Biostatistics & Epidemiology

Wednesday, January 2, 2019

Asymmetry test of EGGER

•Linear regression approach to measure funnel plot asymmetry on the natural logarithm scale of the odds ratio

•The standard normal deviate (SND), defined as the odds ratio divided by its standard error, is regressed against the estimate's precision, the latter being defined as the inverse of the standard error

•(regression equation: SND= a+ bxprecision)

•As precision depends largely on sample size, small trials will be close to zero on the × axis

•Null hypothesis –symmetry exists in the funnel plot

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Freeman-Tukey transform

•Freeman-Tukey transform

seek to adjust data to make the distribution more similar to a Normal distribution

•Was specifically designed for Poisson-like data, especially with a mean value >1.

•The FT angular or arcsine transform was developed for Binomial-like data, in particular, data representing proportions or percentages.

Duval and Tweedie’s Trim and Fill method

•Uses an iterative procedure to remove most extreme small studies from positive side of funnel plot, re-computing effect size at each iteration until funnel plot is symmetric about new effect size

•Yield an unbiased estimate of effect size

•Trimming also reduces variance of effects, yielding a too narrow C.I.

•Therefore algorithm then adds original studies back into analysis, and imputes a mirror image for each.

•This fill has no impact on point estimate but serves to correct the variance

the black dots are studies added after the method...

Publication Bias

Publication Bias:

•The publication or non-publication of research findings, depending on the nature and direction of the results (ref. Cochrane Handbook)

•Publication bias exists when the studies included in the analysis differ systematically from all the studies that should have been included.

•Typically, studies with larger than average effects are more likely to be published and this can lead to upward bias in the summary effect

•Publication bias is when studies with positive findings are more likely to be published

•This means that any meta analysis or literature reviews based only on published data will be biased, so researchers should make sure to include unpublished reports in their data as well

Funnel Plot:

•Plots of “trials’ effect estimates”against“sample size”

•Funnel plot is based on the fact that precision in estimating underlying treatment effect will increase as sample size of component studies increases

•Results from small studies will scatter widely at bottomofgraph, with spreadnarrowing among larger studies

•In absence of biasplot will resemble a symmetrical inverted funnel

•Conversely, if there is bias, funnel plots will often be skewed and asymmetrical

•Symmetry (or asymmetry) - visual examination(so it is subjective)

How to calculate relative risk from odds ratio ?

Q. How to calculate relative risk from odds ratio ?

Random and Fixed effect model

Random vs. fixed effect model

Tuesday, January 1, 2019

I square statistics

•Test of heterogeneity

•I2 can be calculated from Cochrane Q according to the formula:

•The percentage of the variability in effect estimates that is due to heterogeneity rather than sampling error (chance).

•Any negative values of I2 are considered equal to 0, so that the range of I2 values is between 0% and 100%.

•A meta-analysis with

•I2= 0 means that all variability in effect size estimates is due to sampling error

•I2= 50 means that half of the total variability among effect sizes is by true heterogeneity between studies

•I2percentages of around 25% , 50% and 75% would mean low, medium, and high heterogeneity, respectively

Cochrane Q

•Cochrane Q – indicates the presence or absence of heterogeneity without measuring the effect

•The Q test is computed by summing the squared deviations of each study’s effect estimate from the overall effect estimate, weighting the contribution of each study by its inverse variance

Confidence Interval and Prediction Interval

•Confidence interval (C.I.) the width of the diamond: in 95% of cases mean effect size will fall inside the diamond

•Quantifies accuracy of the mean

•Only considers error of estimation of mean

•Prediction interval (P.I.) horizontal line to either end of the diamond: in 95% of cases the true effect in a new study will fall inside the horizontal lines

•P.I. addresses the actual dispersion of effect sizes

•Considers both true dispersion as well as error

Sampling

Probability sampling:

Each population element has a known probability or chance of being chosen for sample

E.g. Simple random sampling, stratified sampling, cluster sampling,

multistage sampling, systematic random sampling

Non-probability sampling:

One cannot be assured of having known probability of each population element

E.g. Volunatary sampling, Convenient sampling