1 Library

library(epiDisplay) # dataset & nice output table

Loading required package: foreign

Loading required package: survival

Loading required package: MASS

Loading required package: nnet

library(gtsummary)  # descriptive table


Attaching package: 'gtsummary'

The following object is masked from 'package:MASS':

    select

library(survival)   # clogit
library(broom)      # tidy
library(mfp)        # frac poly
library(knitr)      # for nice display of results
library(gofcat)     # model fit


Attaching package: 'gofcat'

The following object is masked from 'package:survival':

    retinopathy

2 Datasets

Now we use two built-in datasets

?VC1to1  # Datasets on a matched case-control study of esophageal cancer

starting httpd help server ... done

data(VC1to1)
cancer = VC1to1
str(cancer)

'data.frame':   52 obs. of  5 variables:
 $ matset : num  1 1 2 2 3 3 4 4 5 5 ...
 $ case   : num  1 0 1 0 1 0 1 0 1 0 ...
 $ smoking: num  1 1 1 1 1 1 1 1 0 1 ...
 $ rubber : num  0 0 0 1 1 1 0 1 0 0 ...
 $ alcohol: num  0 0 1 0 0 0 0 1 1 0 ...
 - attr(*, "datalabel")= chr ""
 - attr(*, "time.stamp")= chr "24 Jul 2005 23:36"
 - attr(*, "formats")= chr [1:5] "%9.0g" "%9.0g" "%9.0g" "%9.0g" ...
 - attr(*, "types")= int [1:5] 102 102 102 102 102
 - attr(*, "val.labels")= chr [1:5] "" "" "" "" ...
 - attr(*, "var.labels")= chr [1:5] "" "" "" "" ...
 - attr(*, "version")= int 7
 - attr(*, "label.table")=List of 5
  ..$ : NULL
  ..$ : NULL
  ..$ : NULL
  ..$ : NULL
  ..$ : NULL

summary(cancer)

     matset          case        smoking           rubber      
 Min.   : 1.0   Min.   :0.0   Min.   :0.0000   Min.   :0.0000  
 1st Qu.: 7.0   1st Qu.:0.0   1st Qu.:1.0000   1st Qu.:0.0000  
 Median :13.5   Median :0.5   Median :1.0000   Median :0.0000  
 Mean   :13.5   Mean   :0.5   Mean   :0.8077   Mean   :0.3269  
 3rd Qu.:20.0   3rd Qu.:1.0   3rd Qu.:1.0000   3rd Qu.:1.0000  
 Max.   :26.0   Max.   :1.0   Max.   :1.0000   Max.   :1.0000  
    alcohol      
 Min.   :0.0000  
 1st Qu.:0.0000  
 Median :1.0000  
 Mean   :0.5192  
 3rd Qu.:1.0000  
 Max.   :1.0000

head(cancer, 10)  # 1-1 matching

?infert  # Infertility after Spontaneous and Induced Abortion
abort = infert
str(abort)

'data.frame':   248 obs. of  8 variables:
 $ education     : Factor w/ 3 levels "0-5yrs","6-11yrs",..: 1 1 1 1 2 2 2 2 2 2 ...
 $ age           : num  26 42 39 34 35 36 23 32 21 28 ...
 $ parity        : num  6 1 6 4 3 4 1 2 1 2 ...
 $ induced       : num  1 1 2 2 1 2 0 0 0 0 ...
 $ case          : num  1 1 1 1 1 1 1 1 1 1 ...
 $ spontaneous   : num  2 0 0 0 1 1 0 0 1 0 ...
 $ stratum       : int  1 2 3 4 5 6 7 8 9 10 ...
 $ pooled.stratum: num  3 1 4 2 32 36 6 22 5 19 ...

summary(abort)

   education        age            parity         induced      
 0-5yrs : 12   Min.   :21.00   Min.   :1.000   Min.   :0.0000  
 6-11yrs:120   1st Qu.:28.00   1st Qu.:1.000   1st Qu.:0.0000  
 12+ yrs:116   Median :31.00   Median :2.000   Median :0.0000  
               Mean   :31.50   Mean   :2.093   Mean   :0.5726  
               3rd Qu.:35.25   3rd Qu.:3.000   3rd Qu.:1.0000  
               Max.   :44.00   Max.   :6.000   Max.   :2.0000  
      case         spontaneous        stratum      pooled.stratum 
 Min.   :0.0000   Min.   :0.0000   Min.   : 1.00   Min.   : 1.00  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:21.00   1st Qu.:19.00  
 Median :0.0000   Median :0.0000   Median :42.00   Median :36.00  
 Mean   :0.3347   Mean   :0.5766   Mean   :41.87   Mean   :33.58  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:62.25   3rd Qu.:48.25  
 Max.   :1.0000   Max.   :2.0000   Max.   :83.00   Max.   :63.00

abort = abort[order(abort$stratum), ]
head(abort, 10)  # 1-2 matching

3 1-1 Matching

3.1 Descriptive

str(cancer)

