-
Notifications
You must be signed in to change notification settings - Fork 0
/
s4.html
902 lines (857 loc) · 49.1 KB
/
s4.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
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<title>Chapter 7 Step 4: Outcome modelling | Understanding Propensity Score Matching</title>
<meta name="description" content="Chapter 7 Step 4: Outcome modelling | Understanding Propensity Score Matching." />
<meta name="generator" content="bookdown 0.28 and GitBook 2.6.7" />
<meta property="og:title" content="Chapter 7 Step 4: Outcome modelling | Understanding Propensity Score Matching" />
<meta property="og:type" content="book" />
<meta property="og:description" content="Chapter 7 Step 4: Outcome modelling | Understanding Propensity Score Matching." />
<meta name="github-repo" content="ehsanx/UnderstandingPropensityScore" />
<meta name="twitter:card" content="summary" />
<meta name="twitter:title" content="Chapter 7 Step 4: Outcome modelling | Understanding Propensity Score Matching" />
<meta name="twitter:description" content="Chapter 7 Step 4: Outcome modelling | Understanding Propensity Score Matching." />
<meta name="author" content="Ehsan Karim" />
<meta name="date" content="2023-03-19" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="apple-mobile-web-app-capable" content="yes" />
<meta name="apple-mobile-web-app-status-bar-style" content="black" />
<link rel="prev" href="s3.html"/>
<link rel="next" href="compare.html"/>
<script src="libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/fuse.min.js"></script>
<link href="libs/gitbook-2.6.7/css/style.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-table.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-bookdown.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-highlight.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-search.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-fontsettings.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-clipboard.css" rel="stylesheet" />
<link href="libs/anchor-sections-1.1.0/anchor-sections.css" rel="stylesheet" />
<link href="libs/anchor-sections-1.1.0/anchor-sections-hash.css" rel="stylesheet" />
<script src="libs/anchor-sections-1.1.0/anchor-sections.js"></script>
<script src="libs/kePrint-0.0.1/kePrint.js"></script>
<link href="libs/lightable-0.0.1/lightable.css" rel="stylesheet" />
<script type="text/javascript">
// toggle visibility of R source blocks in R Markdown output
function toggle_R() {
var x = document.getElementsByClassName('r');
if (x.length == 0) return;
function toggle_vis(o) {
var d = o.style.display;
o.style.display = (d == 'block' || d == '') ? 'none':'block';
}
for (i = 0; i < x.length; i++) {
var y = x[i];
if (y.tagName.toLowerCase() === 'pre') toggle_vis(y);
}
var elem = document.getElementById("myButton1");
if (elem.value === "Hide Global") elem.value = "Show Global";
else elem.value = "Hide Global";
}
document.write('<input onclick="toggle_R();" type="button" value="Hide Global" id="myButton1" style="position: absolute; top: 10%; right: 2%; z-index: 200"></input>')
</script>
<style type="text/css">
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #7d9029; } /* Attribute */
code span.bn { color: #40a070; } /* BaseN */
code span.bu { color: #008000; } /* BuiltIn */
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4070a0; } /* Char */
code span.cn { color: #880000; } /* Constant */
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
code span.dt { color: #902000; } /* DataType */
code span.dv { color: #40a070; } /* DecVal */
code span.er { color: #ff0000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #40a070; } /* Float */
code span.fu { color: #06287e; } /* Function */
code span.im { color: #008000; font-weight: bold; } /* Import */
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
code span.op { color: #666666; } /* Operator */
code span.ot { color: #007020; } /* Other */
code span.pp { color: #bc7a00; } /* Preprocessor */
code span.sc { color: #4070a0; } /* SpecialChar */
code span.ss { color: #bb6688; } /* SpecialString */
code span.st { color: #4070a0; } /* String */
code span.va { color: #19177c; } /* Variable */
code span.vs { color: #4070a0; } /* VerbatimString */
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
</style>
<style type="text/css">
/* Used with Pandoc 2.11+ new --citeproc when CSL is used */
div.csl-bib-body { }
div.csl-entry {
clear: both;
}
.hanging div.csl-entry {
margin-left:2em;
text-indent:-2em;
}
div.csl-left-margin {
min-width:2em;
float:left;
}
div.csl-right-inline {
margin-left:2em;
padding-left:1em;
}
div.csl-indent {
margin-left: 2em;
}
</style>
<link rel="stylesheet" href="style.css" type="text/css" />
</head>
<body>
<div class="book without-animation with-summary font-size-2 font-family-1" data-basepath=".">
<div class="book-summary">
<nav role="navigation">
<ul class="summary">
<li><a href="./">Understanding Propensity Score Matching</a></li>
<li class="divider"></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Preamble</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#description"><i class="fa fa-check"></i>Description</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#main-references"><i class="fa fa-check"></i>Main references</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#version-history"><i class="fa fa-check"></i>Version history</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#prerequisites"><i class="fa fa-check"></i>Prerequisites</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#license"><i class="fa fa-check"></i>License</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#comments"><i class="fa fa-check"></i>Comments</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="1" data-path="terms.html"><a href="terms.html"><i class="fa fa-check"></i><b>1</b> Defining Parameter</a>
