Trajectories of Antibiotic Use in Early Life as a Marker of Susceptibility to Asthma

Trajectories of Antibiotic Use in Early Life as a Marker of Susceptibility to Asthma

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## Trajectories of Antibiotic Use in Early Life as a Marker of Susceptibility to Asthma

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**Danielle Belgrave - PhD Student - Work in Progress**Trajectories of Antibiotic Use in Early Life as a Marker of Susceptibility to Asthma A Comparison of the Bayesian and Frequentist Approach**Background**• Antibiotic exposure associated with development of asthma • By interfering with bacterial gut flora • By modifying the course of bacterial infections. • Further research required to determine whether observed associations are causal, the result of confounding by indication or reverse causation • Impact of antibiotic use on asthma as causal analysis**Hypothesis**• Antibiotic use rather than being causally related to asthma may be a prognostic indicator of susceptibility to infections • Antibiotic use picks up a signal of something that occurs very early in life, and which is completed by 24 months of age or is a stable feature • Children can be characterized in terms of susceptibility based on patterns of antibiotic use • This phenotype is predictive of contemporaneous and future asthma and wheeze symptoms**Objectives**• To establish homogeneous susceptibility classes based on differences in monthly patterns of Antibiotic use in the first 2 years of life, while considering the impact of associated factors using longitudinal latent class analysis • To validate latent phenotypic classes using external covariates • Compare Frequentist and Bayesian Machine Learning approaches to this analysis**Data Description**• Manchester Asthma and Allergy Study • Population-based birth cohort study • 1185 subjects were recruited prenatally and followed prospectively • Antibiotic and Paracetamol prescriptions and symptoms of asthma/wheezing from the primary care medical records of 916 children • Oral Steroid • Hospital Admission • Exacerbation • Asthma/ Wheeze events**Statistical methods**Frequentist Approach**Latent Class Analysis (1)**• Children’s susceptibility characterized using latent class model • Assume that each child belongs to one of a set of N latent classes, with the number of classes and their size not known a priori • Other than random temporal fluctuation, each child’s pattern of antibiotic use is to be explained by their belonging to a particular class of susceptibility • Children in same class are similar with respect to the observed variables in the sense that their observed scores are assumed to come from the same probability distributions**Latent Class Analysis (2)**• Latent Classes are homogeneous • Longitudinal Logistic Regression Model • Predicted antibiotic use at each month was given by a logistic model with predictors : • Age • Child attended nursery before receiving their first antibiotic • Number of older siblings • The susceptibility latent class**Latent Class Analysis (3)**• Trajectory model: allows us to hypothesize that there may be subgroups of children who have changing levels of susceptibility over time • Random-intercept model: assume relative susceptibility remained constant over time Logit{Pr(yij= 1| x, ci = k)} = β0+ β1[t] + β2[tstart of day-care] + +β3[has older siblings] + ξk+ ξk[t] yij= Event of antibiotic use for child i at time j Pr(ci= k) is multinomial over k classes and independent across children**Latent Class Analysis (4)**• Bayesian Information Criteria (BIC) goodness-of-fit statistics for ascertaining the “best” model with respect to number of classes and time complexity • BIC: a measure that combines the log-likelihood value with the number of parameters, penalizing models with additional parameters. • Validation Model: Cox regression model to asthma or wheeze occurrence using the latent class phenotypic definition of susceptibility as a predictor**Cox Regression Model**• Question: Does susceptibility represent a higher risk of asthma severity? • A framework for investigating event occurrence • Examines whether variation in the risk of event occurrence varies systematically with predictors • Features of the data:- • We know the precise instant when events occur • There exist an infinite number of these events because any division of continuous time can always be made finer • The probability of observing any particular event time is infinitesimally small and approaches 0 as time’s divisions get finer**Describing Event Occurrence**• Survival Function: S(tij) = Pr(‘surviving’ longer than time t) = Pr(Ti > tj) T is a continuous random variable Tiis individual i’s event time tjclocks the infinite number of instants when events can occur • The survival probability for individual i at time tj is the probability that his/her event time will exceed tj**Describing Event Occurrence**• Hazard Function: Assesses the conditional risk – at a particular moment – that an individual who has not yet done so will experience the event • Cumulative Hazard Function: Assesses at each point in time, the total amount of accumulated risk that individual i has faced from the beginning of time until the present**Cox Regression Model**• Proportional hazards assumption: the hazard for any individual is a fixed proportion of the hazard for any other individual log h(tij) = logh0(tij) + βClassi h(tij) = h0(tj)eβClassi • Assumptions • For each value of the predictors there is a postulated log hazard function • Each of these log hazard functions has an identical shape • The distance between each of these log hazard functions is identical at every instant**Latent Classes and Asthma/Wheeze in First 3 Years of Life**(Time to 1st Event) • Risk of Asthma/Wheeze increases • with increasing susceptibility class • Hazard of asthma/wheeze for • children with ‘high susceptibility’ 3.6 times • than for ‘resilient’ class (p<0.001) • Hazard of asthma/wheeze for children • with ‘high susceptibility’ 1.7 times than for • ‘normal immune response’ class (p<0.001)**Latent Classes and Asthma/Wheeze After Age 3 (Time to 1st**Event) • Risk of Asthma/Wheeze increases • with increasing susceptibility class • Hazard of asthma/wheeze for children • with ‘high susceptibility’ 2.7 times than for • ‘normal’ class (p<0.005) • Hazard of asthma/wheeze for children • with ‘high susceptibility’ 1.7 times than • for ‘normal immune response’ class • (p<0.005)**Latent Classes and Asthma/Wheeze Exacerbation in First 3**Years of Life • Risk of exacerbation increases with • increasing susceptibility class • Hazard of exacerbation for children • with ‘susceptibility to infection’ 5 times • than for ‘resilient’ class (p<0.001) • Hazard of exacerbation for children with ‘susceptibility to infection’ 1.93 times than • for ‘medium susceptibility’ class (p<0.01)**Latent Classes and Asthma/Wheeze Exacerbation After Age 3**• Risk of exacerbation not significantly • different for low susceptibility groups • Hazard of exacerbation for children • with ‘susceptibility’ 2.7 times than for • ‘resilient’ class (p<0.005) • Hazard of exacerbation for children with ‘high susceptibility’ 1.9 times than for • ‘normal’ class (p=0.02)**Confounding By Indication?**Pearson χ²= 4.8772 Pr = 0.560**Statistical Analysis**Alternative Approach: Bayesian Machine Learning using Infer.NET**Classification-Bayesian Machine Learning**• Quantify uncertainty in model parameters by defining a prior belief of that parameters: uninformative conjugate priors • Assume that each child belongs to one of a set of N latent classes, with the number of classes and their size not known a priori • Children in same class are similar with respect to the observed variables in the sense that their observed scores are assumed to come from the same probability distributions**Mixture of Continuous-Time Logistic Regressions**Logit{Pr(yij= 1| x, ci = k)} = βk+ β1kt +β2k[tstart of day-care] +β3k[has older siblings] Dir. p N Disc. c M C x V. Gauss. Dot Prod. b Ranges: N: Child C: Susceptibility M: Month Gauss. Variables: c: Latent class of child x: Feature vector (observed) (incl. bias, month in time window) b: Parameter vector y: Antibiotic use (observed) Logist. y**Hierarchical Mixture of Continuous-Time Logistic Regressions**Dir. V. Gauss. p m N Disc. C c V. Gauss. M b x Dot Prod. Ranges: N: Child C: Susceptibility M: Month Gauss. Variables: c: Latent class of child x: Feature vector (observed) (incl. bias, month in time window) b: Parameter vector m:Shared mean of parameter vector y: Antibiotic use (observed) Logist. y**Mixture of Discrete-Time Logistic Regressions**Dir. Logit{Pr(yij= 1| x, ci = k)} = βkj+ β1kjt +β2kj[tstart of day-care] +β3kj[has older siblings] p N Disc. c M x C Dot Prod. V. Gauss. Ranges: N: Child C: Susceptibility M: Month b Gauss. Variables: c: Latent lass of child x: Feature vector (observed) (incl. bias) b: Parameter vector y: Antibiotic use (observed) Logist. y**Hierarchical Mixture of Discrete-Time Logistic Regressions**Dir. p V. Gauss. N m Disc. c M x C Dot Prod. V. Gauss. Ranges: N: Child C: Susceptibility M: Month b Gauss. Variables: c: Latent lass of child x: Feature vector (observed) (incl. bias) b: Parameter vector m: Shared mean of parameter vector y: Antibiotic use (observed) Logist. y**Results**• Resilient Class: Probability of receiving antibiotics increases over 1st 9 months and then decreases till age 24 • Susceptible Class: Probability of receiving antibiotics increases over 1st8months and then decreases till age 24**Logit{Pr(yij= 1| x, ci = k)} = βkw+ β1kw**+β2kw[tstart of day-care] +β3kw[has older siblings] Mixture of Piecewise-Linear Logistic Regressions Dir. p N Disc. W c M x C Dot Prod. V. Gauss. b Ranges: N: Child C: Susceptibility W: Time Window M: Month in Time Window Gauss. Variables: c: Latent class of child x: Feature vector (observed) (incl. bias, month in time window) b: Parameter vector y: Antibiotic use (observed) Logist. y**Hierarchical Mixture of Piecewise-Linear Logistic**Regressions Dir. V. Gauss. p m N Disc. C c W V. Gauss. x M b Dot Prod. Ranges: N: Child C: Susceptibility W: Time Window M: Month in Time Window Gauss. Variables: c: Latent class of child x: Feature vector (observed) (incl. bias, month in time window) b: Parameter vector m: Shared mean of parameter vector y: Antibiotic use (observed) Logist. y**Latent Classes and Asthma/Wheeze in First 3 Years of Life**(Time to 1st Event) • Hazard of asthma/wheeze for susceptible class 2.2 times than for ‘normal’ class • (p<0.001) • Hazard of asthma/wheeze for • children with ‘high susceptibility’ 3.6 times • than for ‘resilient’ class (p<0.001) • Hazard of asthma/wheeze for children • with ‘high susceptibility’ 1.7 times than for • ‘normal immune response’ class (p<0.001)**Latent Classes and Asthma/Wheeze After Age 3 (Time to 1st**Event) • Hazard of asthma/wheeze for susceptible class 1.8 times than for ‘normal’ class • (p<0.001) • Hazard of asthma/wheeze for children • with ‘high susceptibility’ 2.7 times than for • ‘normal’ class (p<0.005) • Hazard of asthma/wheeze for children • with ‘high susceptibility’ 1.7 times than • for ‘normal immune response’ class • (p<0.005)**Latent Classes and Asthma/Wheeze Exacerbation in First 3**Years of Life • Hazard of asthma/wheeze for susceptible class 2 times than for ‘normal’ class • (p<0.001) • Hazard of exacerbation for children • with ‘susceptibility to infection’ 5 times • than for ‘resilient’ class (p<0.001) • Hazard of exacerbation for children with ‘susceptibility to infection’ 1.93 times than • for ‘normal susceptibility’ class (p<0.01)