Linear probability models
- `t1` and `t0`: binarized count: if > 0 -> 1, else 0
- `t0`: dummy and centered so `mean(t0)` is 0
# frequentist
## condition (treatment) effect
- see quasipoisson count results: [[230718_135343 frequentist fixed-effects meta for studies 1 3 4]]
```r
# treatment effect
# ITT
threshold estimate se low high pval
1: 40 -0.0012 0.0017 -0.0046 0.0021 0.4780
2: 45 -0.0019 0.0017 -0.0054 0.0015 0.2647
3: 50 -0.0016 0.0018 -0.0051 0.0020 0.3823
4: 55 -0.0012 0.0019 -0.0049 0.0024 0.5154
5: 60 -0.0009 0.0019 -0.0047 0.0028 0.6200
6: 65 -0.0006 0.0020 -0.0044 0.0033 0.7740
7: 70 -0.0008 0.0020 -0.0048 0.0031 0.6882
8: 75 -0.0007 0.0020 -0.0047 0.0033 0.7326
9: 80 -0.0008 0.0021 -0.0049 0.0032 0.6819
# ATT
threshold estimate se low high pval
1: 40 -0.0020 0.0028 -0.0075 0.0035 0.4851
2: 45 -0.0032 0.0029 -0.0088 0.0024 0.2688
3: 50 -0.0025 0.0030 -0.0083 0.0033 0.4019
4: 55 -0.0019 0.0031 -0.0078 0.0041 0.5420
5: 60 -0.0013 0.0031 -0.0075 0.0048 0.6755
6: 65 -0.0007 0.0032 -0.0071 0.0057 0.8286
7: 70 -0.0011 0.0033 -0.0076 0.0054 0.7399
8: 75 -0.0009 0.0034 -0.0075 0.0057 0.7906
9: 80 -0.0011 0.0034 -0.0077 0.0055 0.7412
```
![[1690155122.png]]
![[1690155123.png]]
## condition-t0 interaction effect
![[1690155216.png]]
![[1690155247.png]]
## t0 effect
![[1690155398.png]]
![[1690155401.png]]
# bayesian
- see quasipoisson count results: [[230719_184036 bayesian fixed-effects meta for studies 1 3 4]]
```r
threshold estimate CI CI_low CI_high evid_ratio post_prob type
1: 40 -4e-04 0.95 -0.0025 0.0015 1.8532 0.6495 Intent-to-treat effect
2: 45 -6e-04 0.95 -0.0028 0.0013 2.7280 0.7318 Intent-to-treat effect
3: 50 -5e-04 0.95 -0.0027 0.0015 2.0991 0.6773 Intent-to-treat effect
4: 55 -4e-04 0.95 -0.0025 0.0017 1.7377 0.6347 Intent-to-treat effect
5: 60 -3e-04 0.95 -0.0024 0.0017 1.4984 0.5998 Intent-to-treat effect
6: 65 -2e-04 0.95 -0.0023 0.0019 1.2426 0.5541 Intent-to-treat effect
7: 70 -2e-04 0.95 -0.0024 0.0018 1.3620 0.5766 Intent-to-treat effect
8: 75 -2e-04 0.95 -0.0023 0.0019 1.2998 0.5652 Intent-to-treat effect
9: 80 -2e-04 0.95 -0.0024 0.0019 1.3674 0.5776 Intent-to-treat effect
10: 40 -3e-04 0.95 -0.0029 0.0020 1.5443 0.6070 Treatment effect on the treated
11: 45 -6e-04 0.95 -0.0034 0.0018 2.0130 0.6681 Treatment effect on the treated
12: 50 -4e-04 0.95 -0.0031 0.0020 1.6604 0.6241 Treatment effect on the treated
13: 55 -3e-04 0.95 -0.0028 0.0021 1.4332 0.5890 Treatment effect on the treated
14: 60 -2e-04 0.95 -0.0026 0.0023 1.2521 0.5560 Treatment effect on the treated
15: 65 -1e-04 0.95 -0.0026 0.0023 1.1189 0.5281 Treatment effect on the treated
16: 70 -2e-04 0.95 -0.0027 0.0023 1.1977 0.5450 Treatment effect on the treated
17: 75 -1e-04 0.95 -0.0026 0.0024 1.1366 0.5320 Treatment effect on the treated
18: 80 -2e-04 0.95 -0.0027 0.0025 1.2056 0.5466 Treatment effect on the treated
```
![[_mainfig_count_conditionC.png]]
![[_mainfig_count_conditionC-t0SC.png]]
![[_mainfig_count_t0SC.png]]