<ul>
<li class="chapter" data-level="1.1" data-path="terms.html"><a href="terms.html#epidemiological-research-goals"><i class="fa fa-check"></i><b>1.1</b> Epidemiological research goals</a></li>
<li class="chapter" data-level="1.2" data-path="terms.html"><a href="terms.html#potential-outcome"><i class="fa fa-check"></i><b>1.2</b> Potential outcome</a></li>
<li class="chapter" data-level="1.3" data-path="terms.html"><a href="terms.html#parameters-of-interest"><i class="fa fa-check"></i><b>1.3</b> Parameters of interest</a>
<ul>
<li class="chapter" data-level="1.3.1" data-path="terms.html"><a href="terms.html#te"><i class="fa fa-check"></i><b>1.3.1</b> TE</a></li>
<li class="chapter" data-level="1.3.2" data-path="terms.html"><a href="terms.html#ate"><i class="fa fa-check"></i><b>1.3.2</b> ATE</a></li>
<li class="chapter" data-level="1.3.3" data-path="terms.html"><a href="terms.html#interpretation-of-ate"><i class="fa fa-check"></i><b>1.3.3</b> Interpretation of ATE</a></li>
<li class="chapter" data-level="1.3.4" data-path="terms.html"><a href="terms.html#identifiability-assumptions"><i class="fa fa-check"></i><b>1.3.4</b> Identifiability Assumptions</a></li>
<li class="chapter" data-level="1.3.5" data-path="terms.html"><a href="terms.html#att"><i class="fa fa-check"></i><b>1.3.5</b> ATT</a></li>
<li class="chapter" data-level="1.3.6" data-path="terms.html"><a href="terms.html#interpretation-of-att"><i class="fa fa-check"></i><b>1.3.6</b> Interpretation of ATT</a></li>
<li class="chapter" data-level="1.3.7" data-path="terms.html"><a href="terms.html#att-vs.-ate"><i class="fa fa-check"></i><b>1.3.7</b> ATT vs. ATE</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="2" data-path="balance.html"><a href="balance.html"><i class="fa fa-check"></i><b>2</b> Balance and Overlap</a>
<ul>
<li class="chapter" data-level="2.1" data-path="balance.html"><a href="balance.html#balance-1"><i class="fa fa-check"></i><b>2.1</b> Balance</a>
<ul>
<li class="chapter" data-level="2.1.1" data-path="balance.html"><a href="balance.html#measures-of-balance"><i class="fa fa-check"></i><b>2.1.1</b> Measures of Balance</a></li>
</ul></li>
<li class="chapter" data-level="2.2" data-path="balance.html"><a href="balance.html#adjustment"><i class="fa fa-check"></i><b>2.2</b> Adjustment</a>
<ul>
<li class="chapter" data-level="2.2.1" data-path="balance.html"><a href="balance.html#why-adjust"><i class="fa fa-check"></i><b>2.2.1</b> Why adjust?</a></li>
<li class="chapter" data-level="2.2.2" data-path="balance.html"><a href="balance.html#adjustment-methods"><i class="fa fa-check"></i><b>2.2.2</b> Adjustment Methods</a></li>
</ul></li>
<li class="chapter" data-level="2.3" data-path="balance.html"><a href="balance.html#lack-of-overlap"><i class="fa fa-check"></i><b>2.3</b> Lack of overlap</a></li>
</ul></li>
<li class="chapter" data-level="3" data-path="ps.html"><a href="ps.html"><i class="fa fa-check"></i><b>3</b> Propensity score</a>
<ul>
<li class="chapter" data-level="3.1" data-path="ps.html"><a href="ps.html#motivating-problem"><i class="fa fa-check"></i><b>3.1</b> Motivating problem</a></li>
<li class="chapter" data-level="3.2" data-path="ps.html"><a href="ps.html#defining-propensity-score"><i class="fa fa-check"></i><b>3.2</b> Defining Propensity score</a>
<ul>
<li class="chapter" data-level="3.2.1" data-path="ps.html"><a href="ps.html#theoretical-result"><i class="fa fa-check"></i><b>3.2.1</b> Theoretical result</a></li>
<li class="chapter" data-level="3.2.2" data-path="ps.html"><a href="ps.html#assumptions"><i class="fa fa-check"></i><b>3.2.2</b> Assumptions</a></li>
<li class="chapter" data-level="3.2.3" data-path="ps.html"><a href="ps.html#ways-to-use-ps"><i class="fa fa-check"></i><b>3.2.3</b> Ways to use PS</a></li>
</ul></li>
<li class="chapter" data-level="3.3" data-path="ps.html"><a href="ps.html#ps-matching-steps"><i class="fa fa-check"></i><b>3.3</b> PS Matching Steps</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="s1.html"><a href="s1.html"><i class="fa fa-check"></i><b>4</b> Step 1: Exposure modelling</a>
<ul>
<li class="chapter" data-level="4.1" data-path="s1.html"><a href="s1.html#model-specification"><i class="fa fa-check"></i><b>4.1</b> Model specification</a>
<ul>
<li class="chapter" data-level="4.1.1" data-path="s1.html"><a href="s1.html#updating-model-specification"><i class="fa fa-check"></i><b>4.1.1</b> Updating model specification</a></li>
<li class="chapter" data-level="4.1.2" data-path="s1.html"><a href="s1.html#stability-of-ps"><i class="fa fa-check"></i><b>4.1.2</b> Stability of PS</a></li>
</ul></li>
<li class="chapter" data-level="4.2" data-path="s1.html"><a href="s1.html#variables-to-adjust"><i class="fa fa-check"></i><b>4.2</b> Variables to adjust</a>
<ul>
<li class="chapter" data-level="4.2.1" data-path="s1.html"><a href="s1.html#best-approach"><i class="fa fa-check"></i><b>4.2.1</b> Best approach</a></li>
<li class="chapter" data-level="4.2.2" data-path="s1.html"><a href="s1.html#general-guideline-of-type-of-variables"><i class="fa fa-check"></i><b>4.2.2</b> General guideline of type of variables</a></li>
<li class="chapter" data-level="4.2.3" data-path="s1.html"><a href="s1.html#what-not-to-include"><i class="fa fa-check"></i><b>4.2.3</b> What NOT to include</a></li>
<li class="chapter" data-level="4.2.4" data-path="s1.html"><a href="s1.html#mediators"><i class="fa fa-check"></i><b>4.2.4</b> Mediators</a></li>
