Item | Description |
---|---|
Study Title | Genome-wide study of resistance to severe malaria in eleven worldwide populations |
Release date | December 2019 |
Release version | 1 |
Study URL | https://www.malariagen.net/resource/25 |
References | https://doi.org/10.1038/s41467-019-13480-z |
This dataset contains a set of association test summary statistics for association tests between severe malaria cases and population controls collected in eleven populations as shown in the following table:
population | acronym | cases | controls | total |
---|---|---|---|---|
Gambia | Gambia |
2461 | 2518 | 4979 |
Mali | Mali |
259 | 163 | 422 |
Burkina Faso | BurkinaFaso |
711 | 583 | 1294 |
Ghana | Ghana |
391 | 315 | 706 |
Nigeria | Nigeria |
112 | 21 | 133 |
Cameroon | Cameroon |
583 | 634 | 1217 |
Malawi | Malawi |
1161 | 1310 | 2471 |
Tanzania | Tanzania |
410 | 388 | 798 |
Kenya | Kenya |
1529 | 1539 | 3068 |
Vietnam | Vietnam |
703 | 544 | 1247 |
Papua New Guinea | PNG |
379 | 342 | 721 |
TOTAL | 8699 | 8357 | 1705 |
All cases were diagnosed with meeting WHO definitions of severe malaria (see reference [2]), while controls were samples from within the general population and from new births. Underlying genotypes for these samples have also been deposited in the European Genome-Phenome Archive (EGA) under study ID EGAS00001001311
https://ega-archive.org/studies/EGAS00001001311.
This README file contains information on on the following relevant to the dataset:
The summary statistics included here, including allele frequency estimates and association test effect size estimates, parameter standard errors and evidence measures, are made freely available for use. Please include the following text as an acknowledgement in any publication arising from the use of this data: “This study makes use of data generated by MalariaGEN. A full list of the investigators who contributed to the generation of the data is available from www.malariagen.net. Funding for this project was provided by Wellcome Trust (WT077383/Z/05/Z) and the Bill & Melinda Gates Foundation through the Foundation of the National Institutes of Health (566) as part of the Grand Challenges in Global Health Initiative.”
This dataset was created for and described in the following manuscript:
[1] Malaria Genomic Epidemiology Network, “New insights into malaria susceptibility from the genomes of 17,000 individuals from Africa, Asia, and Oceania”, Nature Communications (2019). https://doi.org/10.1038/s41467-019-13480-z; bioRxiv link: https://doi.org/10.1101/535898
Please cite the above article if you make use of data from this release in disseminated work.
This release includes summary statistics from frequentist and Bayesian meta-analysis of association test with severe malaria (SM), as well as severe malaria subphenotypes (CM, SMA and OTHER) as defined in the following table:
Phenotype abbreviation | Description |
---|---|
SM | Severe malaria (equivalent to CM, SMA or OTHER) |
CM | Cerebral malaria |
SMA | Severe malarial anaemia |
OTHER | Other or nonspecific severe malaria |
The following table summarises the available files:
Filename | Description |
---|---|
MalariaGEN_2019_summary_statistics_releasenote.html | This release note |
MalariaGEN_2019_summary_statistics_releasenote.md | This release note as a Markdown document |
MalariaGEN_combined_evidence.csv.gz (1.6Gb) | Summary of meta-analysis, including overall P-values and Bayes factors |
MalariaGEN_case-control:add:effects.csv.gz (666Mb) | Fixed-effect meta-analysis of association with SM, assuming additive effect |
MalariaGEN_case-control:dom:effects.csv.gz (664Mb) | Fixed-effect meta-analysis of association with SM, assuming dominance effect of ‘B’ allele |
MalariaGEN_case-control:rec:effects.csv.gz (390Mb) | Fixed-effect meta-analysis of association with SM, assuming recessive effect of ‘B’ allele |
MalariaGEN_case-control:het:effects.csv.gz (667Mb) | Fixed-effect meta-analysis of association with SM, assuming heterozygote effect |
MalariaGEN_subphenotype:add:effects.csv.gz (1.2Gb) | Fixed-effect meta-analysis of association with SM subtypes, assuming additive effect |
