Prediction vs baseline: a foreword on predictions

Prediction “… is at least two things: Important and hard.”

HIV disease progression is a double stranded problem: both virologic and immunologic. There are theories and mathematical model for viral extinction, viral escape, etc.

The virologic approach alone is not enough to explain all aspects of disease progression. The Virus IS the only cause, but, depletion and its dynamics spans over a wide range of effects.

There is currently no uniform model that can predict a CD4 level at 3 months. If there was a model reliable enough to predict immune collapse or immune recovery, then it could be used in lieu of treatment threshold in various situations such as treatment initiation, intensification, treatment interruptions, etc.

Patients who are still in the reconstitution phase of their immune system should not be invited to interrupt treatment, but how do we monitor the reconstitution other than looking a instant snapshots of CD4 counts and % ?

Therefore prediction is important…It is hard too…

There are many ways to make predictions. Dynamic, statistic, random, …

Dynamic prediction was invented by Newton and Leibniz. One key point is to realize that the immune system is not Quantic. It is not at CD4 400 at 8:00 and CD4 1200 at 8:05. PBMC measurement fluctuate, go up and down but in continous fashion, simply because Blood is a well mixed media, circulated by the heart. It is in close interaction with the lymph network, which is not circulated.

A car navigation algorithm is a good example of a set of rules that are at both deterministic and not time dependant.

A map tells you where you should turn next, it can tell you that you will not be able to turn before your have reached that point, but it does not tell you when you will reach the point.

In that case you ‘know’ what is going to happen, but not exactly when. Whereas blood sampling is time defined.

Consciously or not, we all make predictions. Any patient with low CD4 count takes meds in hope for a higher count. If a low to UD viral load seems to be a necessary condition, it is not a warranty for increased or higher CD4 counts.

A dynamic prediction should also be able to perform better than a baseline prediction. Baseline predictions are very conservative, they stay course.

A baseline prediction on a time series of CD4/CD8 ratio of 1.3 ; 1.3 ; 1.4 predicts 1.4 and if the reading is 1.3 or 1.5 you’re happy with it… But if the reading is 1.9 and if at least one predictive models was telling you 2.0 you are going to give this model some credit.

A dynamic model proves its worth when you are able to predict or forecast something out of the ordinary (eclipse, storms, …)

You are vacationing in a nice sunny resort. Since you have arrived wheather has been perfect: you are planning some outdoor activity for tomorrow: this is baseline forecasting: business as usual. If someone tell you that tommorrow you will have heavy showers, this is a divergeant prediction. If you are being told to expect a snow storm this is an extravagant prediction

So a good dynamic prediction should be superior in making progressive (i.e. non regressive) predictions

Looking at :
http://en.wikipedia.org/wiki/Alternating_current

http://en.wikipedia.org/wiki/File:Types_of_current_by_Zureks.jpg

and in detail at
http://en.wikipedia.org/wiki/File:Sine_wave_2.svg
A sine wave, over one cycle (360°). The dashed line
represents the root mean square (RMS) value at about 0.707

The baseline prediction is 0.7, at any point of time.
The baseline prediction for point 180 is 0.7 (on a scale 0 to 1) but dynamic prediction is 0, much further away from 0.7

So when looking at how good a dynamics model is (in comparaison to a baseline model) one should not only look at the difference between predicted and actual: there will be a difference, but also look at baseline prediction as a comparator

So, before we look at the actual datapoint, let’s restate the dynamic prediction and a baseline prediction (aka business as usual)

time series are:
at data point minus 6 months:
CD4: 983 (38%)
CD8: 700 (27%) 
ratio CD4/CD8 1.4
at data point minus 4 months:
CD4: 1091 (37%)
CD8:855 (29%)
CD4/CD8: 1.3
at data point minus 2 months:
CD4: 1305 (44%)
CD8 771/ (26%)
CD4/CD8=1.7

Baseline prediction (business as usual, mean average of last 3)
CD4 : (983 + 1091 + 1305)/3 = 1126
CD8 : (700 + 855 + 771)/3 = 775
CD4 % : (38 + 37 + 44) / 3 = 40
CD8 % : (27 + 29 + 26) / 3 = 27.3
Ratio CD4/CD8 = 40/27.3 = 1.45

Our Dynamic prediction (published before blood draw)
CD4 % around 49
CD4 > 1100 but less than 1300; estimated at 1100
CD8 % around 23
CD8 estimated at 520
CD4/CD8 around 2.1

So the dynamic prediction differs from baseline prediction
CD4 : 26/1100 = 3 % (almost no difference)
CD4%: (49-40)/40 = 23%
CD8 : (775-520)/775 = 33 %
CD8%: (27-23)/27 = 15%
CD4/CD8 : (2.1 - 1.45)/1.45 = 45 % (a sizable difference)

Dynamics prediction is therefore non-regressive on
CD4/CD8 followed by CD8, CD4%, CD8% and far behind by CD4 (almost no difference)

The added value for the dynamic model should be assessed on
CD4/CD8 followed by CD8, etc.

Actual values:
CD4: 1130 (46%)
CD8 491/ (20%)
CD4/CD8=2.3

Comparison: Actual values (dynamic prediction) [Baseline prediction]:

CD4 : 1130 (1100) [1126]
CD4%: 46 (49) [40]
CD8 : 491 (520) [775]
CD8%: 20 (23) [27]
CD4/CD8=2.3 (2.1) [1.45]

The dynamic model prediction is more satisfactory than the baseline (moving average) prediction.
The dynamics model was very good at predicting that things would move (differ markedly), predicted the direction of the move and its amplitude.

In next posts we will graph these, look at past and future of the predictive tool

tracker : HIVPharmaCure-T1