A longitudinal modelling study estimates acute symptoms of community acquired pneumonia recover to baseline by 10 days

Our aims were to address three fundamental questions relating to the symptoms of community-acquired pneumonia (CAP): Do patients completely recover from pneumonia symptoms? How long does this recovery take? Which factors influence symptomatic recovery? We prospectively recruited patients at two hospitals in Liverpool, UK, into a longitudinal, observational cohort study and modelled symptom recovery from CAP. We excluded patients with cancer, immunosuppression or advanced dementia, and those who were intubated or palliated from admission. We derived a statistical model to describe symptom patterns. We recruited 169 (52% male) adults. Multivariable analysis demonstrated that the time taken to recover to baseline was determined by the initial severity of symptoms. Severity of symptoms was associated with comorbidity and was inversely related to age. The pattern of symptom recovery was exponential and most patients’ symptoms returned to baseline by 10 days. These results will inform the advice given to patients regarding the resolution of their symptoms. The recovery model described here will facilitate the use of symptom recovery as an outcome measure in future clinical trials.


Model form
An initial exploratory analysis by Peter Diggle using R (www.r-project.org) led to the derivation of a model with the following functional form:-Time (days) = t If t < 0 CAPsym = δ If t ≥ 0 CAPsym = (α + δ) + (β -α -δ) * e (-t/γ) δ is the pre-pneumonia CAP-sym score recalled from 30 days prior to hospital admission α is the difference between δ (pre-admission CAP-sym) and CAP-sym at recovery β (beta) is the maximum CAP-sym score obtained upon admission γ (gamma) is a rate constant for the decay in CAP-sym score (rate of recovery)

Non-linear mixed effects modelling
Nonlinear mixed effect modelling (NONMEM®, version 7.3, ICON, Dublin) was applied to CAP-sym data and inter-individual variability (IIV) was included on the four parameters using an exponential function e.g. shown for δ:- TVδ is the population estimate of δ η i is the inter-individual variability assumed to have a mean of zero and variance ω 2 Residual variability was described using a combined proportional-additive error model: is the j th model predicted CAP-sym score in individual i ε p and ε a are the proportional and additive model components for individual i and measurement j respectively with a mean of zero and variance σ 2 .

Derivation of recovery time by half-life.
Beginning with the model form described above:i.
Algebraically this means moving (α + δ) to the left hand side in i and ii, so: iii.
(t2 -t1) = ln(2) * γ "gamma half-life" = ln(2) * γ  : degrees of freedom based on χ 2 distribution (corresponds to the number of parameters added or removed from the model); ΔOFV threshold: change in OFV that must be exceeded for a significant addition/removal of parameters from the model; θ 1 : typical or reference value of δ or β; θ 2-6 : changes in δ or β with regards to a specific covariate in comparison to the reference δ or β (θ 1 ); MISSING, ACTIVE, QUIT, FEMALE, COPD, STATIN, SCORE1, SCORE2, SCORE3,4, SCORE1,2, SCORE3,4, SCORE5,6: indicator variables for missing categorical covariates, smoking status, female sex, suffering from COPD, using statins, CURB65 and Charlson comorbidity index groups, taking the value of 1 for the presence of a specific covariate group or otherwise takes the value of 0.