<li class="chapter" data-level="4.2.5" data-path="s1.html"><a href="s1.html#unmeasured-confounding"><i class="fa fa-check"></i><b>4.2.5</b> Unmeasured confounding</a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="s1.html"><a href="s1.html#model-selection"><i class="fa fa-check"></i><b>4.3</b> Model selection</a>
<ul>
<li class="chapter" data-level="4.3.1" data-path="s1.html"><a href="s1.html#based-on-association-with-outcome"><i class="fa fa-check"></i><b>4.3.1</b> Based on association with outcome</a></li>
<li class="chapter" data-level="4.3.2" data-path="s1.html"><a href="s1.html#based-on-association-with-exposure"><i class="fa fa-check"></i><b>4.3.2</b> Based on association with exposure</a></li>
</ul></li>
<li class="chapter" data-level="4.4" data-path="s1.html"><a href="s1.html#alternative-modelling-strategies"><i class="fa fa-check"></i><b>4.4</b> Alternative modelling strategies</a></li>
<li class="chapter" data-level="4.5" data-path="s1.html"><a href="s1.html#ps-estimation"><i class="fa fa-check"></i><b>4.5</b> PS estimation</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="s2.html"><a href="s2.html"><i class="fa fa-check"></i><b>5</b> Step 2: Propensity score Matching</a>
<ul>
<li class="chapter" data-level="5.1" data-path="s2.html"><a href="s2.html#matching-method-nn"><i class="fa fa-check"></i><b>5.1</b> Matching method NN</a></li>
<li class="chapter" data-level="5.2" data-path="s2.html"><a href="s2.html#initial-fit"><i class="fa fa-check"></i><b>5.2</b> Initial fit</a></li>
<li class="chapter" data-level="5.3" data-path="s2.html"><a href="s2.html#fine-tuning-add-caliper"><i class="fa fa-check"></i><b>5.3</b> Fine tuning: add caliper</a></li>
<li class="chapter" data-level="5.4" data-path="s2.html"><a href="s2.html#things-to-keep-track-of"><i class="fa fa-check"></i><b>5.4</b> Things to keep track of</a></li>
<li class="chapter" data-level="5.5" data-path="s2.html"><a href="s2.html#matches"><i class="fa fa-check"></i><b>5.5</b> Matches</a></li>
<li class="chapter" data-level="5.6" data-path="s2.html"><a href="s2.html#other-matching-algorithms"><i class="fa fa-check"></i><b>5.6</b> Other matching algorithms</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="s3.html"><a href="s3.html"><i class="fa fa-check"></i><b>6</b> Step 3: Balance and overlap</a>
<ul>
<li class="chapter" data-level="6.1" data-path="s3.html"><a href="s3.html#assessment-of-balance-by-smd"><i class="fa fa-check"></i><b>6.1</b> Assessment of Balance by SMD</a></li>
<li class="chapter" data-level="6.2" data-path="s3.html"><a href="s3.html#smd-vs.-p-values"><i class="fa fa-check"></i><b>6.2</b> SMD vs. P-values</a></li>
<li class="chapter" data-level="6.3" data-path="s3.html"><a href="s3.html#vizualization-for-overlap"><i class="fa fa-check"></i><b>6.3</b> Vizualization for Overlap</a></li>
<li class="chapter" data-level="6.4" data-path="s3.html"><a href="s3.html#variance-ratio-1"><i class="fa fa-check"></i><b>6.4</b> Variance ratio</a></li>
<li class="chapter" data-level="6.5" data-path="s3.html"><a href="s3.html#close-inspection-of-boundaries"><i class="fa fa-check"></i><b>6.5</b> Close inspection of boundaries</a></li>
<li class="chapter" data-level="6.6" data-path="s3.html"><a href="s3.html#unsatirfactory-balance"><i class="fa fa-check"></i><b>6.6</b> Unsatirfactory balance</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="s4.html"><a href="s4.html"><i class="fa fa-check"></i><b>7</b> Step 4: Outcome modelling</a>
<ul>
<li class="chapter" data-level="7.1" data-path="s4.html"><a href="s4.html#crude-outcome-model"><i class="fa fa-check"></i><b>7.1</b> Crude outcome model</a></li>
<li class="chapter" data-level="7.2" data-path="s4.html"><a href="s4.html#double-adjustment"><i class="fa fa-check"></i><b>7.2</b> Double-adjustment</a></li>
<li class="chapter" data-level="7.3" data-path="s4.html"><a href="s4.html#adjusted-outcome-model"><i class="fa fa-check"></i><b>7.3</b> Adjusted outcome model</a></li>
<li class="chapter" data-level="7.4" data-path="s4.html"><a href="s4.html#variance-considerations"><i class="fa fa-check"></i><b>7.4</b> Variance considerations</a>
<ul>
<li class="chapter" data-level="7.4.1" data-path="s4.html"><a href="s4.html#cluster-option"><i class="fa fa-check"></i><b>7.4.1</b> Cluster option</a></li>
<li class="chapter" data-level="7.4.2" data-path="s4.html"><a href="s4.html#bootstrap"><i class="fa fa-check"></i><b>7.4.2</b> Bootstrap</a></li>
</ul></li>
<li class="chapter" data-level="7.5" data-path="s4.html"><a href="s4.html#estimate-obtained"><i class="fa fa-check"></i><b>7.5</b> Estimate obtained</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="compare.html"><a href="compare.html"><i class="fa fa-check"></i><b>8</b> PS vs. Regression</a>
<ul>
<li class="chapter" data-level="8.1" data-path="compare.html"><a href="compare.html#data-simulation"><i class="fa fa-check"></i><b>8.1</b> Data Simulation</a></li>
<li class="chapter" data-level="8.2" data-path="compare.html"><a href="compare.html#treatment-effect-from-counterfactuals"><i class="fa fa-check"></i><b>8.2</b> Treatment effect from counterfactuals</a></li>
<li class="chapter" data-level="8.3" data-path="compare.html"><a href="compare.html#treatment-effect-from-regression"><i class="fa fa-check"></i><b>8.3</b> Treatment effect from Regression</a></li>
<li class="chapter" data-level="8.4" data-path="compare.html"><a href="compare.html#treatment-effect-from-ps"><i class="fa fa-check"></i><b>8.4</b> Treatment effect from PS</a></li>
<li class="chapter" data-level="8.5" data-path="compare.html"><a href="compare.html#non-linear-model"><i class="fa fa-check"></i><b>8.5</b> Non-linear Model</a>
<ul>
<li class="chapter" data-level="8.5.1" data-path="compare.html"><a href="compare.html#data-generation"><i class="fa fa-check"></i><b>8.5.1</b> Data generation</a></li>
