#### Correcting mortality for loss to follow-up

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 (*M*_{C }) in patients that started ART is the average of mortality in patients retained in care (not lost to follow-up, *M*_{NL}) and mortality in patients lost to follow-up (*M*_{L} _{}), weighted by the proportion of patients lost to follow-up (*r*):

*MC* = (1-*r*)**M*_{NL} + *r***M*_{L}_{}

*M*_{NL} 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). * M*_{L} _{}can then be estimated by tracing a representative sample of patients lost to follow-up to ascertain their vital status (tracing method). Note that *M*_{NL}, *M*_{L} _{}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,* M*_{L}_{}at 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 *M*_{NL}, and *r *must refer to one year after starting ART.

**Go to calculator **using meta method...

##### Further technical details

Estimates of *M*_{c} with 95% confidence intervals are derived using Monte Carlo simulations with 10,000 iterations. These simulations allow for uncertainty in* M*_{NL}by 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 (*N*_{L}) given the number at risk of loss to follow-up (*N*_{R}). The tracing method estimates *M*_{L} similar to *M*_{NL}, 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 (*N*_{R}), 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 *N*_{R}.

For further detail see *Egger et al. 2011*.