-
Notifications
You must be signed in to change notification settings - Fork 24
/
slides.html
executable file
·466 lines (399 loc) · 16.5 KB
/
slides.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Forecasting</title>
<meta name="author" content="Sarah Cobey">
<meta name="apple-mobile-web-app-capable" content="yes" />
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent" />
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<link rel="stylesheet" href="../reveal/css/reveal.min.css">
<link rel="stylesheet" href="../reveal/css/theme/trvrb.css" id="theme">
<link rel="stylesheet" href="../reveal/css/font-awesome/css/font-awesome.min.css">
<!-- For syntax highlighting -->
<link rel="stylesheet" href="../reveal/lib/css/zenburn.css">
<!--[if lt IE 9]>
<script src="lib/js/html5shiv.js"></script>
<![endif]-->
</head>
<body>
<div style="position: absolute; top:10px; left:10px; z-index:100;">
<a href="/sismid/forecasting">
<i class="fa fa-times-circle" style="color: #bbb; opacity: 0.1;"></i>
</a>
</div>
<div class="reveal">
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section data-background="#CC3333">
<h2 class="title">Forecasting</h2>
</section>
<section>
<h3>Forecasting is a big problem</h3>
<img class="stretch" src="images/globe.png">
</section>
<section>
<h3>Rapid progress</h3>
<p>Actual v. predicted distances of Atlantic cyclones
<img class="stretch" src="images/cyclone_error.jpg">
<div class="citation">
<a href="http://www.sciencedirect.com.proxy.uchicago.edu/science/article/pii/S0169534716301185">
Gandon et al. 2016
</a>
</div>
</section>
<section>
<h3>General, overlapping approaches</h3>
<p>Machine learning
<p>Statistical models
<p>Nonlinear forecasting
<p>"Mechanistic" modeling
</section>
<section>
<h3>DREAM challenges</h3>
<p>Inference of gene regulatory networks
<p>from knockout, observational, and synthetic data
<img src="images/dream.png">
<div class="citation">
<a href="http://bioinformatics.oxfordjournals.org/content/early/2012/03/29/bioinformatics.bts143.full.pdf">
Kuffner et al. 2012
</a>
</div>
<p>Compete Lasso, random forests, Bayesian networks, mutual information, ANOVA, etc.
</section>
<section>
<h3>Ecological niche modeling</h3>
<img src="images/channel.png">
<div class="citation">
<a href="http://www.nature.com/nmeth/journal/v9/n6/full/nmeth.1975.html">
Larsen et al. 2012
</a>
</div>
<p>An artificial neural network that included microbial interactions performed best.
</section>
<section>
<h3>Nonlinear forecasting</h3>
<p>Reconstruct attractor ("library") from time series
<p>Use attractor to make short-term predictions</p>
<div class="citation">
<a href="http://www.nature.com/nature/journal/v344/n6268/abs/344734a0.html">
Sugihara and May 1990
</a>
</div>
</section>
<section>
<h3>Forecasting communities</h3>
<img class="stretch" src="images/community.jpg">
<div class="citation">
<a href="http://rspb.royalsocietypublishing.org/content/283/1822/20152258">Deyle et al. 2015</a>
</div>
</section>
<section>
<h3>Dynamics may be chaotic</h3>
<img class="stretch" src="images/lorenz.png">
</section>
<section>
<h3>Predictions with chaos: short shelf life</h3>
<p>Trajectories in chaotic attractors diverge
<p> $$ \lvert \delta \textbf{Z}(t)\rvert \approx e^{\lambda t}\lvert\delta\textbf{Z}_0\rvert$$
<p> $\lambda$ is the Lyapunov exponent
<p> (so with chaos, $\lambda>0$)
</section>
<section>
<section>
<h3>How to forecast</h3>
<ul>
<li>Choose an embedding dimension $E$ and lag $\tau$</li>
<li>Each point in $E$-dimensional space: $\{x_t,x_{t-\tau},x_{t-2\tau},...,x_{t-(E-1)\tau}\}$</li>
<li>Construct these points from the time series</li>
<li>Define a point to predict ("predictee")</li>
