Endometrial Cancer and Oestrogens

1:4 matched case-control study, real data

The study

In the 1970s, several studies linked the use of conjugated oestrogens after the menopause to endometrial cancer. In a Los Angeles retirement community, each of 63 women with endometrial cancer was matched with four women without it, living in the same community, of the same marital status and born within one year of the case. The data are a classic of the matched case-control literature (Breslow and Day 1980), available in R as Epi::bdendo. They ship with the module: in jamovi, Open ▸ Data Library ▸ Conditional Logistic Regression ▸ Endometrial cancer and oestrogens. Or download bdendo.csv.

Variable Content
set matched set, 1–63
case 1 = endometrial cancer, 0 = control
est ever used oestrogens: Yes, No
dur duration of conjugated oestrogen use: 0 = none (some of these women used other oestrogens), 1–4 = 1–11, 12–46, 48–92 and 96 months in these data (missing for 17 women)
duration months of oestrogen use
cest dose of conjugated oestrogen, 0–3
gall history of gallbladder disease
hyp hypertension
ob obesity (missing for 50 women)
non use of non-oestrogen drugs
age, agegrp, age3 age, and age in groups (matched on)

Step 1: describe the data

  1. Analyses ▸ Regression ▸ Logistic Regression ▸ Conditional (Matched). case to Dependent Variable, set to Matching Variable, and est, gall, hyp, ob and non to Factors.
  2. In Descriptives, tick Descriptive table.
Descriptives
case = 0 case = 1 Total
case n (%) 252 (80.0%) 63 (20.0%) 315 (100.0%)
est No 125 (49.6%) 7 (11.1%) 132 (41.9%)
est Yes 127 (50.4%) 56 (88.9%) 183 (58.1%)
gall No 228 (90.5%) 46 (73.0%) 274 (87.0%)
gall Yes 24 (9.5%) 17 (27.0%) 41 (13.0%)
hyp No 170 (67.5%) 37 (58.7%) 207 (65.7%)
hyp Yes 82 (32.5%) 26 (41.3%) 108 (34.3%)
ob No 82 (39.4%) 16 (28.1%) 98 (37.0%)
ob Yes 126 (60.6%) 41 (71.9%) 167 (63.0%)
ob Missing 44 (17.5%) 6 (9.5%) 50 (15.9%)
non No 76 (30.2%) 7 (11.1%) 83 (26.3%)
non Yes 176 (69.8%) 56 (88.9%) 232 (73.7%)

The first row gives the numbers of controls and cases. The rest compares them: oestrogens were used by 56 (88.9%) of the cases and 127 (50.4%) of the controls, and gallbladder disease was more common in cases. The table describes every woman whose case/control status and matched set are known. Percentages of a factor are of the women with a known value, and a Missing row appears only for a variable with missing values: here ob, unknown for 50 women. The models, in contrast, use only the women complete for every variable, 265 of the 315.

Step 2: univariable and multivariable odds ratios

The coefficient table gives, for each factor, its reference level (OR = 1) and the odds ratio of every other level against it, with the confidence interval and p.

  1. In Model Coefficients, tick Univariable and multivariable, which adds the odds ratio of each variable alone, and Forest plot.
Matched Sets
Per set = Cases Controls Sets Observations
0 1 2 2
0 2 1 2
0 3 1 3
0 4 2 8
1 1 3 6
1 2 2 6
1 3 22 88
1 4 30 150

Note. 6 uninformative sets (no case or no control left)

Model Coefficients - case
OR Lower Upper p OR Lower Multivariable Upper Multivariable p
est No 1.000 1.000
est Yes 7.276 2.786 19.003 0.000 6.910 2.513 19.001 < .001
gall No 1.000 1.000
gall Yes 3.538 1.638 7.641 0.001 3.594 1.517 8.513 .004
hyp No 1.000 1.000
hyp Yes 1.233 0.666 2.282 0.506 0.723 0.347 1.509 .388
ob No 1.000 1.000
ob Yes 1.493 0.741 3.010 0.262 1.544 0.698 3.415 .283
non No 1.000 1.000
non Yes 2.996 1.047 8.567 0.041 1.913 0.617 5.928 .261

Figure 1: The forest plot of the same model: univariable (grey) and multivariable (blue) odds ratios with their intervals; the reference levels at 1.

