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In vitro quantitation of Theileria parva sporozoites for use - TropMed ...

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50 Chapter 3: <strong>Theileria</strong> <strong>parva</strong> extraction methods<br />

______________________________________________________________________________________________<br />

Table 2: Titration sessions <strong>for</strong> comparison <strong>of</strong> extraction methods. M-manual, H-homogeniser<br />

Stabilate<br />

Session M1 M2 H1 H2<br />

1 48 48<br />

2 71 72<br />

3 72 72<br />

4 93 91<br />

5 88 95<br />

6 48 48<br />

TOTALS 212 208 215 211<br />

3.2.4. Statistical analysis<br />

For the comparison <strong>of</strong> extraction methods, the binary results were analysed using a random effect<br />

logistic regression in Stata ® (Stata/SE 8.0 <strong>for</strong> Windows Statistical S<strong>of</strong>tware. Stata Corporation,<br />

Texas). The proportion <strong>of</strong> positive wells was the response variable and the logarithm <strong>of</strong> the stabilate<br />

concentration and the method <strong>of</strong> extraction were <strong>use</strong>d as explanatory variables.<br />

The test session was taken as a random effect given the importance <strong>of</strong> the clustering effect within<br />

test sessions (Marcotty et al., 2004). The model can be written as follows:<br />

⎛ π ⎞<br />

log ⎜ ⎟ = α + β<br />

ln( t . e.)<br />

× ln( t.<br />

e.)<br />

+ β<br />

⎝1−<br />

π ⎠<br />

method<br />

× method<br />

+ ν + ε<br />

where π is the proportion <strong>of</strong> positive wells, α a constant, ln(t.e.) the natural logarithm <strong>of</strong> the<br />

sporozoite dose in tick-equivalents, β ln(t.e.) the coefficient <strong>of</strong> the stabilate dose, method the method<br />

<strong>use</strong>d (0 <strong>for</strong> homogenizer and 1 <strong>for</strong> hand-extraction), β method the coefficient <strong>of</strong> the method, n the<br />

cross-sectional random effect <strong>of</strong> the session and e the residual error.<br />

The coefficients <strong>of</strong> the model were <strong>use</strong>d to estimate ED 50 , the dose that is effective in 50% <strong>of</strong> the<br />

cases, <strong>for</strong> the two methods:<br />

ln<br />

( ED )<br />

50<br />

α + β<br />

method<br />

× method<br />

= −<br />

β<br />

ln( t.<br />

e.)<br />

A comparison <strong>of</strong> the sporozoite yield by the multiplicative model <strong>of</strong> the ratio ED hand /ED machine was<br />

then made by non-linear combinations <strong>of</strong> estimators:<br />

ln<br />

β<br />

⎛<br />

− = −<br />

method<br />

ED ⇒<br />

hand = ⎜<br />

β −<br />

method<br />

machine<br />

exp<br />

β<br />

ln( t.<br />

e.)<br />

EDmachine<br />

⎝ β<br />

ln( t.<br />

e.)<br />

( ED ) ln( ED )<br />

hand<br />

⎞<br />

⎟<br />

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