<li>See where predictee's $E+1$ nearest neighbors wind up $t$ steps into the future</li>
<li>Measure correlations $\rho$ between predictee's observed future state and neighbors' weighted predictions</li>
</ul>
</section>
<section>
<h3>Choosing $E$ and $\tau$</h3>
<p>An unsolved problem
<p>Use $E$ (and $\tau$) that yield best predictions</p>
<img class="stretch" src="images/E_selection.png">
<div class="citation">
<a href="http://www.nature.com/nature/journal/v344/n6268/abs/344734a0.html">Sugihara and May 1990</a>
</div>
</section>
</section>
<section>
<h3>Observational noise v. chaos</h3>
<img class="stretch" src="images/chaos_noise.png">
<div class="citation">
<a href="http://www.nature.com/nature/journal/v344/n6268/abs/344734a0.html">Sugihara and May 1990</a>
</div>
</section>
<section>
<h3>Predicting flu</h3>
<img class="stretch" src="images/subtypes_season.png">
<div class="citation">
<a href="http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1001051">Goldstein et al. 2011</a>
</div>
</section>
<section>
<h3>Epidemic sizes negatively correlated</h3>
<img class="stretch" src="images/subtypes_correlations.png">
<div class="citation">
<a href="http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1001051">Goldstein et al. 2011</a>
</div>
</section>
<section>
<h3>Predict based on cumulative incidence</h3>
<img src="images/cip_equations.png" style="width: 50%; height: 50%;">
<p>where $I(s)$ is the incidence in week $s$, $h$ is a strain-specific incidence threshold, $T$ is the time of crossing $h$, and $Y$ is the strain's whole-season cumulative incidence proxy.
<div class="citation">
<a href="http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1001051">Goldstein et al. 2011</a>
</div>
</section>
<section>
<h3>Predictions v. observations (H3N2)</h3>
<img class="stretch" src="images/h3n2_prediction.png">
<div class="citation">
<a href="http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1001051">Goldstein et al. 2011</a>
</div>
</section>
<section>
<h3>Predicting flu in Hong King</h3>
<p>Aim: Predict peak timing and magnitude
<img src="images/hongkong.png" style="width: 50%; height: 50%;">
<div class="citation">
<a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004383">
Yang et al. 2015
</a>
</div>
</section>
<section>
<h3>Mechanistic model and particle filter</h3>
<img src="images/SI_equations.png">
<div class="citation">
<a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004383">
Yang et al. 2015
</a>
</div>
<p>Achieves 37% accuracy with 1-3 week lead, ~50% at 0 week lead
</section>
<section>
<h3><a href="https://predict.cdc.gov/">Epidemic Prediction Initiative</a>
</section>
<section>
<h3>Forecasting SARS-CoV-2</h3>
<img class="stretch" src="images/birx_ihme.jpg">
<div class="citation">
<a href="https://www.cnn.com/2020/04/08/politics/deborah-birx-social-distancing-models/index.html">
CNN
</a>
</div>
</section>
<section>
<h3>Unusual error</h3>
<img class="stretch" src="images/ihme_error.png">
</section>
<section>
<h3>A statistical model</h3>
<img class="stretch" src="images/ihme_eqns.png">
</section>
<section>
<h3>Some precedent: Farr's Law</h3>
<img class="stretch" src="images/farrs_law_jama.png">
</section>
<section>
<h3><a href="https://covid19forecasthub.org/">(U.S.) COVID-19 Forecast Hub</a>
<div class="citation">
see <a href="https://www.pnas.org/doi/10.1073/pnas.2113561119">
Cramer et al. 2022
</a>
</div>
</section>
<section>
<h3>Comparing models</h3>
<img class="stretch" src="images/model_table.png">
<div class="citation">
<a href="https://www.pnas.org/doi/10.1073/pnas.2113561119">
Cramer et al. 2022
</a>
</div>
</section>
<section>
