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Dynamics of respiratory symptoms during infancy and associations with wheezing at school age

Children with frequent respiratory symptoms in infancy have an increased risk for later wheezing, but the association with symptom dynamics is unknown. We developed an observer-independent method to characterise symptom dynamics and tested their association with subsequent respiratory morbidity. In this birth-cohort of healthy neonates, we prospectively assessed weekly respiratory symptoms during infancy, resulting in a time series of 52 symptom scores. For each infant, we calculated the transition probability between two consecutive symptom scores. We used these transition probabilities to construct a Markov matrix, which characterised symptom dynamics quantitatively using an entropy parameter. Using this parameter, we determined phenotypes by hierarchical clustering. We then studied the association between phenotypes and wheezing at 6 years. In 322 children with complete data for symptom scores during infancy (16 864 observations), we identified three dynamic phenotypes. Compared to the low-risk phenotype, the high-risk phenotype, defined by the highest entropy parameter, was associated with an increased risk of wheezing (odds ratio (OR) 3.01, 95% CI 1.15–7.88) at 6 years. In this phenotype, infants were more often male (64%) and had been exposed to environmental tobacco smoke (31%). In addition, more infants had siblings (67%) and attended childcare (38%). We describe a novel method to objectively characterise dynamics of respiratory symptoms in infancy, which helps identify abnormal clinical susceptibility and recovery patterns of infant airways associated with persistent wheezing.

The absolute frequencies from this table were then replaced by the corresponding relative frequencies (empirical probabilities). The entries in this table can be interpreted as conditional probabilities. For example, if a given infant is currently displaying symptoms corresponding to state x, then the probability that the symptoms will progress to symptom state y is given by the corresponding entry in this matrix ( Figure 1C). Such a table of conditional probabilities is referred to in mathematics as a Markov matrix. [5] Each row in this matrix encodes a discrete probability distribution, namely the probability to progress from a given state to any other of the possible five states. We calculated the average estimated entropy [6] of all the conditional probability distributions defined by the rows of the participant's Markov matrix. This average estimated entropy gives a quantitative measure for the irregularity of the patterns of symptom deterioration and recovery of a given infant. The entropy was estimated using the maximum likelihood estimator, which results from the substitution of the empirical probabilities (i.e. the entries in a given row of a Markov matrix) into the Shannon entropy formula: Where p ji denotes the entries in row j of the Markov matrix, and i is the symptom state score (0→4). When single empirical probabilities p ji happen to be equal to zero, the corresponding term in the above formula is set equal to zero, which corresponds to taking the limit lim →0 log . However, when all entries in an entire row of a given Markov matrix are equal to zero, i.e., when a certain symptom state was never reported or observed during the time window of observation, then the above formula no longer applies, due to the complete lack of information about the corresponding conditional probability distribution. In such cases, the rows consisting of only zero's do not contribute to the calculation of the average entropy.

Additional methods for statistical analysis
The Shannon entropy is defined as the average amount of information needed to specify the state of a random variable governed by a given probability distribution. In the context of statistical physics it can be interpreted as a measure of disorder within a system; higher entropy values correspond to a higher irregularity. [7] For each infant, we calculated the average estimated entropy [6] of all the conditional probability distributions defined by the rows of the participant's Markov matrix. This average estimated entropy gives a quantitative measure of the irregularity in the patterns of symptom deterioration and recovery of a given patient. We used the parameter average entropy to identify phenotypes using the software R version 3.0.2 (http://www.R-project.org) [8] and applying hierarchical clustering. To this end, the separation between entropy values was calculated using the Euclidean distance, and the agglomeration procedure was done according to Ward's minimum variance method. The optimal number of phenotypes was determined based on the majority of indices using the R-package "NbClust". [9] Previous phenotyping studies used symptom occurrence (e.g. rhinitis and wheeze) rather than symptom dynamics during infancy. [10][11][12] Therefore, in order to compare our finding to previous studies, we defined similarly sized "reference phenotypes" based on the frequency distribution of the total number of symptom weeks during infancy.
Using logistic regression analysis, we studied the association of the symptom dynamic phenotypes, the reference phenotypes, and known asthma risk factors (e.g. sex, maternal asthma), with the child's outcomes at six years.
For any wheezing, current wheezing, atopic disease, URTI, and positive prick test of the child, we adjusted the analyses for sex, maternal education, maternal asthma, ETS exposure, childcare, and presence of siblings. For the outcome FeNO, we additionally adjusted for the child's hay fever and inhaled corticosteroid use. For lung function, analyses were adjusted for maternal education, maternal asthma, ETS exposure, childcare, and presence of siblings.
[13] Differences in the distribution of characteristics across phenotypes were assessed using Chi-squared tests for categorical variables, and Kruskal-Wallis for continuous variables, and a Bonferronicorrected significance level was used to account for multiple pair-wise testing. We used the weighted kappastatistic [14] to compare agreement between the symptom dynamic and reference phenotypes. For sensitivity analyses, we repeated the analysis in infants who had ≥one episode of symptom score ≥three, and also within an additional, independent sample from our cohort of 242 infants. In order to explore whether the entropy distribution found was an artefact of our analysis, we re-categorized the symptom states (0, 1, 2, (3+4)→3), simulated data, and perturbed the existing data. Analyses were done using Stata 11.2 software (StataCorp, College Station, Tex), figures using Matlab R2015b (The MathWorks, Inc., Natick, MA, USA).