MalariaGEN_subphenotype:dom:effects.csv.gz (1.2Gb) | Fixed-effect meta-analysis of association with SM subtypes, assuming dominance effect of ‘B’ allele |
MalariaGEN_subphenotype:rec:effects.csv.gz (695Mb) | Fixed-effect meta-analysis of association with SM subtypes, assuming recessive effect of ‘B’ allele |
MalariaGEN_subphenotype:het:effects.csv.gz (1.2Gb) | Fixed-effect meta-analysis of association with SM subtypes, assuming heterozygote effect |
MalariaGEN_case-control:add:bfs.csv.gz (8.3Gb) | Bayesian meta-analysis of association with SM, assuming additive effect |
MalariaGEN_case-control:dom:bfs.csv.gz (7.8Gb) | Bayesian meta-analysis of association with SM, assuming dominance effect of ‘B’ allele |
MalariaGEN_case-control:rec:bfs.csv.gz (3.7Gb) | Bayesian meta-analysis of association with SM, assuming recessive effect of ‘B’ allele |
MalariaGEN_case-control:het:bfs.csv.gz (8.2Gb) | Bayesian meta-analysis of association with SM, assuming heterozygote effect |
MalariaGEN_subphenotype:add:bfs.csv.gz (2.1Gb) | Bayesian meta-analysis of association with SM subtypes, assuming additive effect |
MalariaGEN_subphenotype:dom:bfs.csv.gz (2.0Gb) | Bayesian meta-analysis of association with SM subtypes, assuming dominance effect of ‘B’ allele |
MalariaGEN_subphenotype:rec:bfs.csv.gz (1.1Gb) | Bayesian meta-analysis of association with SM subtypes, assuming recessive effect of ‘B’ allele |
MalariaGEN_subphenotype:het:bfs.csv.gz (2.0Gb) | Bayesian meta-analysis of association with SM subtypes, assuming heterozygote effect |
MalariaGEN_case-control:add:per_population.csv.gz (3.2Gb) | Per-population results for association with SM, assuming additive effect |
MalariaGEN_case-control:dom:per_population.csv.gz (3.1Gb) | Per-population results for association with SM, assuming dominance effect of ‘B’ allele |
MalariaGEN_case-control:rec:per_population.csv.gz (3.2Gb) | Per-population results for association with SM, assuming recessive effect of ‘B’ allele |
MalariaGEN_case-control:het:per_population.csv.gz (3.2Gb) | Per-population results for association with SM, assuming heterozygote effect |
MalariaGEN_subphenotype:add:per_population.csv.gz (6.3Gb) | Per-population results for association with SM subtypes, assuming additive effect |
MalariaGEN_subphenotype:dom:per_population.csv.gz (6.2Gb) | Per-population results for association with SM subtypes, assuming dominance effect of ‘B’ allele |
MalariaGEN_subphenotype:rec:per_population.csv.gz (3.2Gb) | Per-population results for association with SM subtypes, assuming recessive effect of ‘B’ allele |
MalariaGEN_subphenotype:het:per_population.csv.gz (6.3Gb) | Per-population results for association with SM subtypes, assuming heterozygote effect |
Below we describe the contents of each of the files provided in this dataset.
A full set of methods can be found in [1]. In brief, genotypes were obtained by typing each sample on the Illumina Omni 2.5M platform, followed by imputation into the 1000 Genomes Reference panel (1000GP) and into a custom panel (“combined panel”) obtained by adding additional whole-genome sequenced samples (https://ega-archive.org/studies/EGAS00001003648) to the 1000GP. Additionally, HLA alleles were imputed using HLA*IMP:02 and glycophorin region CNV alleles were imputed using a panel described previously (Leffler et al, https://doi.org/10.1126/science.aam6393).
Association tests were conducted by logistic regression in each of the eleven populations in Table 1, include 5 principal components as covariates, using SNPTEST (http://www.well.ox.ac.uk/~gav/snptest). Association test results were then meta-analysed using BINGWA (http://www.well.ox.ac.uk/~gav/bingwa), under both frequentist fixed-effect meta-analysis and a flexible bayesian meta-analysis framework described in [1].
Additionally, we implemented a multinomial logistic regression method to test each genetic variant against severe malaria subtype as defined in our data (CM, SMA or other severe malaria; c.f. table 2). Case samples identified as having both CM and SMA were excluded from these tests. Subphenotype association test results were also meta-analysed using BINGWA in a multivariate meta-analysis framework.
