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To upload data for a single patient, create a text file where each row has three numbers: the well size (# cells), the number of replicates for this size, and the number of positive outcomes for this size. The values may be delimited by either white space or commas. For example, your file could look like this:

900,9,1
400,5,2
100,10,2

For multiple patients, simply add rows with a greater-than sign followed by the patient name (in homage to fasta format). For example,

>patient1
900,9,0
100,10,2
>patient2
400,5,2
500,10,1
>patient3
600,10,1
500,4,3
300,5,2

In this mode, the app will produce a graph showing the infection frequencies (IUPM) across the set of patients.

About This Calculator

To measure the frequency of HIV-1 latency, The Siliciano Lab developed an assay some years ago that uses uninfected donor cells to grow HIV-1 out of cells from infected patients at various dilutions^{1, 2}. This calculator, written by Daniel Rosenbloom and made into a web app by Oliver Elliott, computes the frequency of latent infection based on which dilutions of patient cells are positive for HIV-1 growth.

Interpreting the Output Statistics

• The maximum likelihood estimate and confidence interval provide a good estimate of the infection frequency, assuming that (1) many cells (>100s) are used in the assay, and (2) each cell in each well has the same probability of being infected.
• The p-value can be used to detect very strange, or unlikely, results in the limiting dilution assay. For instance, if several large wells are negative but several small wells are positive, the resulting p-value will be very low, indicating that there may have been cross-contamination, improper labeling of wells, insufficiently mixed cells, or another failure of the assay. (Frequent users of this calculator should note: Every 100 assays that you run, you should expect to see a p-value below 0.01, just by chance!)
• For all-negative well outcomes, the maximum likelihood estimate is formally zero. To provide more useful information, a posterior median estimate is given instead. This value reports the median of the Bayesian posterior distribution, using a uniform prior. If you had a reasonable prior belief that your assay could turn up at least one positive well, then this is a decent rough estimate. A higher bound is also provided, at the 95th percentile of the posterior distribution; this is a good upper bound. The p-value is not a meaningful output in this case, so it is not shown.
• If you have all-positive assay results, then close this app and use smaller wells!

Functionality

This calculator features three ways to input data. The "Custom Well Sizes" pane allows you to input data with maximum flexibility. The "Constant Limiting Dilution" pane, on the other hand, will automatically compute your well sizes given the starting well size and a dilution factor. While these are both useful, regular users may prefer the convenience of pasting data in bulk or uploading it from a text file. To use this feature, format your text such that each row has three numbers: the well size (# cells), the number of replicates for this size, and the number of positive outcomes for this size. The upload/paste feature also allows you input data for multiple patients. In this mode, the app will produce a graph showing the infection frequencies (IUPM) across the set of patients.

Source Code

The complete source code is available on GitHub (including a bug fix & commit log).

If you use IUPMStats, please cite the following article:

Daniel I S Rosenbloom, Oliver Elliott, Alison L Hill, Timothy J Henrich, Janet M Siliciano, Robert F Siliciano. Designing and interpreting limiting dilution assays: general principles and applications to the latent reservoir for HIV-1. bioRxiv doi: http://dx.doi.org/10.1101/018911.

References

¹ Chun, T.-W., Carruth, L., Finzi, D., Shen, X., DiGiuseppe, J. A., Taylor, H., Hermankova, M., Chadwick, K., Margolick, J., Quinn, T. C., Kuo, Y.-H., Brookmeyer, R., Zeiger, M. A., Barditch-Crovo, P., Siliciano, R. F. Quantification of latent tissue reservoirs and total body viral load in HIV-1 infection. Nature 387, 183–188 (1997).

² Laird G. M., Rosenbloom D. I. S., Lai J., Siliciano R. F., Siliciano J. D. Measuring the frequency of latent HIV-1 in resting CD4+ T cells using a limiting dilution co-culture assay. To appear in HIV Protocols (3rd ed).