'data.frame':   52 obs. of  5 variables:
 $ matset : num  1 1 2 2 3 3 4 4 5 5 ...
 $ case   : num  1 0 1 0 1 0 1 0 1 0 ...
 $ smoking: num  1 1 1 1 1 1 1 1 0 1 ...
 $ rubber : num  0 0 0 1 1 1 0 1 0 0 ...
 $ alcohol: num  0 0 1 0 0 0 0 1 1 0 ...
 - attr(*, "datalabel")= chr ""
 - attr(*, "time.stamp")= chr "24 Jul 2005 23:36"
 - attr(*, "formats")= chr [1:5] "%9.0g" "%9.0g" "%9.0g" "%9.0g" ...
 - attr(*, "types")= int [1:5] 102 102 102 102 102
 - attr(*, "val.labels")= chr [1:5] "" "" "" "" ...
 - attr(*, "var.labels")= chr [1:5] "" "" "" "" ...
 - attr(*, "version")= int 7
 - attr(*, "label.table")=List of 5
  ..$ : NULL
  ..$ : NULL
  ..$ : NULL
  ..$ : NULL
  ..$ : NULL

tbl_summary(subset(cancer, select = c(case, smoking, rubber, alcohol)), by = case,
            statistic = list(all_categorical() ~ "{n} ({p}%)"))

Characteristic	0, N = 26¹	1, N = 26¹
smoking	21 (81%)	21 (81%)
rubber	9 (35%)	8 (31%)
alcohol	10 (38%)	17 (65%)
¹ n (%)

3.2 Variable selection

3.2.1 Univariable

clog_smo = clogit(case ~ smoking + strata(matset), data = cancer)
summary(clog_smo)

Call:
coxph(formula = Surv(rep(1, 52L), case) ~ smoking + strata(matset), 
    data = cancer, method = "exact")

  n= 52, number of events= 26 

          coef exp(coef) se(coef) z Pr(>|z|)
smoking 0.0000    1.0000   0.6325 0        1

        exp(coef) exp(-coef) lower .95 upper .95
smoking         1          1    0.2895     3.454

Concordance= 0.5  (se = 0 )
Likelihood ratio test= 0  on 1 df,   p=1
Wald test            = 0  on 1 df,   p=1
Score (logrank) test = 0  on 1 df,   p=1

clog_rub = clogit(case ~ rubber + strata(matset), data = cancer)
summary(clog_rub)

Call:
coxph(formula = Surv(rep(1, 52L), case) ~ rubber + strata(matset), 
    data = cancer, method = "exact")

  n= 52, number of events= 26 

          coef exp(coef) se(coef)      z Pr(>|z|)
rubber -0.2231    0.8000   0.6708 -0.333    0.739

       exp(coef) exp(-coef) lower .95 upper .95
rubber       0.8       1.25    0.2148     2.979

Concordance= 0.519  (se = 0.081 )
Likelihood ratio test= 0.11  on 1 df,   p=0.7
Wald test            = 0.11  on 1 df,   p=0.7
Score (logrank) test = 0.11  on 1 df,   p=0.7

clog_alc = clogit(case ~ alcohol + strata(matset), data = cancer)
summary(clog_alc)

Call:
coxph(formula = Surv(rep(1, 52L), case) ~ alcohol + strata(matset), 
    data = cancer, method = "exact")

  n= 52, number of events= 26 

          coef exp(coef) se(coef)     z Pr(>|z|)  
alcohol 1.5041    4.5000   0.7817 1.924   0.0544 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

        exp(coef) exp(-coef) lower .95 upper .95
alcohol       4.5     0.2222    0.9723     20.83

Concordance= 0.635  (se = 0.082 )
Likelihood ratio test= 4.82  on 1 df,   p=0.03
Wald test            = 3.7  on 1 df,   p=0.05
Score (logrank) test = 4.45  on 1 df,   p=0.03

