Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions...
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Transcript of Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions...
![Page 1: Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions and approximations Imputation method (substituting missing.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e6c5503460f94b6b0d7/html5/thumbnails/1.jpg)
Guide to Handling Missing Information• Contacting researchers
• Algebraic recalculations, conversions and approximations
• Imputation method (substituting missing data)
![Page 2: Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions and approximations Imputation method (substituting missing.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e6c5503460f94b6b0d7/html5/thumbnails/2.jpg)
Imputation Method
- When recalculations not possible-e.g. no standard deviation for a study- Use available data from other studies or other
meta-analysis
a. Within study imputation
b. Multiple imputations
Imputation Method
![Page 3: Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions and approximations Imputation method (substituting missing.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e6c5503460f94b6b0d7/html5/thumbnails/3.jpg)
Within-study imputation
= Standard deviation (SD) for missing data from study j
=Mean from study with missing SD
=Summation of all known SD from different studies
=Summation of means from different studies other than j
Method 1.(Means)
SDj~
Xj
_
Ʃik SDi
(Ʃik Xi)
_
SDj= Xj Ʃik SDi
_______
Ʃik Xi
_~
![Page 4: Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions and approximations Imputation method (substituting missing.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e6c5503460f94b6b0d7/html5/thumbnails/4.jpg)
Assumptions
•Assumes SD to mean ratio is at the same scale for all studies- Experimental scales can differ tremendously between different taxonomic groups or experimental designs
SDj= Xj Ʃik SDi
_______
Ʃik Xi
~ -
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-Regression techniques- Reports sample size but missing information
to calculate pooled SD (required for Hedge’s d).
α = Interceptβ = slope of the linear regression of n vs s
nj = observed sample size of the study with missing data
Method 2.(sample size)
sj=α+β(nj)~
![Page 6: Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions and approximations Imputation method (substituting missing.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e6c5503460f94b6b0d7/html5/thumbnails/6.jpg)
Assumptions• Assumes n (observed sample size of the study
with missing data) is a good predictor s.
sj=α+β(nj)~
K= number of studies with complete information on s and n (sample size of individual study)
Method 3.No. of studies
sj= Ʃik sj √ni_____K √nj
~
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Method 4. Follman et al. (1992) Furukawa et al. (2006)
sj= √Ʃik [(ni-1)Ϭ2
i]__________√Ʃi
k (ni-1)
Ϭ2= variance n= sample size of individual study
~
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Assumptions
• Some degree of homogeneity among the observed SD and X across studies
• Assume information is missing at random and not due to reporting biases (non-random)
-Imputations retain their original units. -Large variations among estimates will bias
imputations.
_
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Multiple imputations• Use random sampling approach
• Average repeated sampling for missing data
Overall imputed synthesis
![Page 10: Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions and approximations Imputation method (substituting missing.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e6c5503460f94b6b0d7/html5/thumbnails/10.jpg)
Advantage of multiple imputations
• Variability is explicitly modeled therefore do no treat imputed value as true observation
• e.g. Does not account for error associated with α or β.
sj=α+β(nj)~
![Page 11: Guide to Handling Missing Information Contacting researchers Algebraic recalculations, conversions and approximations Imputation method (substituting missing.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e6c5503460f94b6b0d7/html5/thumbnails/11.jpg)
Methods: Multiple imputations• Various methods: use maximum likelihood or
Bayesian models.• Requires specialized software• e.g. Hot Deck- To calculate pooled s but
several SD values missing- Random sample of s drawn with replacement possible s- Process repeated with replacement from
possible s- Repeat till we get “m” number of complete
data sets
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Methods: Hot deckcalculate effect size= δ for each(m) dataCalculate variance = Ϭ2 (δl) set
δ = Ʃlm = 1 δl
__
_.___m
Variance= Ϭ2(δ)= Ʃl
m = 1 Ϭ2(δl) + (1+1) Ʃlm= 1(δl – δ)2
m_________
m_ _________
m-1
. _ _ .Pooled effect size
Rubin and Schenker (1991)If 30% data missing->m= 3If 50% data missing->m= 5
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Non-parametric analyses and bootstrapping
• Alternative to Hedge’s d• Using weighting scheme • Does not require SD• E.g log response ratiolnR= ln XT
XC
If sample size available but no SDϬ2=(lnR)= nT nC
nT+nC
_____
T= treatmentC= control
___ Inverse of a simplified estimate of variance
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Effects of Imputation• No standardized method for imputation-> biasRubin and Schenker (1991) e.g.• Appropriateness of imputed data can be
evaluated using a sensitivity analysis• Benefits despite potential bias- Improved variance estimate (i.e. smaller CI) over
exclusion- May potentially improve representation of null
studies