Additional methods for sensitivity analysis
We performed several sensitivity analyses: 1) We repeated the analysis in infants having ≥one episode of symptom score ≥three.
2) Robustness of the identified phenotypes was investigated within an additional, independent sample from our cohort of 242 infants. This sample included infants not seen for follow-up, and hence, these infants were not included in the main analysis in the first place. This sample served as an independent data set for an external validation of the method.
3) To explore whether the distribution of entropy was an artefact of our analysis approach, we re-categorized the symptom states (0, 1, 2, (3+4)→3), simulated different data sets, and perturbed the existing data sets. 4) To the best of our knowledge, this is the first prospective cohort reporting respiratory symptoms during infancy at such a high resolution and accuracy. However, in theory, or in clinical practice, some symptomatic transitions may not be reported or acquired. The aim of this sensitivity analysis was to investigate the effect of correcting for potentially unobserved events. In particular, we hypothetically investigated the scenario of analysingwith our methoda population at higher risk for respiratory symptoms compared to our study population. To this end, we estimated the average entropy using an estimator that takes into account the issue of unobserved events (Schuerman and Grassberger). [15] Within this approach, unobserved or unreported symptom transitions are artificially introduced into the data set according to the expected value of a 'posterior' distribution of event occurrences resulting from a Bayesian analysis [16] of the data set. However, for the sake of consistency, when all entries in an entire row of a given Markov matrix were equal to zero, i.e., when a certain symptom state was never reported or observed during the time window of observation, then, such a row did not contribute to the calculation of the average entropy using the Schuerman and Grassberger [15] estimator. These calculations were done using the R-package "entropy". [17]