<li class="chapter" data-level="8.5.2" data-path="compare.html"><a href="compare.html#regression"><i class="fa fa-check"></i><b>8.5.2</b> Regression</a></li>
<li class="chapter" data-level="8.5.3" data-path="compare.html"><a href="compare.html#ps-1"><i class="fa fa-check"></i><b>8.5.3</b> PS</a></li>
<li class="chapter" data-level="8.5.4" data-path="compare.html"><a href="compare.html#machine-learning"><i class="fa fa-check"></i><b>8.5.4</b> Machine learning</a></li>
<li class="chapter" data-level="8.5.5" data-path="compare.html"><a href="compare.html#regression-is-doomed"><i class="fa fa-check"></i><b>8.5.5</b> Regression is doomed?</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="9" data-path="misspecify.html"><a href="misspecify.html"><i class="fa fa-check"></i><b>9</b> PS vs. Double robust methods</a>
<ul>
<li class="chapter" data-level="9.1" data-path="misspecify.html"><a href="misspecify.html#complex-data-simulation"><i class="fa fa-check"></i><b>9.1</b> Complex Data Simulation</a>
<ul>
<li class="chapter" data-level="" data-path="misspecify.html"><a href="misspecify.html#true-exposure-model"><i class="fa fa-check"></i>True Exposure Model</a></li>
<li class="chapter" data-level="" data-path="misspecify.html"><a href="misspecify.html#true-outcome-model"><i class="fa fa-check"></i>True Outcome Model</a></li>
<li class="chapter" data-level="" data-path="misspecify.html"><a href="misspecify.html#outcomes-and-exposures-are-complex-functions-of-measured-covariates"><i class="fa fa-check"></i>Outcomes and exposures are complex functions of measured covariates</a></li>
</ul></li>
<li class="chapter" data-level="9.2" data-path="misspecify.html"><a href="misspecify.html#understanding-finite-sample-bias"><i class="fa fa-check"></i><b>9.2</b> Understanding finite sample bias</a></li>
<li class="chapter" data-level="9.3" data-path="misspecify.html"><a href="misspecify.html#estimation-using-different-methods"><i class="fa fa-check"></i><b>9.3</b> Estimation using different methods</a>
<ul>
<li class="chapter" data-level="9.3.1" data-path="misspecify.html"><a href="misspecify.html#regression-1"><i class="fa fa-check"></i><b>9.3.1</b> Regression</a></li>
<li class="chapter" data-level="9.3.2" data-path="misspecify.html"><a href="misspecify.html#propensity-score"><i class="fa fa-check"></i><b>9.3.2</b> Propensity score</a></li>
<li class="chapter" data-level="9.3.3" data-path="misspecify.html"><a href="misspecify.html#double-machine-learning-method"><i class="fa fa-check"></i><b>9.3.3</b> Double machine learning method</a></li>
<li class="chapter" data-level="9.3.4" data-path="misspecify.html"><a href="misspecify.html#augmented-inverse-probability-weighting"><i class="fa fa-check"></i><b>9.3.4</b> Augmented Inverse probability weighting</a></li>
<li class="chapter" data-level="9.3.5" data-path="misspecify.html"><a href="misspecify.html#double-robust-method-tmle"><i class="fa fa-check"></i><b>9.3.5</b> Double robust method (TMLE)</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="10" data-path="guide.html"><a href="guide.html"><i class="fa fa-check"></i><b>10</b> Reporting Guidelines</a>
<ul>
<li class="chapter" data-level="10.1" data-path="guide.html"><a href="guide.html#discipline-specific-reviews"><i class="fa fa-check"></i><b>10.1</b> Discipline-specific Reviews</a></li>
<li class="chapter" data-level="10.2" data-path="guide.html"><a href="guide.html#suggested-guidelines"><i class="fa fa-check"></i><b>10.2</b> Suggested Guidelines</a></li>
<li class="chapter" data-level="10.3" data-path="guide.html"><a href="guide.html#additional-topics"><i class="fa fa-check"></i><b>10.3</b> Additional topics</a></li>
</ul></li>
<li class="chapter" data-level="11" data-path="final.html"><a href="final.html"><i class="fa fa-check"></i><b>11</b> Final Words</a>
<ul>
<li class="chapter" data-level="11.1" data-path="final.html"><a href="final.html#common-misconception"><i class="fa fa-check"></i><b>11.1</b> Common misconception</a></li>
<li class="chapter" data-level="11.2" data-path="final.html"><a href="final.html#benifits-of-ps"><i class="fa fa-check"></i><b>11.2</b> Benifits of PS</a></li>
<li class="chapter" data-level="11.3" data-path="final.html"><a href="final.html#limitations-of-ps"><i class="fa fa-check"></i><b>11.3</b> Limitations of PS</a></li>
<li class="chapter" data-level="11.4" data-path="final.html"><a href="final.html#when-ps-may-not-be-useful"><i class="fa fa-check"></i><b>11.4</b> When PS may not be useful?</a></li>
<li class="chapter" data-level="11.5" data-path="final.html"><a href="final.html#software"><i class="fa fa-check"></i><b>11.5</b> Software</a></li>
<li class="chapter" data-level="11.6" data-path="final.html"><a href="final.html#further-resources"><i class="fa fa-check"></i><b>11.6</b> Further Resources</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
<li class="divider"></li>
<li><a href="https://ehsank.com/" target="blank">Ehsan Karim</a></li>
</ul>
</nav>
</div>
<div class="book-body">
<div class="body-inner">
<div class="book-header" role="navigation">
<h1>
<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Understanding Propensity Score Matching</a>
</h1>
</div>
<div class="page-wrapper" tabindex="-1" role="main">
<div class="page-inner">
<section class="normal" id="section-">
<div id="s4" class="section level1 hasAnchor" number="7">
<h1><span class="header-section-number">Chapter 7</span> Step 4: Outcome modelling<a href="s4.html#s4" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<ul>
<li>Some flexibility in choosing outcome model
<ul>
<li>considered independent of exposure modelling</li>
<li>some propose double robust approach</li>
<li>adjusting imbalanced covariates only?
