bacteria.RdTests of the presence of the bacteria H. influenzae in children with otitis media in the Northern Territory of Australia.
bacteria
This data frame has 220 rows and the following columns:
presence or absence: a factor with levels
n and y.
active/placebo: a factor with levels a and p.
hi/low compliance: a factor with levels hi amd
lo.
numeric: week of test.
subject ID: a factor.
a factor with levels placebo, drug and
drug+, a re-coding of ap and hilo.
Dr A. Leach tested the effects of a drug on 50 children with a history of otitis media in the Northern Territory of Australia. The children were randomized to the drug or the a placebo, and also to receive active encouragement to comply with taking the drug.
The presence of H. influenzae was checked at weeks 0, 2, 4, 6 and 11: 30 of the checks were missing and are not included in this data frame.
Dr Amanda Leach via Mr James McBroom.
Menzies School of Health Research 1999--2000 Annual Report. p.20. http://www.menzies.edu.au/icms_docs/172302_2000_Annual_report.pdf.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
contrasts(bacteria$trt) <- structure(contr.sdif(3), dimnames = list(NULL, c("drug", "encourage"))) ## fixed effects analyses summary(glm(y ~ trt * week, binomial, data = bacteria))#> #> Call: #> glm(formula = y ~ trt * week, family = binomial, data = bacteria) #> #> Deviance Residuals: #> Min 1Q Median 3Q Max #> -2.2144 0.4245 0.5373 0.6750 1.0697 #> #> Coefficients: #> Estimate Std. Error z value Pr(>|z|) #> (Intercept) 1.97548 0.30053 6.573 4.92e-11 *** #> trtdrug -0.99848 0.69490 -1.437 0.15075 #> trtencourage 0.83865 0.73482 1.141 0.25374 #> week -0.11814 0.04460 -2.649 0.00807 ** #> trtdrug:week -0.01722 0.10570 -0.163 0.87061 #> trtencourage:week -0.07043 0.10964 -0.642 0.52060 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> (Dispersion parameter for binomial family taken to be 1) #> #> Null deviance: 217.38 on 219 degrees of freedom #> Residual deviance: 203.12 on 214 degrees of freedom #> AIC: 215.12 #> #> Number of Fisher Scoring iterations: 4 #>#> #> Call: #> glm(formula = y ~ trt + week, family = binomial, data = bacteria) #> #> Deviance Residuals: #> Min 1Q Median 3Q Max #> -2.2899 0.3885 0.5400 0.7027 1.1077 #> #> Coefficients: #> Estimate Std. Error z value Pr(>|z|) #> (Intercept) 1.96018 0.29705 6.599 4.15e-11 *** #> trtdrug -1.10667 0.42519 -2.603 0.00925 ** #> trtencourage 0.45502 0.42766 1.064 0.28735 #> week -0.11577 0.04414 -2.623 0.00872 ** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> (Dispersion parameter for binomial family taken to be 1) #> #> Null deviance: 217.38 on 219 degrees of freedom #> Residual deviance: 203.81 on 216 degrees of freedom #> AIC: 211.81 #> #> Number of Fisher Scoring iterations: 4 #>#> #> Call: #> glm(formula = y ~ trt + I(week > 2), family = binomial, data = bacteria) #> #> Deviance Residuals: #> Min 1Q Median 3Q Max #> -2.4043 0.3381 0.5754 0.6237 1.0051 #> #> Coefficients: #> Estimate Std. Error z value Pr(>|z|) #> (Intercept) 2.2479 0.3560 6.315 2.71e-10 *** #> trtdrug -1.1187 0.4288 -2.609 0.00909 ** #> trtencourage 0.4815 0.4330 1.112 0.26614 #> I(week > 2)TRUE -1.2949 0.4104 -3.155 0.00160 ** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> (Dispersion parameter for binomial family taken to be 1) #> #> Null deviance: 217.38 on 219 degrees of freedom #> Residual deviance: 199.18 on 216 degrees of freedom #> AIC: 207.18 #> #> Number of Fisher Scoring iterations: 5 #># conditional random-effects analysis library(survival) bacteria$Time <- rep(1, nrow(bacteria)) coxph(Surv(Time, unclass(y)) ~ week + strata(ID), data = bacteria, method = "exact")#> Call: #> coxph(formula = Surv(Time, unclass(y)) ~ week + strata(ID), data = bacteria, #> method = "exact") #> #> coef exp(coef) se(coef) z p #> week -0.16256 0.84996 0.05472 -2.971 0.00297 #> #> Likelihood ratio test=9.85 on 1 df, p=0.001696 #> n= 220, number of events= 177#> Call: #> coxph(formula = Surv(Time, unclass(y)) ~ factor(week) + strata(ID), #> data = bacteria, method = "exact") #> #> coef exp(coef) se(coef) z p #> factor(week)2 0.1983 1.2193 0.7241 0.274 0.7842 #> factor(week)4 -1.4206 0.2416 0.6665 -2.131 0.0331 #> factor(week)6 -1.6615 0.1899 0.6825 -2.434 0.0149 #> factor(week)11 -1.6752 0.1873 0.6780 -2.471 0.0135 #> #> Likelihood ratio test=15.45 on 4 df, p=0.003854 #> n= 220, number of events= 177#> Call: #> coxph(formula = Surv(Time, unclass(y)) ~ I(week > 2) + strata(ID), #> data = bacteria, method = "exact") #> #> coef exp(coef) se(coef) z p #> I(week > 2)TRUE -1.6701 0.1882 0.4817 -3.467 0.000527 #> #> Likelihood ratio test=15.15 on 1 df, p=9.927e-05 #> n= 220, number of events= 177# PQL glmm analysis library(nlme) summary(glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID, family = binomial, data = bacteria))#>#>#>#>#>#>#> Linear mixed-effects model fit by maximum likelihood #> Data: bacteria #> AIC BIC logLik #> NA NA NA #> #> Random effects: #> Formula: ~1 | ID #> (Intercept) Residual #> StdDev: 1.410637 0.7800511 #> #> Variance function: #> Structure: fixed weights #> Formula: ~invwt #> Fixed effects: y ~ trt + I(week > 2) #> Value Std.Error DF t-value p-value #> (Intercept) 2.7447864 0.3784193 169 7.253294 0.0000 #> trtdrug -1.2473553 0.6440635 47 -1.936696 0.0588 #> trtencourage 0.4930279 0.6699339 47 0.735935 0.4654 #> I(week > 2)TRUE -1.6072570 0.3583379 169 -4.485311 0.0000 #> Correlation: #> (Intr) trtdrg trtncr #> trtdrug 0.009 #> trtencourage 0.036 -0.518 #> I(week > 2)TRUE -0.710 0.047 -0.046 #> #> Standardized Within-Group Residuals: #> Min Q1 Med Q3 Max #> -5.1985361 0.1572336 0.3513075 0.4949482 1.7448845 #> #> Number of Observations: 220 #> Number of Groups: 50