Estimating Growth Rates Using Only a Single Point per Patient Cromer, D. Tey, S.K., Khanna, R., Davenport M.P. J. Virol, In Press

Deborah Cromer

Why do we need a new method? • Standard Growth estimates require two points • Often only a single measurement per patient is available – Screening tests (e.g. Cancer) – Treatment following detection (e.g. HIV, Malaria) – Growth rate changes early on (e.g. CMV)

• Naïve estimates “infer” a second point – This can result in an underestimate of growth rate

First Positive reading, Vi

Viral Load / Tumour Size(log scale)

A

Naïve estimate of growth rate

Actual growth rate, gi Detection Threshold, L

Unknown last Negative reading

Virus may have been absent

Time since last negative reading

Developing the single point method

Viral Load (log scale)

Vi

gi

Detection Threshold, L

For each patient we define: • Vi = observed pathogen (known) • Ti = time since the last negative reading (known) • pi = proportion of time for which the pathogen has been above the detection threshold (unknown) – assume

p Below thresh

i Growing above threshold

Ti Time since last negative reading

• gi = growth rate of pathogen (unknown) – assume

Developing the single point method

Viral Load (log scale)

Vi

We want to determine the growth rate distribution, • We have

gi

Detection Threshold, L

p Below thresh

i Growing above threshold

Ti Time since last negative reading

• We define

• Then Qi is made of known values and has distribution:

Results of the Single Point Method • We use the known values of Q to determine the unknown distribution of the growth rates.

• Estimated average growth rate is double that of the naïve estimate.

How does the method perform?

Does Growth Rate Change over time?

CMV growth rate and immune reconstitution • CMV complications are associated with immune reconstitution, but the effect on viral growth rate is undefined. • We used lymphocyte count as a marker of immune reconstitution. • Find that CMV growth rate is nearly double in patients with very low lymphocyte counts. • Difference is no longer detectable one week after CMV emergence.

CMV growth and imune reconstitution

Conclusions • Have developed a new method to estimate the mean and standard deviation of pathogen growth rates using only a single point per patient. • Estimates agree extremely well with those using a standard two-point growth estimate. • CMV growth rate slows over time. • Patients with better immune reconstitution have slower CMV growth initially.

Acknolegements • Miles Davenport • Siok-Keen Tey • Rajiv Khanna