<ul>
<li>double-adjustment may address residual confounding <span class="citation">(<a href="#ref-nguyen2017double" role="doc-biblioref">Nguyen et al. 2017</a>)</span></li>
</ul></li>
</ul></li>
</ul>
<div id="crude-outcome-model" class="section level2 hasAnchor" number="7.1">
<h2><span class="header-section-number">7.1</span> Crude outcome model<a href="s4.html#crude-outcome-model" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Estimate the effect of treatment on outcomes using propensity score-matched sample</p>
<div class="sourceCode" id="cb76"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb76-1"><a href="s4.html#cb76-1" aria-hidden="true" tabindex="-1"></a>fit3 <span class="ot"><-</span> <span class="fu">glm</span>(cholesterol<span class="sc">~</span>diabetes,</span>
<span id="cb76-2"><a href="s4.html#cb76-2" aria-hidden="true" tabindex="-1"></a> <span class="at">family=</span>binomial, <span class="at">data =</span> matched.data)</span>
<span id="cb76-3"><a href="s4.html#cb76-3" aria-hidden="true" tabindex="-1"></a><span class="fu">publish</span>(fit3)</span></code></pre></div>
<pre><code>## Variable Units OddsRatio CI.95 p-value
## diabetes 0.90 [0.54;1.50] 0.6984</code></pre>
</div>
<div id="double-adjustment" class="section level2 hasAnchor" number="7.2">
<h2><span class="header-section-number">7.2</span> Double-adjustment<a href="s4.html#double-adjustment" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Estimate the effect of treatment on outcomes using propensity score-matched sample, and adjust for imbalanced covariate</p>
<div class="sourceCode" id="cb78"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb78-1"><a href="s4.html#cb78-1" aria-hidden="true" tabindex="-1"></a>fit3r <span class="ot"><-</span> <span class="fu">glm</span>(cholesterol<span class="sc">~</span>diabetes <span class="sc">+</span> race,</span>
<span id="cb78-2"><a href="s4.html#cb78-2" aria-hidden="true" tabindex="-1"></a> <span class="at">family=</span>binomial, <span class="at">data =</span> matched.data)</span>
<span id="cb78-3"><a href="s4.html#cb78-3" aria-hidden="true" tabindex="-1"></a><span class="fu">publish</span>(fit3r)</span></code></pre></div>
<pre><code>## Variable Units OddsRatio CI.95 p-value
## diabetes 0.89 [0.54;1.49] 0.6657
## race Black Ref
## Hispanic 0.96 [0.46;2.02] 0.9165
## Other 1.32 [0.63;2.78] 0.4581
## White 0.58 [0.30;1.13] 0.1095</code></pre>
</div>
<div id="adjusted-outcome-model" class="section level2 hasAnchor" number="7.3">
<h2><span class="header-section-number">7.3</span> Adjusted outcome model<a href="s4.html#adjusted-outcome-model" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Adjust for all covariates, again! (suggested)</p>
<div class="sourceCode" id="cb80"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb80-1"><a href="s4.html#cb80-1" aria-hidden="true" tabindex="-1"></a>out.formula <span class="ot"><-</span> <span class="fu">as.formula</span>(<span class="fu">paste</span>(<span class="st">"cholesterol"</span>, <span class="st">"~ diabetes +"</span>, </span>
<span id="cb80-2"><a href="s4.html#cb80-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">paste</span>(baselinevars, </span>
<span id="cb80-3"><a href="s4.html#cb80-3" aria-hidden="true" tabindex="-1"></a> <span class="at">collapse =</span> <span class="st">"+"</span>)))</span>
<span id="cb80-4"><a href="s4.html#cb80-4" aria-hidden="true" tabindex="-1"></a>out.formula</span></code></pre></div>
<pre><code>## cholesterol ~ diabetes + gender + age + race + education + married +
## bmi</code></pre>
<div class="sourceCode" id="cb82"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb82-1"><a href="s4.html#cb82-1" aria-hidden="true" tabindex="-1"></a>fit3b <span class="ot"><-</span> <span class="fu">glm</span>(out.formula,</span>
<span id="cb82-2"><a href="s4.html#cb82-2" aria-hidden="true" tabindex="-1"></a> <span class="at">family=</span>binomial, <span class="at">data =</span> matched.data)</span>
<span id="cb82-3"><a href="s4.html#cb82-3" aria-hidden="true" tabindex="-1"></a><span class="fu">publish</span>(fit3b)</span></code></pre></div>
<pre><code>## Variable Units OddsRatio CI.95 p-value
## diabetes 0.86 [0.51;1.46] 0.5794126
## gender Female Ref
## Male 0.38 [0.21;0.69] 0.0012767
## age 0.95 [0.93;0.97] < 1e-04
## race Black Ref
## Hispanic 0.72 [0.31;1.65] 0.4346787
## Other 0.77 [0.34;1.73] 0.5224157
## White 0.51 [0.25;1.04] 0.0649791
## education College Ref
## High.School 0.70 [0.39;1.24] 0.2215142
## School 0.93 [0.35;2.43] 0.8791455
## married Married Ref
## Never.married 0.48 [0.15;1.54] 0.2173180
## Previously.married 0.84 [0.45;1.57] 0.5900732
## bmi 0.93 [0.89;0.97] 0.0005547</code></pre>
<p>The above analysis do not take matched pair into consideration while regressing.</p>
</div>
<div id="variance-considerations" class="section level2 hasAnchor" number="7.4">
<h2><span class="header-section-number">7.4</span> Variance considerations<a href="s4.html#variance-considerations" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Literature proposes different strategies:</p>
<ul>
<li>do not control for pairs / clusters
<ul>
<li>use <code>glm</code> as is</li>
</ul></li>
<li>control for pairs / clusters
<ul>
<li>use <code>cluster</code> option (preferred)</li>
<li>use GEE or</li>
<li>use conditional logistic</li>
</ul></li>
</ul>
<div id="cluster-option" class="section level3 hasAnchor" number="7.4.1">
<h3><span class="header-section-number">7.4.1</span> Cluster option<a href="s4.html#cluster-option" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Here is an example using cluster option:</p>
<div class="sourceCode" id="cb84"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb84-1"><a href="s4.html#cb84-1" aria-hidden="true" tabindex="-1"></a><span class="fu">require</span>(jtools)</span>
<span id="cb84-2"><a href="s4.html#cb84-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summ</span>(fit3b, <span class="at">rubust =</span> <span class="st">"HC0"</span>, <span class="at">confint =</span> <span class="cn">TRUE</span>, <span class="at">digists =</span> <span class="dv">3</span>, </span>
<span id="cb84-3"><a href="s4.html#cb84-3" aria-hidden="true" tabindex="-1"></a> <span class="at">cluster =</span> <span class="st">"subclass"</span>, <span class="at">model.info =</span> <span class="cn">FALSE</span>, </span>
<span id="cb84-4"><a href="s4.html#cb84-4" aria-hidden="true" tabindex="-1"></a> <span class="at">model.fit =</span> <span class="cn">FALSE</span>, <span class="at">exp =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
<table class="table table-striped table-hover table-condensed table-responsive" style="width: auto !important; margin-left: auto; margin-right: auto;border-bottom: 0;">
<thead>
<tr>
<th style="text-align:left;">
</th>
<th style="text-align:right;">
exp(Est.)
