`myco.Rd`

These data are in a paper by JNK Rao and colleagues, on score tests
for complex survey data. External information (not further specified) suggests
the functional form for the `Age`

variable.

`data("myco")`

A data frame with 516 observations on the following 6 variables.

`Age`

Age in years at the midpoint of six age strata

`Scar`

Presence of a BCG vaccination scar

`n`

Sampled number of cases (and thus controls) in the age stratum

`Ncontrol`

Number of non-cases in the population

`wt`

Sampling weight

`leprosy`

case status 0/1

The data are a simulated stratified case-control study drawn from a population study conducted in a region of Malawi (Clayton and Hills, 1993, Table 18.1). The goal was to examine whether BCG vaccination against tuberculosis protects against leprosy (the causative agents are both species of _Mycobacterium_). Rao et al have a typographical error: the number of non-cases in the population in the 25-30 age stratum is given as 4981 but 5981 matches both the computational output and the data as given by Clayton and Hills.

JNK Rao, AJ Scott, and C Rao, J., Scott, A., & Skinner, C. (1998). QUASI-SCORE TESTS WITH SURVEY DATA. Statistica Sinica, 8(4), 1059-1070.

Clayton, D., & Hills, M. (1993). Statistical Models in Epidemiology. OUP

```
data(myco)
dmyco<-svydesign(id=~1, strata=~interaction(Age,leprosy),weights=~wt,data=myco)
m_full<-svyglm(leprosy~I((Age+7.5)^-2)+Scar, family=quasibinomial, design=dmyco)
m_age<-svyglm(leprosy~I((Age+7.5)^-2), family=quasibinomial, design=dmyco)
anova(m_full,m_age)
#> Working (Rao-Scott+F) LRT for Scar
#> in svyglm(formula = leprosy ~ I((Age + 7.5)^-2) + Scar, design = dmyco,
#> family = quasibinomial)
#> Working 2logLR = 10.47836 p= 0.0013711
#> df=1; denominator df= 502
## unweighted model does not match
m_full
#> Stratified Independent Sampling design (with replacement)
#> svydesign(id = ~1, strata = ~interaction(Age, leprosy), weights = ~wt,
#> data = myco)
#>
#> Call: svyglm(formula = leprosy ~ I((Age + 7.5)^-2) + Scar, design = dmyco,
#> family = quasibinomial)
#>
#> Coefficients:
#> (Intercept) I((Age + 7.5)^-2) Scar
#> -4.4777 -370.5582 -0.5479
#>
#> Degrees of Freedom: 515 Total (i.e. Null); 502 Residual
#> Null Deviance: 27.99
#> Residual Deviance: 27.24 AIC: NA
glm(leprosy~I((Age+7.5)^-2)+Scar, family=binomial, data=myco)
#>
#> Call: glm(formula = leprosy ~ I((Age + 7.5)^-2) + Scar, family = binomial,
#> data = myco)
#>
#> Coefficients:
#> (Intercept) I((Age + 7.5)^-2) Scar
#> 0.1126 48.7230 -0.4392
#>
#> Degrees of Freedom: 515 Total (i.e. Null); 513 Residual
#> Null Deviance: 715.3
#> Residual Deviance: 709.6 AIC: 715.6
```