Lab 2
General Instructions
Your response should include a Quarto file (.qmd) and an HTML document that is the result of applying your Quarto file to the data we’ve provided.
A Quarto template for Lab 2 is found in the templates section of our 500-data page.
Data
Lab 2 uses the canc3.csv data file, which is available in the data folder on the 500-data page.
We have completed the data collection in a simulated study of 400 subjects with cancer, where 150 have received an intervention, while the remaining 250 received usual care control. The primary aims of the study are to learn about the impact of the intervention on patient survival and whether or not the patient enters hospice.
The Codebook
The data file includes 400 observations, on 12 variables.
| Variable | Description | Notes |
|---|---|---|
subject |
Study ID number | 1-250 are control, 251-400 are intervention |
treated |
Treatment status | 1 = intervention (150), 0 = control (250) |
age |
Patient age | At study entry, Observed range: 34, 93 years |
female |
Patient sex | 1 = female (n = 258), 0 = male (n = 142) |
race |
Patient’s race | 1 = Caucasian / White (n = 317), 0 = not (n = 83) |
married |
Marital status | At study entry: 1 = Married (n = 245), 0 = not (n = 155) |
typeca |
Type of cancer | 3 categories: 1 = GI/colorectal (n = 177), 2 = Lung (n = 129), 3 = GYN (n = 94). |
stprob |
5-year survival | Model probability of 5-year survival, based on type and stage of cancer. Observed range: 0.01, 0.72 |
charlson |
Charlson score | Comorbidity index at baseline: higher scores indicate greater comorbidity. Observed range: 0-7. |
ecog |
ECOG score | 0 = fully active, 1 = restricted regarding physically strenuous activity, 2 = ambulatory, can self-care, otherwise limited, 3 = capable of only limited self-care. |
alive |
Mortality Status | Alive at study conclusion & 1 = alive (n = 245), 0 = dead (n = 155) |
hospice |
Hospice Status | Entered hospice before death or study end & 1 = hospice (n = 143), 0 = no (n = 257) |
Note: You are welcome to treat ecog and charlson as either quantitative or categorical variables in developing your response.
Task 1.
Ignoring the covariate information, provide an appropriate (unadjusted) estimate (with point estimate and 95% confidence interval) of the effect of the intervention on each of the two binary outcomes; first survival, and then hospice entry. Be sure to describe the effect in English sentences, so that both the direction and magnitude are clear, and also be sure to specify the method you used in generating your estimates.
Task 2.
Next, fit a propensity score model to the data, using the eight pieces of covariate information, including age, gender, race, marital status, cancer type (which must be treated in R as a factor rather than just a continuous predictor) the model survival probability, Charlson index and ECOG. Do not include interactions between terms.
Task 3.
Evaluate Rubin’s Rule 1 and Rubin’s Rule 2 for the data taken as a whole. What can you conclude about the balance across the two exposure groups prior to using the propensity score? What do these results suggest about your model in Task 1?
Task 4.
Use direct adjustment for the (logit of) the propensity score in a logistic regression model for the hospice outcome to evaluate the intervention’s effect on hospice entry, developing a point estimate (this should be an odds ratio) and a 95% confidence interval.
Task 5.
In our first propensity score matching attempt with the canc3 data, we’ll apply a 1:1 match without replacement. Do the matching, and then evaluate the balance associated with this approach, as follows.
Task 5a.
Evaluate the degree of covariate imbalance before and after propensity score matching for each of the eight covariates and for the (linear and raw) propensity score. Do so by plotting the standardized differences. Your plot should include standardized differences that identify the three cancer types (one remaining as baseline) individually, one each for any other covariates you treat as quantitative, and an appropriate set of indicators for any others you treat as categorical, plus one for the linear propensity score, and one for the raw propensity score.
Task 5b.
Evaluate the balance imposed by your 1:1 match via calculation of Rubin’s Rule 1 and Rule 2 results, and comparing them to our results obtained prior to propensity adjustment in Task 3.
Task 5c.
Finally, find a point estimate (and 95% confidence interval) for the effect of the treatment on the hospice outcome, based on your 1:1 match on the propensity score. Since the outcomes are binary, you should be using a conditional logistic regression to establish odds ratio estimates, while accounting for the pairs.
Task 6.
Compare your unadjusted (Task 1), propensity score-adjusted (by regression: Task 4) and propensity matching (Task 5) estimates of the effect of the intervention on the hospice outcome in a table (or better, graph.) What can you conclude?