If not analyzed by clogit, will get n (pairs) + p coefficients, try for alcohol

blogs_alc = glm(case ~ alcohol + factor(matset), data = cancer, family = "binomial")
summary(blogs_alc)


Call:
glm(formula = case ~ alcohol + factor(matset), family = "binomial", 
    data = cancer)

Coefficients:
                   Estimate Std. Error z value Pr(>|z|)   
(Intercept)      -2.138e-14  1.414e+00   0.000  1.00000   
alcohol           3.008e+00  1.106e+00   2.721  0.00651 **
factor(matset)2  -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)3   1.569e-14  2.000e+00   0.000  1.00000   
factor(matset)4  -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)5  -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)6  -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)7  -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)8   1.583e-14  2.000e+00   0.000  1.00000   
factor(matset)9  -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)10  1.972e-14  2.000e+00   0.000  1.00000   
factor(matset)11 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)12 -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)13  2.010e-14  2.000e+00   0.000  1.00000   
factor(matset)14 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)15 -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)16 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)17 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)18 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)19  2.100e-14  2.000e+00   0.000  1.00000   
factor(matset)20 -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)21 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)22 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)23 -3.008e+00  2.285e+00  -1.316  0.18806   
factor(matset)24 -1.504e+00  2.380e+00  -0.632  0.52749   
factor(matset)25  2.126e-14  2.000e+00   0.000  1.00000   
factor(matset)26 -1.504e+00  2.380e+00  -0.632  0.52749   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 72.087  on 51  degrees of freedom
Residual deviance: 62.451  on 25  degrees of freedom
AIC: 116.45

Number of Fisher Scoring iterations: 4

If analyzed by blogit w/out stratum for alcohol, note the difference in estimated coefficient

blog_alc = glm(case ~ alcohol, data = cancer, family = "binomial")
summary(blog_alc)


Call:
glm(formula = case ~ alcohol, family = "binomial", data = cancer)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)  
(Intercept)  -0.5754     0.4167  -1.381   0.1673  
alcohol       1.1060     0.5766   1.918   0.0551 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 72.087  on 51  degrees of freedom
Residual deviance: 68.265  on 50  degrees of freedom
AIC: 72.265

Number of Fisher Scoring iterations: 4

3.2.2 Multivariable

clog = clogit(case ~ smoking + rubber + alcohol + strata(matset), data = cancer)
summary(clog)

Call:
coxph(formula = Surv(rep(1, 52L), case) ~ smoking + rubber + 
    alcohol + strata(matset), data = cancer, method = "exact")

  n= 52, number of events= 26 

            coef exp(coef) se(coef)      z Pr(>|z|)  
smoking  0.04321   1.04416  0.86916  0.050   0.9604  
rubber  -0.68078   0.50622  0.94518 -0.720   0.4714  
alcohol  1.66701   5.29629  0.82878  2.011   0.0443 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

        exp(coef) exp(-coef) lower .95 upper .95
smoking    1.0442     0.9577    0.1901     5.736
rubber     0.5062     1.9754    0.0794     3.228
alcohol    5.2963     0.1888    1.0435    26.880

Concordance= 0.654  (se = 0.107 )
Likelihood ratio test= 5.55  on 3 df,   p=0.1
Wald test            = 4.11  on 3 df,   p=0.3
Score (logrank) test = 5.05  on 3 df,   p=0.2

clog1 = clogit(case ~ rubber + alcohol + strata(matset), data = cancer)
summary(clog1)

Call:
coxph(formula = Surv(rep(1, 52L), case) ~ rubber + alcohol + 
    strata(matset), data = cancer, method = "exact")

  n= 52, number of events= 26 

           coef exp(coef) se(coef)      z Pr(>|z|)  
rubber  -0.6545    0.5197   0.7824 -0.837   0.4029  
alcohol  1.6674    5.2982   0.8275  2.015   0.0439 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

        exp(coef) exp(-coef) lower .95 upper .95
rubber     0.5197     1.9241    0.1122     2.408
alcohol    5.2982     0.1887    1.0466    26.822

Concordance= 0.654  (se = 0.1 )
Likelihood ratio test= 5.55  on 2 df,   p=0.06
Wald test            = 4.12  on 2 df,   p=0.1
Score (logrank) test = 5.05  on 2 df,   p=0.08

anova(clog1, clog, test = "lrt") # w/out & w smoking

anova(clog_alc, clog1, test = "lrt")  # w/out & w rubber

anova(clog_rub, clog1, test = "lrt")  # w/out & w alcohol

3.3 Variable assessment

3.3.1 Discordant pairs

with(cancer, matchTab(case, smoking, matset))