</th>
<th style="text-align:right;">
2.5%
</th>
<th style="text-align:right;">
97.5%
</th>
<th style="text-align:right;">
z val.
</th>
<th style="text-align:right;">
p
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;font-weight: bold;">
(Intercept)
</td>
<td style="text-align:right;">
100.02
</td>
<td style="text-align:right;">
8.74
</td>
<td style="text-align:right;">
1144.55
</td>
<td style="text-align:right;">
3.70
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
diabetes
</td>
<td style="text-align:right;">
0.86
</td>
<td style="text-align:right;">
0.51
</td>
<td style="text-align:right;">
1.46
</td>
<td style="text-align:right;">
-0.55
</td>
<td style="text-align:right;">
0.58
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
genderMale
</td>
<td style="text-align:right;">
0.38
</td>
<td style="text-align:right;">
0.21
</td>
<td style="text-align:right;">
0.69
</td>
<td style="text-align:right;">
-3.22
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
age
</td>
<td style="text-align:right;">
0.95
</td>
<td style="text-align:right;">
0.93
</td>
<td style="text-align:right;">
0.97
</td>
<td style="text-align:right;">
-4.47
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
raceHispanic
</td>
<td style="text-align:right;">
0.72
</td>
<td style="text-align:right;">
0.31
</td>
<td style="text-align:right;">
1.65
</td>
<td style="text-align:right;">
-0.78
</td>
<td style="text-align:right;">
0.43
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
raceOther
</td>
<td style="text-align:right;">
0.77
</td>
<td style="text-align:right;">
0.34
</td>
<td style="text-align:right;">
1.73
</td>
<td style="text-align:right;">
-0.64
</td>
<td style="text-align:right;">
0.52
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
raceWhite
</td>
<td style="text-align:right;">
0.51
</td>
<td style="text-align:right;">
0.25
</td>
<td style="text-align:right;">
1.04
</td>
<td style="text-align:right;">
-1.85
</td>
<td style="text-align:right;">
0.06
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
educationHigh.School
</td>
<td style="text-align:right;">
0.70
</td>
<td style="text-align:right;">
0.39
</td>
<td style="text-align:right;">
1.24
</td>
<td style="text-align:right;">
-1.22
</td>
<td style="text-align:right;">
0.22
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
educationSchool
</td>
<td style="text-align:right;">
0.93
</td>
<td style="text-align:right;">
0.35
</td>
<td style="text-align:right;">
2.43
</td>
<td style="text-align:right;">
-0.15
</td>
<td style="text-align:right;">
0.88
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
marriedNever.married
</td>
<td style="text-align:right;">
0.48
</td>
<td style="text-align:right;">
0.15
</td>
<td style="text-align:right;">
1.54
</td>
<td style="text-align:right;">
-1.23
</td>
<td style="text-align:right;">
0.22
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
marriedPreviously.married
</td>
<td style="text-align:right;">
0.84
</td>
<td style="text-align:right;">
0.45
</td>
<td style="text-align:right;">
1.57
</td>
<td style="text-align:right;">
-0.54
</td>
<td style="text-align:right;">
0.59
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
bmi
</td>
<td style="text-align:right;">
0.93
</td>
<td style="text-align:right;">
0.89
</td>
<td style="text-align:right;">
0.97
</td>
<td style="text-align:right;">
-3.45
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
</tbody>
<tfoot>
<tr>
<td style="padding: 0; " colspan="100%">
<sup></sup> Standard errors: MLE
</td>
</tr>
</tfoot>
</table>
</div>
<div id="bootstrap" class="section level3 hasAnchor" number="7.4.2">
<h3><span class="header-section-number">7.4.2</span> Bootstrap<a href="s4.html#bootstrap" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<ul>
<li>Bootstrap for matched pair for WOR <span class="citation">(<a href="#ref-austin2014use" role="doc-biblioref">Austin and Small 2014</a>)</span>
<ul>
<li>straightforward method to estimate SE</li>
<li>may not be appropriate for WR</li>
</ul></li>
<li>Following is an example of block bootstrap; see MatchIt package <a href="https://cran.r-project.org/web/packages/MatchIt/vignettes/estimating-effects.html">vignettes</a> for additional details.</li>
</ul>
<div class="sourceCode" id="cb85"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb85-1"><a href="s4.html#cb85-1" aria-hidden="true" tabindex="-1"></a><span class="co"># For binary outcomes</span></span>
<span id="cb85-2"><a href="s4.html#cb85-2" aria-hidden="true" tabindex="-1"></a><span class="co"># with covariate adjustment and bootstrapping</span></span>
<span id="cb85-3"><a href="s4.html#cb85-3" aria-hidden="true" tabindex="-1"></a>pair_ids <span class="ot"><-</span> <span class="fu">levels</span>(matched.data<span class="sc">$</span>subclass)</span>
<span id="cb85-4"><a href="s4.html#cb85-4" aria-hidden="true" tabindex="-1"></a>est_fun <span class="ot"><-</span> <span class="cf">function</span>(pairs, i) {</span>
<span id="cb85-5"><a href="s4.html#cb85-5" aria-hidden="true" tabindex="-1"></a> <span class="co"># See MatchIt vignettes</span></span>
<span id="cb85-6"><a href="s4.html#cb85-6" aria-hidden="true" tabindex="-1"></a> <span class="co">#Compute number of times each pair is present</span></span>
