A log-normal distribution model of the effect of bacteria and ear fenestration on hearing loss: a Bayesian approach

Chronic ear infection is a potentially life-threatening illness that medical doctors typically treat with ear surgery. Despite the success of this treatment, complications can occur due to bacteria infection. Surgeons believe that this infection causes the patient to have clinically significant hearing damage. In order to understand such complications, surgeons must quantify the effect of bacteria, their toxins and ear surgery on hearing loss. To this end, the other two authors of this paper performed two experiments on guinea pigs to measure hearing thresholds following a bacterial infection and surgery of the inner ear. The response variable in these experiments is hearing thresholds measured in decibels (dB). The problem in analysing such experiments is that the hearing threshold observations often suffer from missing data and censoring mechanisms of various types. Additionally, the distribution of hearing thresholds has heavy tails and is peaked. In order to account for the above statistical issues, we present a Bayesian method with a location-shifted log-normal distribution. The method accounts for the uncertainty in the data collection mechanism and the parameters associated with a location-shifted log-normal distribution. We refer to one of the parameters as the "location-shift" parameter. The Bayesian approach provides a posterior distribution of the location-shift parameter that we compare with values estimated in previously published studies. The immediate goal of our proposed method was to quantify the effects of ear surgery and bacteria infection on hearing loss. Thus, we present the merits of the method in the form of a case study, and report posterior distributions of mean hearing loss, probability of clinically significant hearing loss and relative risk. The results show that surgeon 2, using the surgical procedure "oval window", poses a greater than 40 per cent chance of a 15dB hearing loss regardless of injection of bacteria or not. However, surgeon 1, using the surgical procedure "semicircular canal", does not pose a significantly greater than 40 per cent chance of a 15dB hearing loss unless there is a Pseudomonas aeruginosa-induced infection.