es_from_rr_se {metaConvert}

Convert a risk ratio value and standard error to three effect measures (SMD, OR, COR)

Description

Convert a risk ratio value and standard error to three effect measures (SMD, OR, COR)

Usage

es_from_rr_se(
  rr,
  logrr,
  logrr_se,
  baseline_risk,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  smd_to_cor = "viechtbauer",
  rr_to_or = "metaumbrella",
  reverse_rr
)

Arguments

rr

risk ratio value

logrr

log risk ratio value

logrr_se

standard error of the log risk ratio

baseline_risk

proportion of cases in the non-exposed group

n_exp

number of participants in the exposed group

n_nexp

number of participants in the non-exposed group

n_cases

number of cases/events

n_controls

number of controls/no-event

smd_to_cor

formula used to convert the SMD value (converted from RR) into a coefficient correlation (see es_from_cohen_d).

rr_to_or

formula used to convert the rr value into an odds ratio (see details).

reverse_rr

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the (log) risk ratio (RR) value and its standard error to odds ratio (OR) and number needed to treat.

To estimate the odds ratio and its standard error, various formulas can be used.

A. First, the approach described in Grant (2014) can be used. However, in the paper, only the formula to convert an RR value to a OR value is described. To derive the variance, we used this formula to convert the bounds of the 95% CI, which were then used to obtain the variance.

This argument requires (rr + baseline_risk + rr_ci_lo + rr_ci_up) to generate a RR. The following formulas are used (br = baseline_risk):

or = \frac{rr * (1 - br)}{1 - rr * br}

or\_ci\_lo = \frac{rr\_ci\_lo}{1 - br + br*rr\_ci\_lo}

or\_ci\_up = \frac{rr\_ci\_up}{1 - br + br*rr\_ci\_up}

logor\_se = \frac{log(or\_ci\_up) - log(or\_ci\_lo)}{2 * qnorm(.975)}

B. Second, the formulas implemented in the metaumbrella package can be used (or_to_rr = "metaumbrella_exp"). This argument requires (rr + logrr_se + n_exp + n_nexp) to generate a OR. More precisely, we previously developed functions that simulate all combinations of the possible number of cases and controls in the exposed and non-exposed groups compatible with the actual value of the RR. Then, the functions select the contingency table whose standard error coincides best with the standard error reported. The RR value and its standard are obtained from this estimated contingency table.

C. Third, it is possible to transpose the RR to a OR (rr_to_or = "transpose"). This argument requires (rr + logrr_se) to generate a OR. It is known that OR and RR are similar when the baseline risk is small. Therefore, users can request to simply transpose the RR value & standard error into a OR value & standard error.

or = rr

logor\_se = logrr\_se

D. Fourth, it is possible to recreate the 2x2 table using the dipietrantonj's formulas (rr_to_or = "dipietrantonj"). This argument requires (rr + logrr_ci_lo + logrr_ci_lo) to generate a OR. Information on this approach can be retrieved in Di Pietrantonj (2006).

To estimate the NNT, the formulas used are :

nnt = \frac{1}{br * (1 - rr)}

To estimate the Cohen's d value and its standard error, the function first converts the RR value and standard error into OR and standard error, and then converts these values into Cohen's d using the following formulas:

cohen\_d = \log(or) * \frac{\sqrt{3}}{\pi}

cohen\_d\_se = \sqrt{\frac{logor\_se^2 * 3}{\pi^2}}

Value

This function estimates and converts between several effect size measures.

natural effect size measure	RR
converted effect size measure	OR + NNT
required input data	See 'Section 3. Risk Ratio'
	https://metaconvert.org/html/input.html

References

Di Pietrantonj C. (2006). Four-fold table cell frequencies imputation in meta analysis. Statistics in medicine, 25(13), 2299–2322. https://doi.org/10.1002/sim.2287

Gosling, C. J., Solanes, A., Fusar-Poli, P., & Radua, J. (2023). metaumbrella: the first comprehensive suite to perform data analysis in umbrella reviews with stratification of the evidence. BMJ mental health, 26(1), e300534. https://doi.org/10.1136/bmjment-2022-300534

Grant R. L. (2014). Converting an odds ratio to a range of plausible relative risks for better communication of research findings. BMJ (Clinical research ed.), 348, f7450. https://doi.org/10.1136/bmj.f7450

Veroniki, A. A., Pavlides, M., Patsopoulos, N. A., & Salanti, G. (2013). Reconstructing 2x2 contingency tables from odds ratios using the Di Pietrantonj method: difficulties, constraints and impact in meta-analysis results. Research synthesis methods, 4(1), 78–94. https://doi.org/10.1002/jrsm.1061

Examples

es_from_rr_se(rr = 2.12, logrr_se = 0.242, n_exp = 120, n_nexp = 44)