Probit analysis for viral infectivity neutralization

[Andrew Tan-2]

Dear all,

I am assessing the suitability of the SPSS probit analysis technique in
(virus) neutralization experiments. Inputs from both virology and statistics
perspectives would be very much appreciated.

Specifically, we need to determine a vaccine dilution level that will
achieve 50% neutralization. This is measured by viral plaque assays that
provide inputs for the probit analysis that we wish to perform:

Dilution No. of plaques
1:10 0
1:20 0
1:40 0
1:80 0
1:160 4
1:320 10.5
1:640 13
1:1280 15
1:2560 26
1:5120 43.5
1:10240 44

In this experiment, 43 (or more) plaques formed imply no neutralization.

Considering the data that is available,

1. How should we express the dilution factor in SPSS?

Can I express this independent variable "as is", i.e. as a scale variable
with values 0.1, 0.05, ..., 0.0001 to denote the above dilutions? Would data
transformation be necessary?

2. More importantly, how do I express the proportion of responses to
observations?

Performing this analysis in SPSS requires both the number of observations as
well as responses, but in our instance we have only a response-variable (No.
of plaques).

Where assays are involved, it does not seem correct or possible to determine
the total number of observations. How can we then correctly model the
dilution-neutralization function (so as to ascertain the dilution required
for a 50% neutralization, to about 21.5 plaques)?

3. In fact, am I making a mistake to consider neutralization in this
instance as dichotomous? If not, should Neutralization = 1 when plaques
formation is 21.5, or when it is 0?

Any views on probit analysis for such objectives are welcome. If there are
techniques or software that may be more relevant, please let me know.

Thanks very much and regards,

Andrew

[Max Jasper]

Hi Andrew,

Try this Probit:

*-----------------------------------------------------.
PROBIT
  pct.neutral  OF total  WITH dil.inv
  /LOG
  /MODEL PROBIT
  /PRINT FREQ CI
  /CRITERIA P(.15) ITERATE(20) STEPLIMIT(.1) .
*-----------------------------------------------------.

dil.inv = 1/dilution
total=100 for each level of dilution.

It results in a Chi Sq goodness fit Sig = 0.388

Probit(neutralized)=-4.052+0.438/dil

50% neutralized at 1/dil = 10454.741

Confidence Limits
  Probability 95% Confidence Limits for dil.inv
 95% Confidence Limits for log(dil.inv)(a)
  Estimate Lower Bound Upper Bound Estimate
 Lower Bound Upper Bound
PROBIT .010 51.478 24.611 88.733 3.941 3.203 4.486
 .020 95.947 51.316 153.007 4.564 3.938 5.030
 .030 142.430 81.625 216.648 4.959 4.402 5.378
 .040 191.719 115.553 281.871 5.256 4.750 5.641
 .050 244.145 153.112 349.610 5.498 5.031 5.857
 .060 299.920 194.333 420.435 5.704 5.270 6.041
 .070 359.216 239.254 494.778 5.884 5.478 6.204
 .080 422.190 287.925 573.018 6.045 5.663 6.351
 .090 489.000 340.400 655.515 6.192 5.830 6.485
 .100 559.806 396.735 742.629 6.328 5.983 6.610
 .150 979.919 738.338 1261.094 6.887 6.604 7.140
 .200 1529.115 1185.566 1959.963 7.332
 7.078 7.581
 .250 2239.916 1749.220 2911.161 7.714
 7.467 7.976
 .300 3155.858 2447.740 4208.601 8.057
 7.803 8.345
 .350 4335.931 3310.483 5978.045 8.375
 8.105 8.696
 .400 5861.348 4380.225 8394.851 8.676
 8.385 9.035
 .450 7846.202 5717.253 11712.227 8.968
 8.651 9.368
 .500 10454.741 7406.925 16307.197 9.255
 8.910 9.699
 .550 13930.512 9572.888 22759.599 9.542
 9.167 10.033
 .600 18647.862 12400.342 31995.692 9.833
 9.425 10.373
 .650 25208.339 16178.777 45565.733 10.135
 9.691 10.727
 .700 34634.517 21385.929 66222.178 10.453
 9.970 11.101
 .750 48797.205 28868.038 99244.552 10.795
 10.270 11.505
 .800 71480.298 40276.019 155888.618 11.177
 10.604 11.957
 .850 111541.504 59316.142 264154.879 11.622
 10.991 12.484
 .900 195249.217 96426.979 513528.166 12.182
 11.477 13.149
 .910 223520.866 108417.589 603063.911 12.317
 11.594 13.310
 .920 258892.163 123132.192 718151.221 12.464
 11.721 13.484
 .930 304278.551 141617.824 870257.823 12.626
 11.861 13.677
 .940 364435.453 165550.385 1078599.646 12.806
 12.017 13.891
 .950 447691.021 197803.155 1377865.029 13.012
 12.195 14.136
 .960 570114.724 243785.982 1837365.667 13.254
 12.404 14.424
 .970 767408.463 315170.774 2617660.570 13.551
 12.661 14.778
 .980 1139187.263 443329.954 4191239.018 13.946
 13.002 15.249
 .990 2123285.377 758770.737 8804735.285 14.568
 13.539 15.991
a Logarithm base = 2.718.