<span id="cb85-7"><a href="s4.html#cb85-7" aria-hidden="true" tabindex="-1"></a> numreps <span class="ot"><-</span> <span class="fu">table</span>(pairs[i])</span>
<span id="cb85-8"><a href="s4.html#cb85-8" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb85-9"><a href="s4.html#cb85-9" aria-hidden="true" tabindex="-1"></a> <span class="co">#For each pair p, copy corresponding matched.data row indices numreps[p] times</span></span>
<span id="cb85-10"><a href="s4.html#cb85-10" aria-hidden="true" tabindex="-1"></a> ids <span class="ot"><-</span> <span class="fu">unlist</span>(<span class="fu">lapply</span>(pair_ids[pair_ids <span class="sc">%in%</span> <span class="fu">names</span>(numreps)],</span>
<span id="cb85-11"><a href="s4.html#cb85-11" aria-hidden="true" tabindex="-1"></a> <span class="cf">function</span>(p) <span class="fu">rep</span>(<span class="fu">which</span>(matched.data<span class="sc">$</span>subclass <span class="sc">==</span> p), </span>
<span id="cb85-12"><a href="s4.html#cb85-12" aria-hidden="true" tabindex="-1"></a> numreps[p])))</span>
<span id="cb85-13"><a href="s4.html#cb85-13" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb85-14"><a href="s4.html#cb85-14" aria-hidden="true" tabindex="-1"></a> <span class="co">#Subset matched.data with block bootstrapped ids</span></span>
<span id="cb85-15"><a href="s4.html#cb85-15" aria-hidden="true" tabindex="-1"></a> matched.data_boot <span class="ot"><-</span> matched.data[ids,]</span>
<span id="cb85-16"><a href="s4.html#cb85-16" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb85-17"><a href="s4.html#cb85-17" aria-hidden="true" tabindex="-1"></a> <span class="co">#Fitting outcome the model</span></span>
<span id="cb85-18"><a href="s4.html#cb85-18" aria-hidden="true" tabindex="-1"></a> out.formula <span class="ot"><-</span> <span class="fu">as.formula</span>(<span class="fu">paste</span>(<span class="st">"cholesterol"</span>, <span class="st">"~ diabetes +"</span>, </span>
<span id="cb85-19"><a href="s4.html#cb85-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">paste</span>(baselinevars, </span>
<span id="cb85-20"><a href="s4.html#cb85-20" aria-hidden="true" tabindex="-1"></a> <span class="at">collapse =</span> <span class="st">"+"</span>)))</span>
<span id="cb85-21"><a href="s4.html#cb85-21" aria-hidden="true" tabindex="-1"></a> fit_boot <span class="ot"><-</span> <span class="fu">glm</span>(out.formula,</span>
<span id="cb85-22"><a href="s4.html#cb85-22" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">"logit"</span>), </span>
<span id="cb85-23"><a href="s4.html#cb85-23" aria-hidden="true" tabindex="-1"></a> <span class="at">weights =</span> weights,</span>
<span id="cb85-24"><a href="s4.html#cb85-24" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> matched.data_boot)</span>
<span id="cb85-25"><a href="s4.html#cb85-25" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb85-26"><a href="s4.html#cb85-26" aria-hidden="true" tabindex="-1"></a> <span class="co">#Estimate potential outcomes for each unit</span></span>
<span id="cb85-27"><a href="s4.html#cb85-27" aria-hidden="true" tabindex="-1"></a> <span class="co">#Under control</span></span>
<span id="cb85-28"><a href="s4.html#cb85-28" aria-hidden="true" tabindex="-1"></a> matched.data_boot<span class="sc">$</span>diabetes <span class="ot"><-</span> <span class="dv">0</span></span>
<span id="cb85-29"><a href="s4.html#cb85-29" aria-hidden="true" tabindex="-1"></a> P0 <span class="ot"><-</span> <span class="fu">weighted.mean</span>(<span class="fu">predict</span>(fit_boot, matched.data_boot, <span class="at">type =</span> <span class="st">"response"</span>),</span>
<span id="cb85-30"><a href="s4.html#cb85-30" aria-hidden="true" tabindex="-1"></a> <span class="at">w =</span> matched.data_boot<span class="sc">$</span>weights)</span>
<span id="cb85-31"><a href="s4.html#cb85-31" aria-hidden="true" tabindex="-1"></a> Odds0 <span class="ot"><-</span> P0 <span class="sc">/</span> (<span class="dv">1</span> <span class="sc">-</span> P0)</span>
<span id="cb85-32"><a href="s4.html#cb85-32" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb85-33"><a href="s4.html#cb85-33" aria-hidden="true" tabindex="-1"></a> <span class="co">#Under treatment</span></span>
<span id="cb85-34"><a href="s4.html#cb85-34" aria-hidden="true" tabindex="-1"></a> matched.data_boot<span class="sc">$</span>diabetes <span class="ot"><-</span> <span class="dv">1</span></span>
<span id="cb85-35"><a href="s4.html#cb85-35" aria-hidden="true" tabindex="-1"></a> P1 <span class="ot"><-</span> <span class="fu">weighted.mean</span>(<span class="fu">predict</span>(fit_boot, matched.data_boot, <span class="at">type =</span> <span class="st">"response"</span>),</span>
<span id="cb85-36"><a href="s4.html#cb85-36" aria-hidden="true" tabindex="-1"></a> <span class="at">w =</span> matched.data_boot<span class="sc">$</span>weights)</span>
<span id="cb85-37"><a href="s4.html#cb85-37" aria-hidden="true" tabindex="-1"></a> Odds1 <span class="ot"><-</span> P1 <span class="sc">/</span> (<span class="dv">1</span> <span class="sc">-</span> P1)</span>
<span id="cb85-38"><a href="s4.html#cb85-38" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb85-39"><a href="s4.html#cb85-39" aria-hidden="true" tabindex="-1"></a> <span class="co">#Return marginal odds ratio</span></span>
