Study population
The patients we studied were from Children's Hospital, Zhejiang University School of Medicine, which is a regional children's clinical medical center in southeastern China that serves as the tertiary referral institution for pediatric multiple chalazia in Zhejiang province. Children that were diagnosed with multiple chalazia and examined in the Department of Ophthalmology between 1 June 2016 and 31 December 2016 were retrospectively reviewed in our study. These children were assumed to be a representative sample of all children with multiple chalazia in Zhejiang province. Our research was approved by the Institutional Ethics Committee of Children’s Hospital, and it adhered to the tenets of the Declaration of Helsinki.
Ocular evaluation
Careful ocular examination is essential for diagnosis. An internal chalazion is a firm and purplish palpable nodule on the conjunctiva when the eyelid is everted. Sometimes a chromic internal chalazion develops into a pedicled granuloma that exceeds the palpebral fissure. An external chalazion is obvious on the eyelid skin and appears as a red, elastic nodule with well-defined borders. A marginal chalazion is a small bump along the lid margin. A chalazion is usually non-tender and non-fluctuant, but if infected, a chalazion is painful and red.
Clinical managements and data collection
Patients were recommended to have warm compresses on lids 4 times a day. If local infection was considered, topical treatment with levofloxacin eye drops 5 mg/mL (Cravit; Santen, Japan) 4 times a day and/or oral azithromycin 10 mg/kg (Zithromax; Pfizer, USA) once a day for 3 days would be given. For lesions unresponsive to conservative treatments, lasting for more than 2 months, or showing potential visual or cosmetic risks, I&C surgeries under systemic anesthesia were performed. The specimens were submitted for histopathology examinations to confirm the diagnosis.
To count lesions accurately, we included only patients that had chalazion surgeries because the calculation can then be done under anesthesia. We collected the following information for analysis: age, gender, residence, type of chalazion, number and location of lesions, duration of disease/onset time defined by the guardians, and past history.
Exclusion criteria
We excluded patients whose chalazion received palliative incision or was spontaneously broken right before I&C, and those with skin findings on the eyelid caused by idiot facial aseptic granuloma (IFAG), acne, seborrhea, rosacea or atopy.
Statistical Analysis
Statistical analyses were performed using R software version 4.0.2 (Vienna, Austria. https://www.R-project.org/.) We analyzed the counts of chalazia using two classes of statistical models, one for the total number of chalazia observed at all eyelid locations and another for the number of chalazia observed at each eyelid location. The latter observations are needed to estimate the anatomical distribution of chalazia. The counts of internal and external chalazia were analyzed separately.
To be more specific, we assumed that the total number N of chalazia at all eyelid locations had either a Poisson distribution or a negative binomial distribution, whose mean µ was allowed to differ among patients of different gender, age category, or residence. That is, we assumed either
N ∼ Poisson(µ)
where log(µ) = β1X specifies the mean as a function of observed covariates X and their effects β, or
N ∼ Negative Binomial(µ, α)
where α is a positive, scalar-valued parameter that indicates the level of extra-Poisson variation in N . Our choice of Poisson or negative binomial models was based on an assessment of goodness of fit.
To estimate and make inferences about the anatomical distribution of chalazia, we conditioned on N and assumed the following model:
Y1, Y2, Y3, Y4 ∼ Multinomial(p1, p2, p3, p4)
where Y1, Y2, Y3 and Y4 denote the numbers of chalazia observed at each of four eyelid locations (RUL, RLL, LUL, and LLL, respectively) and where p1, p2, p3 and p4 denote parameters for the proportions of N counts found at each eyelid location. Because this model conditions on the total count N (= Y1 + Y2 + Y3 + Y4), the parameters are necessarily restricted such that 1 = p1 + p2 + p3 + p4. Therefore, only 3 of the parameters are free to be estimated; the fourth parameter is estimated by difference.
We used the method of maximum likelihood to estimate the parameters of these models from data. We also used likelihood-ratio tests to assess the significance of effects of covariates on N and to examine alternative hypotheses about the anatomical distribution of chalazia.
To examine the co-occurrence of internal and external chalazia, we compared the number of internal chalazia per eyelid for two groups of patients, those with one or more external chalazia and those without external chalazia. More specifically, we assumed the following model:
Yi,j ∼ Poisson(λi,j)
where Yi,j denotes the number of internal chalazia on the jth eyelid location (j = 1, . . . , 4) of the ith patient. The parameter λi,j denotes the number of internal chalazia that are expected on the jth eyelid of the ith patient given that external chalazia were present (xi,j = 1) or absent (xi,j = 0). Formally,
log(λi,j) = β0,j(1 − xi,j) + β1,jxi,j
This parameterization of the model implies that β1,j is the logarithm of the mean number of internal chalazia on the jth eyelid of patients with external chalazia. The parameter β0,j corresponds to the same quantity, but for eyelids without an external chalazion. We tested the null hypothesis that β0,j = β1,j to assess whether numbers of internal chalazia depended on the presence or absence of external chalazia.
All the statistics were reported as 2-tailed probabilities, with P values <0.05 being regarded as significant.