Exposure status: smoking = 1 
 
Total number of match sets in the tabulation = 26 
 
Number of controls = 1 
                    No. of controls exposed
No. of cases exposed  0  1
                   0  0  5
                   1  5 16

Odds ratio by Mantel-Haenszel method = 1 
 
Odds ratio by maximum likelihood estimate (MLE) method = 1 
 95%CI= 0.29 , 3.454

with(cancer, matchTab(case, rubber, matset))


Exposure status: rubber = 1 
 
Total number of match sets in the tabulation = 26 
 
Number of controls = 1 
                    No. of controls exposed
No. of cases exposed  0  1
                   0 13  5
                   1  4  4

Odds ratio by Mantel-Haenszel method = 0.8 
 
Odds ratio by maximum likelihood estimate (MLE) method = 0.8 
 95%CI= 0.215 , 2.979

with(cancer, matchTab(case, alcohol, matset))


Exposure status: alcohol = 1 
 
Total number of match sets in the tabulation = 26 
 
Number of controls = 1 
                    No. of controls exposed
No. of cases exposed 0 1
                   0 7 2
                   1 9 8

Odds ratio by Mantel-Haenszel method = 4.5 
 
Odds ratio by maximum likelihood estimate (MLE) method = 4.5 
 95%CI= 0.972 , 20.827

3.4 Interaction

Specify interaction based between rubber * alcohol:

clogx = clogit(case ~ rubber * alcohol + strata(matset), data = cancer)
summary(clogx)  # Interaction not significant

Call:
coxph(formula = Surv(rep(1, 52L), case) ~ rubber * alcohol + 
    strata(matset), data = cancer, method = "exact")

  n= 52, number of events= 26 

                  coef exp(coef) se(coef)      z Pr(>|z|)  
rubber         -0.9829    0.3742   1.1606 -0.847   0.3971  
alcohol         1.4989    4.4768   0.9030  1.660   0.0969 .
rubber:alcohol  0.6341    1.8854   1.5519  0.409   0.6828  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

               exp(coef) exp(-coef) lower .95 upper .95
rubber            0.3742     2.6723   0.03847      3.64
alcohol           4.4768     0.2234   0.76272     26.28
rubber:alcohol    1.8854     0.5304   0.09003     39.48

Concordance= 0.654  (se = 0.1 )
Likelihood ratio test= 5.72  on 3 df,   p=0.1
Wald test            = 4.24  on 3 df,   p=0.2
Score (logrank) test = 5.19  on 3 df,   p=0.2

3.5 Model fit assessment

Not possible for clogit ## Presentation and interpretation Present in table

clogistic.display(clog1)

Conditional logistic regression predicting case : 1 vs 0 

 
                 crude OR(95%CI)   adj. OR(95%CI)    P(Wald's test) P(LR-test)
rubber: 1 vs 0   0.8 (0.21,2.98)   0.52 (0.11,2.41)  0.403          0.392     
                                                                              
alcohol: 1 vs 0  4.5 (0.97,20.83)  5.3 (1.05,26.82)  0.044          0.02      
                                                                              
No. of observations =  52

tbl_regression(clog1, exp = T)

Characteristic	OR¹	95% CI¹	p-value
rubber	0.52	0.11, 2.41	0.4
alcohol	5.30	1.05, 26.8	0.044
¹ OR = Odds Ratio, CI = Confidence Interval

# Details
tidy(clog1, conf.int = T) |> kable(digits = 3)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
rubber	-0.654	0.782	-0.837	0.403	-2.188	0.879
alcohol	1.667	0.827	2.015	0.044	0.046	3.289

tidy(clog1, conf.int = T, exponentiate = T) |> kable(digits = 3)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
rubber	0.520	0.782	-0.837	0.403	0.112	2.408
alcohol	5.298	0.827	2.015	0.044	1.047	26.822

4 1-M Matching

4.1 Descriptive

str(abort)

'data.frame':   248 obs. of  8 variables:
 $ education     : Factor w/ 3 levels "0-5yrs","6-11yrs",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ age           : num  26 26 26 42 42 42 39 39 39 34 ...
 $ parity        : num  6 6 6 1 1 1 6 6 6 4 ...
 $ induced       : num  1 2 2 1 0 0 2 2 2 2 ...
 $ case          : num  1 0 0 1 0 0 1 0 0 1 ...
 $ spontaneous   : num  2 0 0 0 0 0 0 0 0 0 ...
 $ stratum       : int  1 1 1 2 2 2 3 3 3 4 ...
 $ pooled.stratum: num  3 3 3 1 1 1 4 4 4 2 ...

