deletions | additions       diff --git a/subsubsection_Results_from_national_TB__.tex b/subsubsection_Results_from_national_TB__.tex  index ba3ff39..61c813a 100644  --- a/subsubsection_Results_from_national_TB__.tex  +++ b/subsubsection_Results_from_national_TB__.tex 
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It is not clear which method will perform better as validation would require a measurement of incidence. The second method requires a sufficient number of cases on treatment at the time of the survey (at least 30 cases) to be applied. When the number of cases on treatment is too small, the amount of propagated uncertainty renders estimates of incidence unusable.   If both methods can be applied, results from two methods may be combined in a statistical ensemble approach as follows:  The incidence rate obtained using method i is assumed distributed Beta with shape and scale parameters $a_i + 1$ and $b_i + 1$, respectively, and determined using the method of moments: $I_i \sim B(a_i + 1. b_i + 1)$ so that   $$Prob(x=TB)= \int_{0}^{1} x B(a_i,b_i) dx = \frac{a_i+1}{a_i+b_i+2}$$  The combined probability is then expressed as   $$Prob(x=TB) = \frac{\sum{a_i}+1}{\sum{a_i}+\sum{b_i}+2}$$.