RESULTS
Additional results for sensitivity analysis 1) We obtained similar results in infants with ≥one episode of symptom score ≥three (data not shown).
2) In the validation dataset of 242 infants, symptom dynamic phenotypes included 80, 132, and 30 infants, respectively. Phenotypes 1, 2, and 3 had 0.23, 0.79, and 2.03 weeks with severe symptoms, respectively. Risk factors differed across phenotypes: phenotype 1 had an underrepresentation of infants who attended childcare. Phenotype 2 had fewer infants of asthmatic mothers. Phenotype 3, the smallest group, had an overrepresentation of infants born via Caesarean section, and more infants had atopic mothers. Reference phenotypes included 83, 108, and 51 infants, respectively. Phenotypes 1, 2, and 3 had 0.16, 0.68, and 1.91 weeks with severe symptoms, respectively. Phenotype 1 had an underrepresentation of infants with siblings and less infants attended childcare. In phenotype 2, infants were more likely born via Cesarean section. Phenotype 3 had an overrepresentation of males, and more infants had siblings (Table E5).
3) The outcomes of the following sensitivity analysis ruled out the possibility of an artefact in our methodology. Re-categorization of the states (0, 1, 2 (3+4)→3), did not systematically change the average entropy distribution and the identified phenotypes (data not shown). The distribution of the average estimated entropy from the original cohort ( Figure E2A) did not show up in a simulated dataset in which all possible symptom transitions were assumed to be equally likely ( Figure E2B). We perturbed the existing data by shuffling and thereby randomly altering the chronological order of each patient's reported symptoms. The resulting distribution of the average entropy remained qualitatively very similar to the one observed in the unperturbed data ( Figure E2C). This is not surprising, as our method captures the patterns of symptom deterioration and recovery, and not necessarily the temporal symptom pattern. A multimodal distribution was observed when the data was simulated in such a way that the probability of any given symptom transition was determined by the pooled, existing data of the cohort. However, the shape of the distribution changed considerably in this simulated dataset ( Figure  E2D). 4) As elucidated above, we repeated the entire analysis taking into account the issue of unobserved events. [15] After this correction for unobserved events, the analysis of the resulting distribution of entropy values yielded four phenotypes. These phenotypes included 124, 79, 87, and 32 infants, respectively. Phenotypes 1, 2, 3, and 4 had 0.9, 1.2, 0.2, and 0 weeks with severe symptoms. Risk factors differed across phenotypes: phenotype 1 had less infants exposed to tobacco smoke exposure. Phenotype 2 had more males, more infants attended childcare, and more infants had siblings. Fewer infants in phenotype 3 had siblings, and infants were more likely born via Caesarean section. Phenotype 4 had less male infants, more infants were born to atopic mothers, and less infants attended childcare. We considered phenotype 2 a high-risk phenotype, since the prevalence of current wheezing (17%) at six years was the highest. However, compared to the high-risk dynamic phenotype originally obtained, the prevalence of wheezing was proportionally lower. Regarding the association with wheezing at six years, the following changes were observed: in the adjusted logistic regression model, compared to phenotype 1, there was no significant association with current wheezing (adjusted odds ratio; 95% CI) (1.05; 0.44-2.47) at six years of age, compared to significant associations in the high-risk phenotype originally obtained. The sensitivity analyses as described in the previous section 3 were equally applied in the dataset after taking into account the issue of unobserved events ( Figure E3). To summarize, we can conclude that the resulting phenotypes, and their characteristics, do depend on the distribution of symptom severity in the population studied, and on the quality and completeness of the data acquired. In light of this theoretical result, we believe that in a proof-of-principle study, like the present study, further validation using an additional cohort would not necessarily extend our insights. Such a validation in an additional cohort would most likely display a different distribution of symptom severity and may contain more missing values. Data are given as mean ± standard deviation or absolute numbers (percent). Children younger than 5 years were not enrolled for follow-up at 6 years. P-values are for comparison between subjects lost to follow-up, and those who were followed-up. We used the Chi-squared tests for categorical variables, and Kruskal-Wallis for continuous variables. CI: confidence interval; OR: odds ratio. Logistic regression for the outcome wheezing between two and three years of age. Symptom dynamic phenotypes were defined by entropy of transition states, reference phenotypes by weeks with any respiratory symptom. When considering phenotypes as exposure, phenotype one from the reference phenotype, or symptom dynamic phenotype served as baseline, respectively. Numbers in brackets indicate group sizes. # Adjusted for the following binary variables: male gender, low maternal education, maternal asthma, maternal smoking during pregnancy, childcare attendance during infancy, and presence of siblings. + Defined as any wheezing episode between two and three years of age. Symptom dynamic phenotypes were defined by entropy of transition states, reference phenotypes by weeks with any respiratory symptom. When considering phenotypes as exposure, phenotype one from the reference phenotype, or dynamic phenotype, served as baseline, respectively. Numbers in brackets indicate group sizes. * Adjusted for the following variables: male gender, low maternal education, maternal asthma, maternal smoking during pregnancy, childcare attendance during infancy and presence of siblings. Lung function parameters are expressed as z-scores according to Qanjer et al.. [3] FeNO was log-transformed before analyses. Symptom dynamic phenotypes were defined by entropy of transition states, reference phenotypes by weeks with any respiratory symptom. Phenotype one from the reference phenotype, or symptom dynamic phenotype, served as baseline, respectively. Numbers in brackets indicate group sizes. * Adjusted for the following binary variables: maternal education, maternal asthma, maternal smoking during pregnancy, childcare attendance during infancy and presence of siblings. + Additionally adjusted for the following binary variables: sex, hay fever of the child, inhaled corticosteroid use.   The entropy in all four panels was estimated after applying the Schuerman and Grassberger (SG) algorithm. [15]