The meta-analysis results files have the following common columns:
Column | Description |
---|---|
variant_id |
An internal identifier for this variant. This can be used to match between files. |
analysis_id |
An internal identifier reflecting the imputation panel used for this variant, as described below. This can be used to match between files. |
analysis |
A string identifier reflecting the imputation panel used for this variant, as described below. |
chromosome |
The chromosome the variant maps to |
position |
The position the variant maps to |
rsid |
The rsid (or other identifier) of the variant |
alleleA |
The reference allele of the variant |
alleleB |
The non-reference allele of the variant |
A |
The expected count of haploid reference calls (only nonzero for X chromosome variants). |
B |
The expected count of haploid non-reference calls (only nonzero for X chromosome variants). |
AA |
The expected count of diploid homozygous reference allele calls. |
AB |
The expected count of diploid heterozygous calls. |
BB |
The expected count of diploid homozygous non-reference allele calls. |
N |
Total sample size included in the meta-analysis |
Note: In all files the variant_id
column refers to the specific variant (i.e. the specific combination of chromosome, position and alleles) being analysed. The analysis_id
and analysis
columns refer to the imputation reference panel from which the variant was imputed. To match results between files, users should match on both the variant_id
and analysis_id
columns. Imputation refrence panels are detialed in the following table.
analysis_id | analysis | description |
---|---|---|
1 | gwas |
Combined 1000GP / MalariaGEN reference panel (autosomal variants only) |
2 | 1000GP |
1000GP reference panel imputation of autosomal variants |
6 | 1000GP:X |
1000GP reference panel imputation of X chromosome variants |
3 | hlaimp |
Imputation of HLA alleles using HLA:IMP*02 . |
4 | GYP.all |
imputation of glycophorin region SNPs and INDELs, from the panel in [2] |
5 | GYP.cnvs |
imputation of glycophorin region CNVs, from the panel in [2] |
An overview of meta-analysis results can be found in this file:
MalariaGEN_summary_statistics_combined_evidence.csv.gz
This is a gzipped comma-seperated file which contains overall measures of evidence under additive, dominant, recessive and heterozygote modes of inheritance, as well as an overall model-averaged Bayes factor and indication of the best-fitting model.
This file has the following columns:
Column | Description |
---|---|
(common columns) | As described above |
effective_minor_allele_count |
The effective minor allele count, computed across all samples as described below |
included_cohorts |
A string of eleven 1’s and 0’s indicating which per-population estimates were included in meta-analysis. |
case-control:add:pvalue |
P-value under an additive model of association with case/control status |
case-control:dom:pvalue |
P-value under a dominant model of association of the non-reference allele with case/control status |
case-control:rec:pvalue |
P-value under a recessive model of association of the non-reference allele with case/control status |
case-control:het:pvalue |
P-value under a heterozygote model of association with case/control status |
case-control:add:mean_bf |
Model-averaged Bayes factor (BF) under an additive model of association with case/control status |
case-control:dom:mean_bf |
Model-averaged BF under a dominant model of association of the non-reference allele with case/control status |
case-control:rec:mean_bf |
Model-averaged BF under a recessive model of association of the non-reference allele with case/control status |
case-control:het:mean_bf |
Model-averaged BF under a heterozygote model of association with case/control status |
case-control:mean_bf |
Model-averaged BF under a model of association with case/control status, averaged over mode of inheritance using the weights specified in [1]. |
subphenotype:add:pvalue |
P-value under an additive model of association with malaria subtype |
subphenotype:dom:pvalue |
P-value under a dominant model of association of the non-reference allele with malaria subtype |
subphenotype:rec:pvalue |
P-value under a recessive model of association of the non-reference allele with malaria subtype |
subphenotype:het:pvalue |
P-value under a heterozygote model of association with malaria subtype |
subphenotype:add:mean_bf |
Model-averaged BF under an additive model of association with malaria subtype |
subphenotype:dom:mean_bf |
Model-averaged BF under a dominant model of association of the non-reference allele with malaria subtype |
subphenotype:rec:mean_bf |
Model-averaged BF under a recessive model of association of the non-reference allele with malaria subtype |
subphenotype:het:mean_bf |
Model-averaged BF under a heterozygote model of association with malaria subtype |
subphenotype:mean_bf |
Model-averaged BF under a model of association malaria subtype, averaged over mode of inheritance. |
add:mean_bf |
Model-averaged BF under an additive model of association malaria subtype, averaged over case-control and subphenotype effect models using the weights specified in [1] |
dom:mean_bf |
Model-averaged BF under a dominant model of association of the non-reference allele, averaged over case-control and subphenotype effect models using the weights specified in [1] |
rec:mean_bf |
Model-averaged BF under a recessive model of association malaria subtype, averaged over case-control and subphenotype effect models using the weights specified in [1] |
het:mean_bf |
Model-averaged BF under a heterozygote model of association malaria subtype, averaged over case-control and subphenotype effect models using the weights specified in [1] |
mean_bf |
Overall model-averaged BF, using weights specified in [1]. These values are presented in Figure 2 of [1]. |
best_posterior_model |
The model with the highest posterior weight amongst all those included in mean_bf . |
Further notes:
The effective_minor_allele_count
(EMAC) column is computed as the sum over populations of the minor allele count times the IMPUTE info score. Only variants with EMAC >= 250 are included in this release.
