Fig. 1

Sample pertussis case clinical histories, to illustrate data limitations, biases and truncation. These six cases are illustrative of the general timeline of symptom development and clinical care. Time zero is the day of cough onset. Some cases seek medical attention because of a potential exposure (Cases 5 and 6). While both receive antibiotics prior to cough onset, but only case 6 received truly prophylactic treatment. However, this analysis cannot reliably distinguish between these cases in the prophylactic group of observed cases. The cough lengths of such estimates are included in the observed estimates. However, the theoretical analysis cannot distinguish any prophylactic cases from those who received medical treatment in Week + 1 (Case 1). The analysis of this paper created a dataset that replicated the distribution of cough duration (black lines) based on the mean and standard deviation of the natural log transformed surveillance data. The date of drug treatment is our proxy for first medical visit, and is the potential source of bias we are testing as cases are both identified and subsequently stratified on this time point. By calculating the mean of the theoretical distribution we estimated the average cough for anyone who could visit the doctor in the first week of cough. By excluding cases, we can determine who is still eligible to have their first drug treatment in Week + 2. Therefore we must exclude all individuals who already sought care (Cases 1, 5 and 6); this is care-seeking bias. Additionally individuals who have already stopped coughing would also be excluded; this is case exclusion bias (Case 0). This process of excluding cases with events to the left of the cut-point is call left-truncation. By calculating the mean cough length of everyone remaining in the theoretical population after truncation, we can estimate the new mean duration of those who are eligible to see the physician in Week + 2