteristics significantly decreases the effects of oral clefts on hospital admission and/or length of stay among those hospitalized beginning at age group 30-39 years, with larger decreases in the oral cleft effects over age. The oral cleft effects on length of stay decrease by more than half and become insignificant for all age groups above 29 years. Further, the cleft effects on hospital admission decrease by 50% for ages above 39 years and become insignificant for age group 50-59 years.

The larger declines in the oral cleft effects by age after adjusting for individual-level socioeconomic and area characteristics and the overall minimal effect of this adjustment for the 20-29 age group strongly suggest that these declines are due to the indirect cleft effects on hospitalization through affecting individual-level psychosocial and economic performance rather than due to reflecting the effects of parental-level socioeconomic status that are unobserved for the older age groups. Improved individual-level socioeconomic performance has the expected negative effects on hospitalizations, but is negatively correlated with oral cleft status (see Tables 2 and Additional file 3: Table S3, Additional file 4: Table S4, Additional file 5: Table S5, Additional file 6: Table S6 and Additional file 7: Table S7).

In order to further check whether including the individual-level socioeconomic and area characteristics for the older age groups is reflecting their unobserved family socioeconomic background characteristics, we re-estimate the models for ages 19 years and younger excluding all parental socioeconomic, demographic, and area characteristics (Equation 1). Table 5 reports the oral cleft effects on hospitalizations for age groups 0-9 and 10-19 years after this exclusion (detailed regression results are in Additional file 1: Table S1 and Additional file 2: Table S2). The effects from this model are virtually the same as those in the full model adjusting for parental socioeconomic, demographic, and area variables (in Table 3). This provides assurance that the models for the older age groups that do not adjust for parental and family background characteristics are unlikely to be biased by such unobserved family backgrounds and that the changes in cleft effects on hospitalizations with adjusting for individual-level socioeconomic and area characteristics is due to the cleft effects on these characteristics.