The values in the included_cohorts
are strings of eleven 0’s and 1’s. These correspond to the eleven populations in the (roughly west-east) order in Table 1. A 1
indicates that the effect size estimate (for additive, case-control association model) for this population was included in meta-analysis. A 0
indicates that it was excluded due to low per-population minor allele count, low per-population IMPUTE info score, or failure to fit the model.
Model-averaged Bayes factors were computed under the set of prior weights detailed in [1].
Detailed meta-analysis results for fixed-effect meta-analysis under specific mode of inheritance are available in these files:
`MalariaGEN_case-control:[mode]:effects.csv.gz`
`MalariaGEN_subphenotype:[mode]:effects.csv.gz`
where mode
is ‘add’ (for additive model), ‘dom’ (dominant effect of the non-reference allele), ‘rec’ (recessive effect of the non-reference allele), or ‘het’ (heterozygote effect). The case-control
files contain results of meta-analysis of logistic regression against case-control status in each population, and the subphenotype
files contain results of meta-analysis analysis of multinomial logistic regression against malaria subtypes in each population.
The following tables list the columns of these files.
Column | Description |
---|---|
(common columns) | As described above |
included_betas |
A string of eleven 1’s and 0’s indicating which per-population estimates were included in meta-analysis. |
mode |
Assumed mode of inheritance; either “add”, “dom”, “rec”, or “het”. |
beta |
The estimated log odds ratio for effect of the non-reference allele on SM, computed using fixed-effect inverse variance weighted meta-analysis across included cohorts. |
se |
The estimated standard error for beta |
pvalue |
Wald test P-value for beta |
Column | Description |
---|---|
(common columns) | As described above |
included_betas |
A string of eleven 1’s and 0’s indicating which per-population estimates were included in meta-analysis. |
mode |
Assumed mode of inheritance; either “add”, “dom”, “rec”, or “het”. |
beta_1/CM |
Estimate log odds ratio for effect of the non-reference allele on CM, computed using fixed-effect inverse variance weighted meta-analysis across included cohorts. |
se_1 |
Estimated standard error for beta_1/CM |
wald_pvalue_1 |
Wald test P-value for beta_1/CM |
beta_2/OTHER |
Estimated log odds ratio for effect of non-reference allele on nonspecific severe malaria |
se_2 |
Estimated standard error for beta_2/OTHER |
wald_pvalue_2 |
Wald test P-value for beta_2/OTHER |
beta_3/SMA |
Estimated log odds ratio for effect of non-reference allele on severe malaria anaemia |
se_3 |
Estimated standard error for beta_3/SMA |
wald_pvalue_3 |
Wald test P-value for beta_3/SMA |
cov_1,2 |
Estimated covariance between beta_1/CM and beta_2/OTHER |
cov_1,3 |
Estimated covariance between beta_1/CM and beta_3/SMA |
cov_2,3 |
Estimated covariance between beta_2/OTHER and beta_3/SMA |
pvalue |
Overall P-value for beta_1 ..beta_3 |
Detailed meta-analysis results for bayesian meta-analysis under specific mode of inheritance are available in these files:
`MalariaGEN_case-control:[mode]:bfs.csv.gz`
`MalariaGEN_subphenotype:[mode]:bfs.csv.gz`
where [mode]
is one of: add
(additive effect), dom
(dominant effect of the non-reference allele), rec
(recessive effect of the non-reference allele), or het
(heterozygote effect).
Results are presented as a set of Bayes factors (BFs). All Bayes factors were computed assuming an asymptotic approximation and a Gaussian prior on the effect size variance σ^{2}, and we used an equal mixture of σ=0.2, 0.4, 0.6, 0.8 throughout. Details of model assumptions and prior weights can be found in [1].
The following table lists the columns of the case-control Bayesian analysis files.