<h3>Evaluating performance</h3>
<img class="stretch" src="images/model_rank.png">
<div class="citation">
<a href="https://www.pnas.org/doi/10.1073/pnas.2113561119">
Cramer et al. 2022
</a>
</div>
</section>
<section>
<h3>Failure to predict change</h3>
<img class="stretch" src="images/COVID_ensemble_forecasts.png" style="width: 50%; height: 50%;">
<div class="citation">
<a href="https://delphi.cmu.edu/blog/2021/09/30/on-the-predictability-of-covid-19/">
Reich et al. 2021
</a>
</div>
</section>
<section data-transition="fade" data-background="#000000">
<h1 class="title">Evolutionary forecasting</h1>
</section>
<section>
<h3>Influenza vaccine strain selection strategy</h3>
<p class="smaller">
General strategy for antigenically evolving seasonal influenza viruses is attempt to match vaccine strain as close as possible to circulating viruses
</p>
<img class="stretch" src="images/flu_h3n2_tree_vaccines_2014_2022.png">
<div class="citation">
<a href="https://nextstrain.org/flu/seasonal/h3n2/ha/6y">nextstrain.org</a>
</div>
</section>
<section>
<h3>Vaccine strain selection timeline</h3>
<p class="smaller">
Due to manufacturing and distribution, vaccine strain selection occurs in Feb for an fall vaccination campaign ahead of seasonal influenza epidemic
</p>
<img class="stretch" src="images/flu_vaccine_schedule.jpg">
</section>
<section>
<h3>Fitness models project strain frequencies</h3>
<p class="smaller">Future frequency $x_i(t+\Delta t)$ of strain $i$ derives from strain fitness $f_i$ and present day frequency $x_i(t)$, such that</p>
<p class="smaller">$$x_i(t+\Delta t) = \frac{1}{Z(t)} \, x_i(t) \, \mathrm{exp}(f_i \, \Delta t)$$</p>
<p class="smaller">
Strain frequencies at each timepoint are normalized by total frequency $Z(t)$.
This captures clonal interference between competing lineages.
</p>
<img class="stretch" src="images/clonal_interferance.jpg">
<div class="citation">
<a href="http://www.nature.com/nature/journal/v507/n7490/full/nature13087.html">Łuksza and Lässig. 2014</a>
</div>
</section>
<section>
<h3>Match strain forecast to retrospective circulation</h3>
<img class="stretch" src="images/prediction_fitness_model_schematic.png">
<div class="citation">
<a href="https://bedford.io/papers/huddleston-flu-forecasting/">Huddleston et al. 2020</a>
</div>
</section>
<section>
<h3>Strain fitness estimated from viral attributes</h3>
<p class="smaller">The fitness $f$ of strain $i$ is estimated as</p>
<p class="smaller">$$f_i = \beta^\mathrm{A} \, f_i^\mathrm{A} + \beta^\mathrm{B} \, f_i^\mathrm{B} + \ldots$$</p>
<p class="smaller">where $f^A$, $f^B$, etc... are different standardized viral attributes and
$\beta^A$, $\beta^B$, etc... coefficients are trained based on historical evolution</p>
<br>
<table class="smaller">
<thead>
<tr>
<th width="28%">Antigenic drift</th>
<th width="38%">Intrinsic fitness</th>
<th width="33%">Recent growth</th>
</tr>
</thead>
<tbody>
<tr>
<td>epitope mutations</td>
<td>non-epitope mutations</td>
<td>local branching index</td>
</tr>
<tr>
<td>HI titers</td>
<td>DMS data (via Bloom lab)</td>
<td>delta frequency</td>
</tr>
</tbody>
</table>
</section>
<section>
<h3>Model successfully predicts clade growth and best pick from model is generally close to best possible retrospective pick</h3>
<img class="stretch" src="images/prediction_validation_clade_growth_ranking.png">
<div class="citation">
<a href="https://bedford.io/papers/huddleston-flu-forecasting/">Huddleston et al. 2020. eLife.</a>
</div>
</section>
<section class="left-align">
<h3>Main issue</h3>
<p>
Strain fitness $f_i$ is largely fixed by the "fundamentals" of the strain rather than being learned from frequency behavior.
