The notes for the topics on this page can be found in the lecture 22 folder on Canvas.
To conduct conditional logistic regression in R you can use clogit() from the survival package. clogit() follows the same syntax as other linear models in R but includes a strata() argument where you specify the indicator for matching. R will also return odds ratios and 95% CIs for the model’s covariates if you save your model as an object and call summary().
library(tibble)
library(survival)
id <- function() {
x <- vector("numeric")
for (i in 1:17) {
x <- append(x, rep(i, 2))
}
x
}
lbw <- tibble(
pair_id = id(),
low = c(1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0),
lwt = c(130, 110, 120, 103, 110, 107, 102, 182, 105, 105, 100,
108, 130, 118, 94, 130, 138, 90, 89, 118, 190, 113, 130,
124, 120, 120, 130, 150, 142, 107, 102, 215, 105, 121)
)
lbw_model <- clogit(low ~ lwt + strata(pair_id), data = lbw)
summary(lbw_model)## Call:
## coxph(formula = Surv(rep(1, 34L), low) ~ lwt + strata(pair_id),
## data = lbw, method = "exact")
##
## n= 34, number of events= 17
##
## coef exp(coef) se(coef) z Pr(>|z|)
## lwt -0.005283 0.994731 0.011414 -0.463 0.643
##
## exp(coef) exp(-coef) lower .95 upper .95
## lwt 0.9947 1.005 0.9727 1.017
##
## Concordance= 0.471 (se = 0.161 )
## Likelihood ratio test= 0.22 on 1 df, p=0.6
## Wald test = 0.21 on 1 df, p=0.6
## Score (logrank) test = 0.22 on 1 df, p=0.6To conduct conditional logistic regression in SAS you the logistic procedure with the strata statement specified to indicate the matching variable.
title 'Lowbirth Example - 1:1 matching';
data LBW;
input pairid id Age Low LWT Smoke HT UI @@;
cards;
1 25 16 1 130 0 0 0 1 143 16 0 110 0 0 0
2 71 17 1 120 0 0 0 2 93 17 0 103 0 0 0
3 50 18 1 110 1 0 0 3 89 18 0 107 1 0 1
4 33 19 1 102 0 0 0 4 85 19 0 182 0 0 1
5 76 20 1 105 0 0 0 5 87 20 0 105 1 0 0
6 52 21 1 100 0 0 0 6 88 21 0 108 1 0 1
7 67 22 1 130 1 0 0 7 92 22 0 118 0 0 0
8 82 23 1 94 1 0 0 8 130 23 0 130 0 0 0
9 36 24 1 138 0 0 0 9 118 24 0 90 1 0 0
10 32 25 1 89 0 0 0 10 103 25 0 118 1 0 0
11 77 26 1 190 1 0 0 11 95 26 0 113 1 0 0
12 43 27 1 130 0 0 1 12 125 27 0 124 1 0 0
13 04 28 1 120 1 0 1 13 105 28 0 120 1 0 0
14 10 29 1 130 0 0 1 14 114 29 0 150 0 0 0
15 65 30 1 142 1 0 0 15 99 30 0 107 0 0 1
16 56 31 1 102 1 0 0 16 126 31 0 215 1 0 0
17 22 32 1 105 1 0 0 17 106 32 0 121 0 0 0
;
run;
proc logistic data = LBW descending;
strata pairid;
model low = LWT;
run;## Lowbirth Example - 1:1 matching
##
## The LOGISTIC Procedure
##
## Conditional Analysis
##
## Model Information
##
## Data Set WORK.LBW
## Response Variable Low
## Number of Response Levels 2
## Number of Strata 17
## Model binary logit
## Optimization Technique Newton-Raphson ridge
##
##
## Number of Observations Read 34
## Number of Observations Used 34
##
##
## Response Profile
##
## Ordered Total
## Value Low Frequency
##
## 1 1 17
## 2 0 17
##
## Probability modeled is Low=1.
##
##
## Strata Summary
##
## Low
## Response ------ Number of
## Pattern 1 0 Strata Frequency
##
## 1 1 1 17 34
##
## Newton-Raphson Ridge Optimization
##
## Without Parameter Scaling
##
## Convergence criterion (GCONV=1E-8) satisfied.
##
##
## Model Fit Statistics
##
## Without With
## Criterion Covariates Covariates
##
## AIC 23.567 25.347
## SC 23.567 26.873
## -2 Log L 23.567 23.347
##
##
## Testing Global Null Hypothesis: BETA=0
##
## Test Chi-Square DF Pr > ChiSq
##
## Likelihood Ratio 0.2199 1 0.6391
## Score 0.2180 1 0.6405
## Wald 0.2143 1 0.6435
##
##
## Analysis of Conditional Maximum Likelihood Estimates
##
## Standard Wald
## Parameter DF Estimate Error Chi-Square Pr > ChiSq
##
## LWT 1 -0.00528 0.0114 0.2143 0.6435
##
##
## Odds Ratio Estimates
##
## Point 95% Wald
## Effect Estimate Confidence Limits
##
## LWT 0.995 0.973 1.017