# A tibble: 9 × 7
term estimate std.error statistic p.value conf.low conf.high
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) -0.794 0.534 -1.49 0.137 -1.86 0.239
2 `Age at Surgery/Biops… -0.0169 0.00741 -2.28 0.0228 -0.0314 -0.00230
3 SexMale -0.0523 0.167 -0.312 0.755 -0.384 0.274
4 `Race Category`Black 0.460 0.448 1.03 0.305 -0.439 1.33
5 `Race Category`Other 0.476 0.629 0.757 0.449 -0.825 1.68
6 `Race Category`Unknown 0.667 0.436 1.53 0.126 -0.199 1.52
7 `Race Category`White 0.251 0.284 0.886 0.376 -0.284 0.834
8 `TP53 Pathway`Yes 0.452 0.177 2.56 0.0106 0.110 0.804
9 `TMB (nonsynonymous)` 0.0222 0.00833 2.66 0.00777 0.00599 0.0388 Model
Overview
This page presents the statistical model predicting immunotherapy use in patients with lung adenocarcinoma. Since the question is Predictive, we will use a logistic regression to model the data.
Table
According to this table, we can interpret that if you have a TP53 pathway, you are 45.2% more likely to recieve immmunotherapy after a surgery/biopsy. This estimate is statistically significant which is proven by the low p value of 0.0106 and the confidence interval (0.110 to 0.804) not including the number 0.
Data Generating Mechanism
The probability \(p_i\) of a patient receiving post-sample immunotherapy is modeled using logistic regression:
\[\text{logit}(p_i) = \ln\left(\frac{p_i}{1 - p_i}\right) = \beta_0 + \beta_1(\text{Age}_i) + \beta_2(\text{Sex}_{\text{Male}, i}) + \beta_3(\text{Race}_{\text{Black}, i}) + \beta_4(\text{Race}_{\text{Other}, i}) + \beta_5(\text{Race}_{\text{Unknown}, i}) + \beta_6(\text{Race}_{\text{White}, i}) + \beta_7(\text{TP53}_{\text{Yes}, i}) + \beta_8(\text{TMB}_i)\]
Using the estimated parameters from our model:
\[\text{logit}(p_i) = -0.794 - 0.0169(\text{Age}_i) - 0.0523(\text{Sex}_{\text{Male}, i}) + 0.460(\text{Race}_{\text{Black}, i}) + 0.476(\text{Race}_{\text{Other}, i}) + 0.667(\text{Race}_{\text{Unknown}, i}) + 0.251(\text{Race}_{\text{White}, i}) + 0.452(\text{TP53}_{\text{Yes}, i}) + 0.0222(\text{TMB}_i)\]