tbl_summary(subset(abort, select = c(case, spontaneous, induced)), by = case,
            statistic = list(all_categorical() ~ "{n} ({p}%)"))

Characteristic	0, N = 165¹	1, N = 83¹
spontaneous
0	113 (68%)	28 (34%)
1	40 (24%)	31 (37%)
2	12 (7.3%)	24 (29%)
induced
0	96 (58%)	47 (57%)
1	45 (27%)	23 (28%)
2	24 (15%)	13 (16%)
¹ n (%)

4.2 Variable selection

4.2.1 Univariable

clogm_spo = clogit(case ~ spontaneous + strata(stratum), data = abort)
summary(clogm_spo)

Call:
coxph(formula = Surv(rep(1, 248L), case) ~ spontaneous + strata(stratum), 
    data = abort, method = "exact")

  n= 248, number of events= 83 

              coef exp(coef) se(coef)     z Pr(>|z|)    
spontaneous 1.1768    3.2441   0.2315 5.083 3.71e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

            exp(coef) exp(-coef) lower .95 upper .95
spontaneous     3.244     0.3083     2.061     5.107

Concordance= 0.685  (se = 0.046 )
Likelihood ratio test= 33.76  on 1 df,   p=6e-09
Wald test            = 25.84  on 1 df,   p=4e-07
Score (logrank) test = 34.13  on 1 df,   p=5e-09

clogm_ind = clogit(case ~ induced + strata(stratum), data = abort)
summary(clogm_ind)

Call:
coxph(formula = Surv(rep(1, 248L), case) ~ induced + strata(stratum), 
    data = abort, method = "exact")

  n= 248, number of events= 83 

           coef exp(coef) se(coef)     z Pr(>|z|)
induced 0.07374   1.07653  0.20969 0.352    0.725

        exp(coef) exp(-coef) lower .95 upper .95
induced     1.077     0.9289    0.7137     1.624

Concordance= 0.497  (se = 0.047 )
Likelihood ratio test= 0.12  on 1 df,   p=0.7
Wald test            = 0.12  on 1 df,   p=0.7
Score (logrank) test = 0.12  on 1 df,   p=0.7

4.2.2 Multivariable

clogm = clogit(case ~ spontaneous + induced + strata(stratum), data = abort)
summary(clogm)

Call:
coxph(formula = Surv(rep(1, 248L), case) ~ spontaneous + induced + 
    strata(stratum), data = abort, method = "exact")

  n= 248, number of events= 83 

              coef exp(coef) se(coef)     z Pr(>|z|)    
spontaneous 1.9859    7.2854   0.3524 5.635 1.75e-08 ***
induced     1.4090    4.0919   0.3607 3.906 9.38e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

            exp(coef) exp(-coef) lower .95 upper .95
spontaneous     7.285     0.1373     3.651    14.536
induced         4.092     0.2444     2.018     8.298

Concordance= 0.776  (se = 0.044 )
Likelihood ratio test= 53.15  on 2 df,   p=3e-12
Wald test            = 31.84  on 2 df,   p=1e-07
Score (logrank) test = 48.44  on 2 df,   p=3e-11

anova(clogm_ind, clogm)  # inclusion of spontaneous

anova(clogm_spo, clogm)  # inclusion of induced, contrast with p-value for wald test

4.3 Variable assessment

4.3.1 Linearity in logit

Assume spontaneous & induced are numerical for practice purpose

# formula, copy & paste from summary(clogm)
mfp(Surv(rep(1, 248L), case) ~ fp(spontaneous, df = 4, select = 0.05) + 
      fp(induced, df = 4, select = 0.05) + strata(stratum), family = cox, data = abort)

Call:
mfp(formula = Surv(rep(1, 248L), case) ~ fp(spontaneous, df = 4, 
    select = 0.05) + fp(induced, df = 4, select = 0.05) + strata(stratum), 
    data = abort, family = cox)


Deviance table:
         Resid. Dev
Null model   181.5587
Linear model     128.4045
Final model  128.4045

Fractional polynomials:
            df.initial select alpha df.final power1 power2
spontaneous          4   0.05  0.05        1      1      .
induced              4   0.05  0.05        1      1      .


