Propensity Score Methods
As corticosteroid use was not randomly assigned to each encounter, we created a propensity score model 11 for steroid prescription in order to account for potential confounding and selection bias; we used the propensity score estimated from this model to create our PS-matched sample. In this study, the propensity score was the conditional probability that a patient would receive a steroid during their hospitalization, given a set of covariates. For each of our encounters, we estimated the propensity for steroid prescription using a non-parsimonious multivariable logistic regression model (C statistic= 0.8779). We used the following variables in our propensity score model: sex, genotype, inhaled steroids, IgE value, asthma, reactive airway disease or impaired glucose tolerance diagnosis, best baseline spirometry, admission FEV1, change from baseline to admission FEV1, change from admission to midpoint FEV1, change in antibiotics treatment during hospitalization, positive fungal sputum culture, history of nontuberculous mycobacteria, and bacteria present in sputum cultures.
As some patients were represented more than once in our study sample, we initially modeled the propensity score using a random-effects logistic regression model. Likelihood ratio tests indicated that the random-effects model did not outperform the traditional logistic regression model. As well, the estimated ICC from the random-effect model indicated that the odds of steroid administration was only slightly correlated within the individual patient. As few propensity score methodologies and applied works exist using clustered data12, and greater than half of our patient pool was represented by one encounter (54%; only 26% of patients had >=3 encounters), we chose to use a traditional logistic regression when estimating our propensity score and a simple matching algorithm when matching encounters.
We matched encounters 1:1 using a greedy algorithm on the logit of the propensity score and a caliper width of 0.2 the standard deviation of the logit of the propensity score. This resulted in a PS-matched sample of 25 non-steroid encounters and 25 steroid encounters, representing 19 and 17 patients in each group, respectively. We evaluated the balance in the distribution of encounter characteristics between the two groups using t-tests or Somers’ D for continuous variables and chi-square tests for categorical variables; we adjusted these tests for clustered errors as described in the previous section. When modeling the association between our outcomes and steroid administration, we used this PS-matched sample to compare our outcomes among encounters with equivalent likelihood of corticosteroid prescription. All analyses were conducted in Stata/SE, version 15 (StataCorp, College Station, TX).