This calculator provides estimates of mortality (with 95% confidence intervals) in ART programmes in sub-Saharan Africa that are corrected for loss to follow-up.
The calculation is based on the fact that overall corrected mortality (MC ) in patients that started ART is the average of mortality in patients retained in care (not lost to follow-up, MNL) and mortality in patients lost to follow-up (ML ), weighted by the proportion of patients lost to follow-up (r):
MC = (1-r)*MNL + r*ML
MNL and r can be observed directly in the ART programme at a given point in time (for example at one or two years after starting ART). ML can then be estimated by tracing a representative sample of patients lost to follow-up to ascertain their vital status (tracing method). Note that MNL, ML and r must refer to the same time period. See Yu et al, 2007 for an example of a tracing study.
Alternatively, in the absence of local tracing information, MLat one year can be estimated based on a meta-analysis (Brinkhof et al, 2009) of published mortality data from tracing studies in sub-Saharan Africa (meta method). Mortality in patients lost to follow-up was inversely associated with the rate of loss to follow up in the programme: it declined from around 60% to 20% as the percentage of patients lost increased from 5% to 50%. Note that when using the meta method MNL, and r must refer to one year after starting ART.
Estimates of Mc with 95% confidence intervals are derived using Monte Carlo simulations with 10,000 iterations. These simulations allow for uncertainty in MNLby sampling from a normal distribution of predicted Kaplan-Meier survival estimates (log-log transformed) at one year, and in r by sampling from a binomial distribution of the number of patients lost to follow-up (NL) given the number at risk of loss to follow-up (NR). The tracing method estimates ML similar to MNL, by sampling from the predicted Kaplan-Meier survival estimates in the sample of successfully traced patients; the meta method samples from the normal distribution of the predicted logit of death in patients lost to follow-up, given the rate of loss to follow-up in the programme.
Calculations of the proportion lost to follow-up should be based on the patients at risk of loss to follow-up (NR), i.e. patients with sufficient potential follow-up time to allow their status to be determined. For example, assuming the definition for loss to follow-up is “no clinic visit for 6 months or more”, then patients starting ART less than 6 months before the end of the observation period can by definition not be lost to follow-up and should be excluded from NR.