Transformations of covariates:
                         formula
spontaneous I((spontaneous+1)^1)
induced         I((induced+1)^1)

               coef exp(coef) se(coef)     z        p
spontaneous.1 1.986     7.285   0.3524 5.635 1.75e-08
induced.1     1.409     4.092   0.3607 3.906 9.38e-05

Likelihood ratio test=53.15  on 2 df, p=2.869e-12 n= 248

# frac poly output -- linear

4.4 Interaction

Specify interaction based between spontaneous * induced:

clogmx = clogit(case ~ spontaneous * induced + strata(stratum), data = abort)
summary(clogmx)  # Interaction not significant

Call:
coxph(formula = Surv(rep(1, 248L), case) ~ spontaneous * induced + 
    strata(stratum), data = abort, method = "exact")

  n= 248, number of events= 83 

                      coef exp(coef) se(coef)     z Pr(>|z|)    
spontaneous         1.9517    7.0408   0.3768 5.180 2.21e-07 ***
induced             1.3749    3.9548   0.3852 3.569 0.000358 ***
spontaneous:induced 0.1068    1.1127   0.4435 0.241 0.809765    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

                    exp(coef) exp(-coef) lower .95 upper .95
spontaneous             7.041     0.1420    3.3646    14.734
induced                 3.955     0.2529    1.8588     8.414
spontaneous:induced     1.113     0.8987    0.4665     2.654

Concordance= 0.776  (se = 0.044 )
Likelihood ratio test= 53.21  on 3 df,   p=2e-11
Wald test            = 31.92  on 3 df,   p=5e-07
Score (logrank) test = 48.71  on 3 df,   p=2e-10

4.5 Model fit assessment

Not possible for clogit Diagnostics also not available ## Presentation and interpretation Present in table

clogistic.display(clogm)

Conditional logistic regression predicting case : 1 vs 0 

 
                         crude OR(95%CI)   adj. OR(95%CI)     P(Wald's test)
spontaneous (cont. var.) 3.24 (2.06,5.11)  7.29 (3.65,14.54)  < 0.001       
                                                                            
induced (cont. var.)     1.08 (0.71,1.62)  4.09 (2.02,8.3)    < 0.001       
                                                                            
                         P(LR-test)
spontaneous (cont. var.) < 0.001   
                                   
induced (cont. var.)     < 0.001   
                                   
No. of observations =  248

tbl_regression(clogm, exp = T)

Characteristic	OR¹	95% CI¹	p-value
spontaneous	7.29	3.65, 14.5	<0.001
induced	4.09	2.02, 8.30	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

# Details
tidy(clogm, conf.int = T) |> kable(digits = 3)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
spontaneous	1.986	0.352	5.635	0	1.295	2.677
induced	1.409	0.361	3.906	0	0.702	2.116

tidy(clogm, conf.int = T, exponentiate = T) |> kable(digits = 3)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
spontaneous	7.285	0.352	5.635	0	3.651	14.536
induced	4.092	0.361	3.906	0	2.018	8.298

Conditional Logistic Regression

Dr. Wan Nor Arifin

Biostatistics and Research Methodology Unit, Universiti Sains Malaysia
Last update: 23 June 2024

1 Library

2 Datasets

3 1-1 Matching

3.1 Descriptive

3.2 Variable selection

3.2.1 Univariable

3.2.2 Multivariable

3.3 Variable assessment

3.3.1 Discordant pairs

3.4 Interaction

3.5 Model fit assessment

4 1-M Matching

4.1 Descriptive

4.2 Variable selection

4.2.1 Univariable

4.2.2 Multivariable

4.3 Variable assessment

4.3.1 Linearity in logit

4.4 Interaction

4.5 Model fit assessment

Conditional Logistic Regression

Dr. Wan Nor Arifin

Biostatistics and Research Methodology Unit, Universiti Sains Malaysia Last update: 23 June 2024

1 Library

2 Datasets

3 1-1 Matching

3.1 Descriptive

3.2 Variable selection

3.2.1 Univariable

3.2.2 Multivariable

3.3 Variable assessment

3.3.1 Discordant pairs

3.4 Interaction

3.5 Model fit assessment

4 1-M Matching

4.1 Descriptive

4.2 Variable selection

4.2.1 Univariable

4.2.2 Multivariable

4.3 Variable assessment

4.3.1 Linearity in logit

4.4 Interaction

4.5 Model fit assessment

Biostatistics and Research Methodology Unit, Universiti Sains Malaysia
Last update: 23 June 2024