Oestrogen use has an odds ratio of 6.91 (95% CI 2.51–19.00) and gallbladder disease 3.59 (95% CI 1.52–8.51), adjusted for each other and for the other three factors. Alone, oestrogens give 7.28 and gallbladder disease 3.54: adjustment changes little, so these exposures do not confound each other much. Hypertension, obesity and non-oestrogen drugs show no clear association. The univariable odds ratios are computed on the same rows as the model, so the two columns differ only by the adjustment.

The Matched Sets table shows the price of the missing obesity values: 6 sets lost their case and no longer count, and many others lost controls. Since obesity is not associated here, drop hyp, ob and non from the model and refit with est and gall:

Matched Sets
Per set = Cases Controls Sets Observations
1 4 63 315
Model Coefficients - case
OR Lower 95% CI Upper 95% CI p
est No 1.000
est Yes 8.288 3.500 19.624 < .001
gall No 1.000
gall Yes 3.577 1.599 8.004 .002

All 63 sets are back, complete, and the odds ratio for oestrogens is 8.29 (95% CI 3.50–19.62), with a narrower interval.

Step 3: duration of use

A dose-response relation strengthens a causal interpretation. Replace est with dur in Factors. In the Model Builder, put gall in block 1 and dur in block 2, and set the reference level of dur to 0 (no conjugated oestrogen). Tick Trend test (factors with 3+ levels).

Model Comparisons
Model Model χ² df p
1 - 2 31.349 4 < .001
Model Coefficients - case
OR Lower 95% CI Upper 95% CI p p trend
gall No 1.000
gall Yes 3.187 1.318 7.704 .010
dur 0 1.000 < .001 0.000
dur 1 2.970 0.979 9.006 .054
dur 2 4.394 1.723 11.201 .002
dur 3 9.305 3.120 27.746 < .001
dur 4 9.515 3.561 25.426 < .001

The odds ratio rises with each category of duration, from 3.0 in the shortest to 9.5 in the longest. On the reference row of dur, p is the likelihood ratio test of the four categories together (p < .001, the same test as the model comparison), and p trend tests a steady rise across the categories, scored 1, 2, 3, 4, 5 in their order (p < .001).

Duration in months: covariate scaling

The categories of dur lose information. duration holds the months of use itself: put it in Covariates instead of dur in Factors.

Model Coefficients - case
OR Lower 95% CI Upper 95% CI p
gall No 1.000
gall Yes 2.895 1.241 6.756 .014
duration per unit 1.021 1.012 1.030 < .001

The odds ratio of 1.021 is per month of use, a unit too small to read. Open Covariate Scaling, which lists every covariate, and choose per 10 units for duration:

Model Coefficients - case
OR Lower 95% CI Upper 95% CI p
gall No 1.000
gall Yes 2.895 1.241 6.756 .014
duration per 10 units 1.230 1.128 1.341 < .001

Each 10 months of use multiply the odds by 1.23 (95% CI 1.13–1.34). This is the same model (\(1.0209^{10} = 1.23\)), and p does not change. The other choices are per 100 and per 1000 units, and per 1 SD, the standard deviation of the covariate on the rows of the model.

A loosely matched variable

Age was matched within a year, not exactly, so it still varies a little within the sets, and the module estimates it:

Model Coefficients - case
OR Lower 95% CI Upper 95% CI p
est No 1.000
est Yes 8.574 3.579 20.538 < .001
gall No 1.000
gall Yes 3.556 1.595 7.930 .002
age per unit 0.750 0.463 1.216 .244

The odds ratio of 0.75 per year of age is not an age effect. It contrasts women born a few months apart within a set, which says nothing about the role of age, and its wide interval reflects how little information is left. Matching variables belong in the model only as interactions with an exposure (see the infertility use case).

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References

Breslow, N. E., and N. E. Day. 1980. Statistical Methods in Cancer Research. Volume I: The Analysis of Case-Control Studies. IARC Scientific Publications 32. International Agency for Research on Cancer.