Analysis of correlated bronchial responsiveness data

Abstract

Correlated survival data analysis techniques were utilized to determine the efficacy of such techniques to analyze correlated airway responsiveness data. When the survival data are correlated, standard maximum likelihood estimates of the regression coefficients obtained by using the Cox’s model are consistent, but the estimates of standard errors may not be valid or consistent due to within-subject dependencies and hence give rise to wrong interpretations. We used jackknife, bootstrap and the method proposed by Wei, Lin and Weissfeld (WLW) to obtain robust estimates for the standard errors. The data analyzed in this report were obtained from a longitudinal study conducted to investigate the respiratory health effects of initial exposure to grain dust among workers commencing employment in the grain industry in the province of Saskatchewan, Canada. Bronchial responsiveness was determined by histamine inhalation test administered at four different time points. The provocation concentration ( ${\mathrm{PC}}_{20}$ ) of inhaled histamine that produced 20% fall in the lung function parameter forced expired volume in one second ( ${\mathrm{FEV}}_1$ ) was used as an indicator of bronchial responsiveness. Failure was defined as the dose of histamine at which a 20% fall in ${\mathrm{FEV}}_1$ occurred. In provocation tests, censored data may occur due to the failure to reach a determined end point. Censoring occurred when a subject did not have 20% fall in ${\mathrm{FEV}}_1$ with the maximum histamine dose of 8 mg. Significant predictors of bronchial responsiveness were ${\mathrm{FEV}}_1$ , wheezing and height. The estimates of standard errors were similar for jackknife, bootstrap, and WLW, but different from those obtained using standard maximum likelihood method.