cochran_qtest: cochran_qtest
In rpkyle/epimisc: Miscellaneous R functions for basic epidemiologic analysis.

Description Usage Arguments Details Value Author(s) References Examples

The cochran_qtest function performs Cochran's Q-test for heterogeneity. Currently only two strata are supported, though more than two strata may be supported in the future.

1	cochran_qtest(estimate1, lcl1, ucl1, estimate2, lcl2, ucl2)

`estimate1`	The ratio estimate (e.g. RR, OR, HR, IRR) from the first group/study.
`lcl1`	The lower confidence limit for the first group/study estimate.
`ucl1`	The upper confidence limit for the first group/study estimate.
`measure2`	The ratio estimate (e.g. RR, OR, HR, IRR) from the second group/study.
`lcl2`	The lower confidence limit for the second group/study estimate.
`ucl2`	The upper confidence limit for the second group/study estimate.

This function performs a statistical test for heterogeneity by calculating Cochran's Q-statistic. The null hypothesis is that any variation in estimates from the two studies is due to sampling variation, or minor differences in study methodology; in effect, the pooled estimate is equivalent to the stratum-specific estimates. The alternative hypothesis is that the study estimates are heterogeneous. This test is equivalent to the Wald test performed by the wald.hgen.test function also included in the epimisc package, and should produce an identical P-value when used to compare the same estimates.

The resulting statistic has a chi-square distribution with degrees of freedom equal to the number of strata - 1.

`pooled.estimate`	The pooled estimate
`cochran.q`	Value of Cochran's Q-statistic
`P`	P-value calculated using estimated Q-statistic

Ryan Patrick Kyle

Sedgwick P. Meta-analyses: tests of heterogeneity. BMJ. 2012; 344:e3971. Kaufman JS, MacLehose RF. Which of these things is not like the others? Cancer. 2013; 119(24): 4216-4222.

## The function is currently defined as
function (estimate1, lcl1, ucl1, estimate2, lcl2, ucl2) 
{
    var1 <- (((log(ucl1) - log(estimate1))/qnorm(0.025)))^2
    var2 <- (((log(ucl2) - log(estimate2))/qnorm(0.025)))^2
    num_pool <- (log(estimate1)/var1) + (log(estimate2)/var2)
    denom_pool <- (1/var1) + (1/var2)
    pooled <- num_pool/denom_pool
    q <- (((log(estimate1) - pooled)^2)/var1) + (((log(estimate2) - pooled)^2)/var2)
    return(list(pooled.estimate = round(exp(pooled), 2), cochran.q = round(q, 
        2), P = round(1 - pchisq(q, 1), 4)))
  }