mStats (version 3.4.0)

mhor: Calculating Odds Ratios

Description

mhor() calculates odds ratios, Mantel Haenszel pooled estimates and 95% CI.

Usage

mhor(
  data,
  exp,
  case,
  strata = NULL,
  exp_value = NULL,
  case_value = NULL,
  digits = 4
)

Arguments

data

data.frame

exp

exposure or independent variables

case

case or dependent variables (outcomes)

strata

if specified, MH OR is calculated.

exp_value

value for exposure as reference

case_value

value for outcome as reference

digits

specify rounding of numbers. See round.

Value

data.frame

Details

Rows and Columns can be rearranged by specifying exp_value and case_value. This is used when the exposed and case values are not at the right place in 2x2 tables.

Reference row value can be specified in exp_value.

Attributable fractions, Attr. Frac. Exp and Attr. Frac. Pop among exposed and population are calculated when OR is greater than or equal to 1. If OR is less than 1, preventable fractions, Prev. Frac. Exp and Attr. Frac. Pop are calculated.

It produces a table with Odds Ratio, 95% CI as well as p-value. If strata is specified, Mantel-Haenzsel Pooled estimates of Odds Ratio is generated along with Chi-squared test for homogeneity.

Odds Ratio, OR

$$OR = (D1 x H0) / (D0 x H1)$$

Error Factor, EF using Woolf's formula

$$95\% CI = OR / EF or OR x EF$$

$$EF = exp(1.96 x SE(log(OR)))$$

$$SE(log(OR)) = \sqrt{1/D1 + 1/H1 + 1/D0 + 1/H0}$$

Calculating p-value from Wald's z test

$$z = log OR / SE (log OR)$$

Mantel-Haenszel's OR

$$ORMH = Q / R$$

$$Q = \sum{(D1i x H0i) / ni}$$

$$R = \sum{(D0i x H1i) / ni}$$

Calculating CI for MH-OR

$$95\% CI = OR / EF or OR x EF$$

$$SE(ORMH) = \sqrt{V / (Q x R)}$$

$$V = \sum{(Di x Hi x n0i x n1i) / ( (ni)^2 x (ni - 1))}$$

Chi-square test for MHOR, df = 1

$$X^2 (MH), Chi-square value = U^2 / V$$

$$U = O - E$$

$$O = \sum{D1i}$$

$$E = \sum{Di x n1i / ni}$$

Chi-square test for Heterogeneity

$$X^2 = \sum{(D1i x H0i - ORMH x D0i x H1i)^2 / ORMH x Vi x ni^2}$$

References

1. Betty R. Kirkwood, Jonathan A.C. Sterne (2006, ISBN:978<U+2013>0<U+2013>86542<U+2013>871<U+2013>3)

2. B. Burt Gerstman (2013, ISBN:978-1-4443-3608-5)

3. Douglas G Altman (2005, ISBN:0 7279 1375 1)

Examples

# NOT RUN {

### Example from Essential Medical Statistics
# Page 178, Chapter 18: Controlling for confounding: Stratification
lepto <- expandtbl(
    male = c(36, 14, 50, 50), female = c(24, 126, 10, 90),
    exp_name = "area", exp_lvl = c("Rural", "Urban"),
    case_name = "ab", case_lvl = c("Yes", "No"),
    strata_name = "gender"
)

## label variables and data
lepto <- label(lepto, "Prevalence survey of leptospirosis in West Indies")
lepto <- label(lepto, area="Type of area", ab = "Leptospirosis Antibodies",
                  gender="Gener: Male or Female")

## Calculate OR
mhor(lepto, area, ab)

## Calculate MHOR
mhor(lepto, area, ab, gender)


# }