2021-09-01 (updated: 2023-08-31)

Lucy D’Agostino McGowan

Wake Forest University

Rosenbaum and Rubin showed in observational studies, conditioning on **propensity scores** can lead to unbiased estimates of the exposure effect

**There are no unmeasured confounders**- Every subject has a nonzero probability of receiving either exposure

- The exposure-outcome
- The exposure-unmeasured
- The unmeasured confounder-outcome effect

`{action}_{effect}_with_{what}`

`tip_rr_with_continous()`

`adjust_coef_with_r2()`

- New-user design
**Matched**42,217 new metformin users to 42,217 new sulfonylurea users- Fit
**adjusted Cox proportional hazards model**on the matched cohort

**Outcome:**Lung Cancer**Adjusted Hazard Ratio**: 0.87 (0.79, 0.96)

Meadows SO, Engel CC, Collins RL, Beckman RL, Cefalu M, Hawes-Dawson J, et al. 2015 health related behaviors survey: Substance use among US active-duty service members. RAND; 2018.

`tipr`

Example**What if we assume the effect of alcohol consumption on lung cancer after adjusting for other confounders is 2?**

`tipr`

Example**What if we assume the effect of alcohol consumption on lung cancer after adjusting for other confounders is 2?**

**Outcome:**Lung Cancer**Adjusted Hazard Ratio**: 0.87 (0.79, 0.96)

`tipr`

Example**What if we assume the effect of alcohol consumption on lung cancer after adjusting for other confounders is 2?**

`tipr`

Example`tipr`

Example```
# A tibble: 3 × 5
hr_adjusted hr_observed exposed_confounder_prev unexposed_confounder_prev
<dbl> <dbl> <dbl> <dbl>
1 0.805 0.79 0.04 0.06
2 0.887 0.87 0.04 0.06
3 0.978 0.96 0.04 0.06
# ℹ 1 more variable: confounder_outcome_effect <dbl>
```

`tipr`

Example`tipr`

Example`tipr`

Example`tipr`

Example```
# A tibble: 1 × 6
effect_adjusted effect_observed exposed_confounder_prev unexposed_confounder…¹
<dbl> <dbl> <dbl> <dbl>
1 1 0.96 0.04 0.06
# ℹ abbreviated name: ¹unexposed_confounder_prev
# ℹ 2 more variables: confounder_outcome_effect <dbl>,
# n_unmeasured_confounders <dbl>
```

`adjust_*`

functions

`adjust_*`

functions in an array`tip_*`

functions

`adjust_*`

functions in an array`tip_*`

functions in an array`tip_coef_with_r2()`

(measured confounders)- Robustness value
`r_value()`

& E-values`e_value()`

`tip_coef()`

`effect_observed`

: observed exposure - outcome effect**4.32 minutes (95% CI: 0.0009, 8.36)**

`tip_coef()`

`exposure_confounder_effect`

: scaled mean difference between the unmeasured confounder in the exposed and unexposed population

`tip_coef()`

`confounder_outcome_effect`

: relationship between the unmeasured confounder and outcome

`05:00`

`tip_coef()`

function to conduct a sensitivity analysis for the estimate from your previous exercises. Use the lower bound of the confidence interval for the effect and `0.1`

for the exposure-confounder effect.