<span id="cb85-40"><a href="s4.html#cb85-40" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(Odds1 <span class="sc">/</span> Odds0)</span>
<span id="cb85-41"><a href="s4.html#cb85-41" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb85-42"><a href="s4.html#cb85-42" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb85-43"><a href="s4.html#cb85-43" aria-hidden="true" tabindex="-1"></a>boot_est <span class="ot"><-</span> <span class="fu">boot</span>(pair_ids, est_fun, <span class="at">R =</span> <span class="dv">1000</span>)</span>
<span id="cb85-44"><a href="s4.html#cb85-44" aria-hidden="true" tabindex="-1"></a><span class="co"># R must be larger than # of data rows</span></span>
<span id="cb85-45"><a href="s4.html#cb85-45" aria-hidden="true" tabindex="-1"></a>boot_est</span></code></pre></div>
<pre><code>##
## ORDINARY NONPARAMETRIC BOOTSTRAP
##
##
## Call:
## boot(data = pair_ids, statistic = est_fun, R = 1000)
##
##
## Bootstrap Statistics :
## original bias std. error
## t1* 0.8706933 0.04061083 0.2376491</code></pre>
<div class="sourceCode" id="cb87"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb87-1"><a href="s4.html#cb87-1" aria-hidden="true" tabindex="-1"></a><span class="fu">boot.ci</span>(boot_est, <span class="at">type =</span> <span class="st">"bca"</span>)</span></code></pre></div>
<pre><code>## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
##
## CALL :
## boot.ci(boot.out = boot_est, type = "bca")
##
## Intervals :
## Level BCa
## 95% ( 0.5239, 1.3936 )
## Calculations and Intervals on Original Scale</code></pre>
</div>
</div>
<div id="estimate-obtained" class="section level2 hasAnchor" number="7.5">
<h2><span class="header-section-number">7.5</span> Estimate obtained<a href="s4.html#estimate-obtained" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>The example compared <code>diabetic</code> (a treated group; target) vs <code>Not diabetic</code> (untreated).</li>
<li>Thc corresponding treatment effect estimate is known as
<ul>
<li>Average Treatment Effects on the Treated (<strong>ATT</strong>)</li>
</ul></li>
<li>Other estimates from PS analysis (e.g., PS weighting) are possible that compared the whole population
<ul>
<li>what if everyone treated vs. what if nobody was treated (ATE)</li>
</ul></li>
</ul>
<p>You can see further comparison of results <a href="https://ehsanx.github.io/TMLEworkshop/rhc-data-description.html">elsewhere</a>.</p>
</div>
</div>
<h3>References<a href="references.html#references" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-austin2014use" class="csl-entry">
Austin, Peter C, and Dylan S Small. 2014. <span>“The Use of Bootstrapping When Using Propensity-Score Matching Without Replacement: A Simulation Study.”</span> <em>Statistics in Medicine</em> 33 (24): 4306–19.
</div>
<div id="ref-nguyen2017double" class="csl-entry">
Nguyen, Tri-Long, Gary S Collins, Jessica Spence, Jean-Pierre Daurès, PJ Devereaux, Paul Landais, and Yannick Le Manach. 2017. <span>“Double-Adjustment in Propensity Score Matching Analysis: Choosing a Threshold for Considering Residual Imbalance.”</span> <em>BMC Medical Research Methodology</em> 17 (1): 1–8.
</div>
</div>
</section>
</div>
</div>
</div>
<a href="s3.html" class="navigation navigation-prev " aria-label="Previous page"><i class="fa fa-angle-left"></i></a>
<a href="compare.html" class="navigation navigation-next " aria-label="Next page"><i class="fa fa-angle-right"></i></a>
</div>
</div>
<script src="libs/gitbook-2.6.7/js/app.min.js"></script>
<script src="libs/gitbook-2.6.7/js/clipboard.min.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-search.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-sharing.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-fontsettings.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-bookdown.js"></script>
<script src="libs/gitbook-2.6.7/js/jquery.highlight.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-clipboard.js"></script>
<script>
gitbook.require(["gitbook"], function(gitbook) {
gitbook.start({
"sharing": {
"github": false,
"facebook": true,
"twitter": true,
"linkedin": false,
"weibo": false,
"instapaper": false,
"vk": false,
"whatsapp": false,
"all": ["facebook", "twitter", "linkedin", "weibo", "instapaper"]
},
"fontsettings": {
"theme": "white",
"family": "sans",
"size": 2
},
"edit": {
"link": "https://github.com/ehsanx/UnderstandingPropensityScore/edit/master/07-steps4.Rmd",
"text": "Edit"
},
"history": {
"link": null,
"text": null
},
"view": {
"link": null,
"text": null
},
"download": ["UnderstandingPropensityScore.pdf", "UnderstandingPropensityScore.epub"],
"search": {
"engine": "fuse",
"options": null
},
"toc": {
"collapse": "subsection"
}
});
});
</script>
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement("script");
script.type = "text/javascript";
var src = "true";
if (src === "" || src === "true") src = "https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.9/latest.js?config=TeX-MML-AM_CHTML";
if (location.protocol !== "file:")
if (/^https?:/.test(src))
src = src.replace(/^https?:/, '');
script.src = src;
document.getElementsByTagName("head")[0].appendChild(script);
})();
</script>
</body>
</html>