</p>
</section>
<section>
<h3>Genetic relationships of globally sampled SARS-CoV-2 to present</h3>
<img class="stretch" src="images/ncov_variants_tree_unrooted.png">
<div class="citation">
<a href="https://nextstrain.org/ncov/gisaid/global?l=unrooted&m=div">nextstrain.org</a>
</div>
</section>
<section>
<h3>Rapid displacement of existing diversity by emerging variants</h3>
<img class="stretch" src="images/ncov_tree_freq.png">
<div class="citation">
<a href="https://nextstrain.org/ncov/gisaid/global">nextstrain.org</a>
</div>
</section>
<section>
<h3>Population genetic expectation of variant frequency under selection</h3>
<p class="smaller">$x' = \frac{x \, (1+s)}{x \, (1+s) + (1-x)}$ for frequency $x$ in one generation with selective advantage $s$</p>
<p class="smaller">$x(t) = \frac{x_0 \, (1+s)^t}{x_0 \, (1+s)^t + (1-x_0)}$ for initial frequency $x_0$ over $t$ generations</p>
<p class="smaller">Trajectories are linear once logit transformed via $\mathrm{log}(\frac{x}{1 - x})$</p>
<img class="stretch" src="images/ncov_variants_selection_logit_trajectories.png">
</section>
<section>
<h3>Variants show consistent frequency dynamics in logit space</h3>
<img class="stretch" src="images/ncov_variants_omicron_countries_frequencies_logit_2022_04_08.png">
</section>
<!-- <section>
<h3>Variants show consistent frequency dynamics in logit space</h3>
<img class="stretch" src="images/ncov_variants_delta_countries_frequencies_logit_2021_09_07.png">
</section> -->
<section>
<h3>Multinomial logistic regression</h3>
<p class="smaller">
Multinomial logistic regression models the probability of a virus sampled at time $t$ belonging to variant $i$ as
</p>
<p class="smaller">
$$\mathrm{Pr}(X = i) = x_i(t) = \frac{p_i \, \mathrm{exp}(f_i \, t)}{\sum_{1 \le j \le n} p_j \, \mathrm{exp}(f_j \, t) }$$
</p>
<p class="smaller">
where the model has $2n$ parameters consisting of $p_i$ the frequency of variant $i$ at initial timepoint and $f_i$ the
growth rate or fitness of variant $i$ for $n$ variants.
</p>
<p class="smaller">
The model is fit to minimize "log loss" of predicted variant vs observed variant across observations in dataset.
</p>
</section>
<section>
<h3>Multinomial logistic regression fits variant frequencies well</h3>
<img class="stretch" src="images/sarscov2_variant_rt_logistic_regression_2021_09_01.png">
</section>
<section>
<h3>Original VOC viruses had substantially increased transmissibility</h3>
<img class="stretch" src="images/sarscov2_variant_rt_growth_advantage.png">
<div class="citation">
Model from <a href="https://bedford.io/papers/figgins-rt-from-frequency-dynamics/">Figgins and Bedford. 2022. medRxiv.</a>
</div>
</section>
<section>
<h3>Clade and lineage forecasts continuously updated</h3>
<img class="stretch" src="images/ncov_forecasts_clades.png">
<div class="citation">
<a href="https://nextstrain.org/sars-cov-2/forecasts/">Figgins, Lee, Hadfield. nextstrain.org</a>
</div>
</section>
<section>
<p>Multinomial logistic regression should work well for SARS-CoV-2 prediction, except new variants have been emerging
fast enough that the prediction horizon is really quite short</p>
</section>
<section data-background="#99CCFF">
<h3>What other models would you test?</h3>
</section>
<section data-background="#99CCFF">
<h3>What limits prediction with other pathogens?</h3>
</section>
</div>
<script src="../reveal/lib/js/head.min.js"></script>
<script src="../reveal/js/reveal.min.js"></script>
<script src="../reveal/js/config.js"></script>
</body>
</html>