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I have returned to a piece of work and was re-running some statistical analysis. I found differences in the P values (which is > 0.05) and OR confidence intervals which was greater than 1. Is there an error?

logr1 <- glm(fibrous.high ~ age + sex + prs_cat.f, data=df[which(df$age_tert == 1),], family = "binomial")

summary(logr1)


Call:
glm(formula = fibrous.high ~ age + sex + prs_cat.f, family = "binomial", 
    data = df[which(df$age_tert == 1), ])


Deviance Residuals: 
    Min       1Q   Median       3Q      Max

-1.3974  -0.8909  -0.5475   1.1486   1.9787


Coefficients:
                 Estimate Std. Error z value Pr(>|z|)

(Intercept)     -10.55024    3.73270  -2.826  0.00471 **
age               0.17186    0.07029   2.445  0.01449 * 
sex              -0.70726    0.70454  -1.004  0.31545

prs_cat.f31-75%   1.16642    0.86764   1.344  0.17883

prs_cat.f≥76%     1.60185    0.88271   1.815  0.06957 .




Signif. codes:  0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


(Dispersion parameter for binomial family taken to be 1)


Null deviance: 100.12  on 80  degrees of freedom



Residual deviance:  89.25  on 76  degrees of freedom
AIC: 99.25


Number of Fisher Scoring iterations: 4

Confidence intervals:

# exp(cbind(OR = coef(logr1), confint(logr1)))
                          OR        2.5 %      97.5 %
(Intercept)     2.618725e-05 8.536605e-09  0.02264591
age             1.187506e+00 1.044550e+00  1.38011363
sex             4.929952e-01 1.104873e-01  1.84047050
prs_cat.f31-75% 3.210487e+00 6.775618e-01 23.66097294
prs_cat.f≥76%   4.962205e+00 1.022622e+00 37.53934890

Is there a reason why for the prs_cat.f≥76%, the P value is 0.07, but the odds ratio does not cross 1?

Urb
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Pras_V
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1 Answers1

1

There is no error. Rather there is a difference between a profile confidence interval and a Wald confidence interval for the log odds ratio.

Consider the log odds ratio for prs_cat.f≥76%. The 95% profile confidence interval doesn't contain 0.

# 95% profile confidence interval
log(c(1.022622e+00, 37.53934890))
#> [1] 0.02236992 3.62538969

However, the 95% Wald confidence interval contains 0.

# 95% Wald confidence interval
estimate <- 1.60185
std.error <- 0.88271
# 95% Wald confidence interval
estimate + c(-1.96, +1.96) * std.error
#> [1] -0.1282616  3.3319616

To learn more take a look at Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R?

dipetkov
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