Study design
We performed a replicated time-series analysis of asthma and allergic rhinitis symptom fluctuations and ADHD symptom fluctuations in individual participants. The time-series data were collected by means of an online diary study. For a period of 50 days, one of the parents was asked to fill out daily questionnaires; to be done at a specific time, preferably the end of the day between 8 and 9 pm. The questionnaire was applied as a mobile phone application and was used to assess the asthma and allergic rhinitis symptoms, and the ADHD symptoms. One and the same parent were asked to fill out the baseline questionnaire and the daily questionnaires to prevent reporting bias.
Study population
The study population consisted of 21 children in the age of 7–16 years in whom the diagnosis ADHD was established by a child psychiatrist, a child psychologist, or a pediatrician. Asthma or allergic rhinitis was diagnosed by a physician. Children were excluded if they were diagnosed with any chronic disease other than atopic diseases or ADHD. Parents could not participate if they were not fluent in the Dutch language or were, otherwise, unable to fulfill the study procedures or had no access to the Internet. Children and their parents were recruited by their pharmacists through the IADB.nl prescription database and the patient database of a medical center in Rotterdam. Participants were asked to continue care as usual throughout the study. Our local medical ethical committee (METC UMCG) had waived the ethical approval for this observational study design according to the declaration of Helsinki. All participants were asked to fill in an informed consent form before participation of the study.
Measures
At baseline, for each participant, age, sex, and the ratings of the ADHD symptoms [26-item scale Swanson, Nolan, and Pelham Questionnaire (SNAP-26)], atopy [Control of Allergic Rhinitis and Asthma Test (CARAT)], and sleep problems [Children’s Sleep Habits Questionnaire (CSHQ)] as rated by one of the parents in the week before the initiation of the study, were determined to describe the sample characteristics.
To assess the severity of ADHD symptoms during the diary period, we used the SNAP IV questionnaire, which is a frequently used, validated tool in ADHD studies that is based on the 18 DSM-IV ADHD items [
6,
7]. The combined score of inattention and hyperactivity/impulsivity subscale scores was used as rating of ADHD symptoms (18 questions; total score range, 0–54). To assess the asthma and allergic rhinitis symptom severity the adjusted CARAT questionnaire was used (7 questions; total score range, 0–21). The CARAT questionnaire is a validated and consistent way to measure asthma and allergic rhinitis symptoms [
8]. Currently, the Adapt Asthma application, which is based on the CARAT, is already in use to monitor asthma and rhinitis symptoms [
9]. The questions and answer options of the SNAP and the CARAT questionnaire were adapted for daily measurement by changing the phrasing and time periods of the original questions were referring to. In total, parents needed to answer seven questions for atopy and eighteen questions for ADHD daily, with different response categories per question.
Covariates
Co-variables like age, gender, sleep problems, and medication use were determined during inclusion and as part of the daily measurement. To address the possible involvement of sleep problems, as suggested by the previous research into atopic eczema and ADHD [
10,
11], in the fluctuations in ADHD symptoms and atopic symptoms, we added eight questions concerning assessment of daytime sleepiness selected from the CSHQ questionnaire (8 questions; total score range, 7–31) to the daily diary. Higher scores reflect worse sleep. The questions and answer options of the CSHQ questionnaire were adapted for daily measurement during daytime by changing the phrasing and time periods the original questions were referring to. In addition, items on medication use of both atopic and ADHD medication were added to the daily diary (‘How often did your child take a higher dosage of its regular medication due to allergic rhinitis and/or asthma?’; ‘How often did your child take a higher dosage of its regular medication due to ADHD symptoms?’; total score range, 0–3) to account for the possible effects of fluctuations in medication use on symptom expression in the models. Sleep problems and medication use were added as a covariate instead of a confounder, because of the association reported between ADHD and atopic diseases independent of sleep and medication [
4].
Statistical analyses
A vector autoregressive (VAR) model was used to investigate the dynamic associations between changes in symptoms in each individual participant as well as the possible involvement of covariates in this association [
12]. An important feature of the VAR model is the possibility to examine the temporal dynamics between multiple time-series, which allows studying the temporal order of the association between atopy and ADHD symptoms accounting for potential bidirectional effects and effects of time-varying covariates like sleep problems and medication use [
12,
13]. Another important feature of the VAR technique is the ability to separate the dynamic longitudinal part from the simultaneous part of the associations between the variables and to correct for potential feedback effects [
12].
A VAR model consists of a set of regression equations, in which each of the variables is regressed on its own lagged values (autocorrelation) as well as the lagged values of the other variables (cross-lagged associations) [
19]. We build VAR models with two endogenous variables: atopy symptoms and ADHD symptoms. The variable sleep problems were added to the primary model as an extra endogenous variable, because sleep can influence and can be influenced by atopy and ADHD symptoms. Medication use was added to the model as an endogenous variable if there was variation in medication use during the follow-up period. We first investigated the optimal lag number to be used in each of the models (a lag = 1 day), according to a comparison of the final prediction error of each lag model. Since VAR models assume stationarity, we subsequently compared four different types of VAR models (constant, trend, both, and none) to determine if an additional trend or intercept term was needed in the model. Finally, we selected the optimal model with the Akaike Information Criterion (AIC) based on the smallest value of AIC, a measure of relative quality of the fitted model.
To assess the temporal order of the association between atopy and ADHD symptoms, and the possible involvement of sleep problems therein, we determined the independent cross-lagged associations between each variable. In addition, we assessed the contemporaneous correlations between symptoms of atopy, ADHD, and sleep problems per participant to determine the simultaneous associations between (or co-occurrence of) the expression of symptoms. These can be computed from the residuals of the VAR model [
19]. A
p value ≤ 0.05 was considered to be statistically significant. Per individual model, multiple diagnostic tests were performed to test for stability and homoscedasticity of the model [
14]. For six out of the participants, variables were log-transformed for either the score of atopy (participants 10, 11, 13, and 16) or for both atopy and sleep (participants 2 and 3), because the score itself is not normally distributed as observed by the histogram. Models were fitted in R (R Foundation for Statistical Computing, software version 3.4.0, Vienna, Austria) using the package vars.
p values < 0.05 were considered to denote statistically significant associations and
p values < 0.10 were considered to denote the trend of associations.
Simulation studies have shown that, for VAR modeling, a minimum of 30 time points is needed, although larger numbers of observations yield more reliable results [
14]. We chose for a time-series length of 50 measurement points taking into account the possibility of missing data. Missing values on the daily sum scores of ADHD, allergy, and sleep were dealt with using multiple imputations on the individual level [
15]. Considering the percentage of the missing measurements per participant, we obtained five imputed data sets for participants 1, 2, 3, 4, 9, 10, 11, 13, and 16, ten imputed data sets for participants 5, 7, 15, 17, 18, and 21, and 15 imputed data sets for participants 19. The imputed disease ratings were then computed by taking the average scores generated in each imputation. Subsequently, ADHD ratings were calculated by summing up the separate inattentive score and hyperactive score.