Column | Description |
---|---|
(common columns) | As described above |
included_betas |
A string of eleven 1’s and 0’s indicating which per-population estimates were included in meta-analysis. |
mode |
Assumed mode of inheritance; either “add”, “dom”, “rec”, or “het”. |
Gambia:bf |
BF for association using only data from The Gambia |
Mali:bf |
BF for association using only data from Mali |
BurkinaFaso:bf |
BF for association using only data from Burkina Faso |
Ghana:bf |
BF for association using only data from Ghana |
Nigeria:bf |
BF for association using only data from Nigeria |
Cameroon:bf |
BF for association using only data from Camaeroon |
Malawi:bf |
BF for association using only data from Malawi |
Tanzania:bf |
BF for association using only data from Tanzania |
Kenya:bf |
BF for association using only data from Kenya |
Vietnam:bf |
BF for association using only data from Vietnam |
PNG:bf |
BF for association using only data from Papua New Guinea |
fix:[populations]:bf |
BF under fixed-effect model of effect across specified populations, where populations denotes a string of eleven 1’s and 0’s as described below |
cor:[populations]:bf |
BF under correlated-effect model of effect across specified populations |
ind:[populations]:bf |
BF under independent-effect model of effect across specified populations |
str:bf |
BF under a structured effect model across populations |
mean_bf |
Model-averaged BF for case-control effects for the specific mode, across a subset of models with weights as described in [1]. |
max_bf_model |
The model with the highest Bayes factor across all those those tested |
max_bf |
The highest BF |
best_posterior_model |
The model with the highest posterior weight, given the weights specified our manuscript [1] |
best_posterior |
The highest posterior weight |
2nd_best_posterior_model |
The model with the second highest posterior weight |
2nd_best_posterior |
The second highest posterior weight |
Bayes factor columns for population groups are encoded using the populations
indicator, which is a string of 0’s and 1’s indicating whether the effect is assumed nonzero or zero in each population. For this purpose are taken in the order shown in Table 1 (i.e. roughly west-east order). Examples are given below:
Example | Description |
---|---|
fix:11111111111:bf |
Fixed-effect model of effects across all populations |
fix:11111111100:bf |
Fixed-effect model of effects restricted to African populations |
fix:10000000000:bf |
Gambia-specific effect |
cor:11111111100:bf |
Correlated-effect model of effects restricted to African populations |
ind:00000011100:bf |
Independent-effect model of effects restricted to east African populations |
See [1] for full details of models included.
The following table lists the columns of the subphenotype Bayesian analysis files.
Column | Description |
---|---|
(common columns) | As described above |
included_betas |
A string of 1’s and 0’s (3 per each of the eleven populations) indicating which per-population estimates were included in meta-analysis. |
Gambia:bf |
BF using only data from The Gambia, assuming independent effects between phenotypes |
Mali:bf |
BF using only data from Mali, assuming independent effects between phenotypes |
BurkinaFaso:bf |
BF using only data from Burkina Faso, assuming independent effects between phenotypes |
Ghana:bf |
BF using only data from Ghana, assuming independent effects between phenotypes |
Nigeria:bf |
BF using only data from Nigeria, assuming independent effects between phenotypes |
Cameroon:bf |
BF using only data from Camaeroon, assuming independent effects between phenotypes |
Malawi:bf |
BF using only data from Malawi, assuming independent effects between phenotypes |
Tanzania:bf |
BF using only data from Tanzania, assuming independent effects between phenotypes |
Kenya:bf |
BF using only data from Kenya, assuming independent effects between phenotypes |
Vietnam:bf |
BF using only data from Vietnam, assuming independent effects between phenotypes |
PNG:bf |
BF using only data from Papua New Guinea, assuming independent effects between phenotypes |
cm_sma_other_cor:bf |
BF for correlated-effect model of effects on CM, SMA and OTHER cases |
cm_sma_other_fix:bf |
BF for fixed-effect model of effects on CM, SMA and OTHER cases (similar to a case-control effect) |
cm_sma_other_ind:bf |
BF for independent-effect model of effects on CM, SMA and OTHER cases |
cm_sma_cor:bf |
BF for correlated-effect model of effects on CM and SMA cases |
cm_sma_fix:bf |
BF for fixed-effect model of effects on CM and SMA cases |
cm_sma_ind:bf |
BF for independent-effect model of effects on CM and SMA cases |
cm_other_cor:bf |
BF for correlated-effect model of effects on CM and OTHER cases |
cm_other_fix:bf |
BF for fixed-effect model of effects on CM and OTHER cases |
cm_other_ind:bf |
BF for independent-effect model of effects on CM and OTHER cases |
sma_other_cor:bf |
BF for correlated-effect model of effects on SMA and OTHER cases |
sma_other_fix:bf |
BF for fixed-effect model of effects on SMA and OTHER cases |
sma_other_ind:bf |
BF for independent-effect model of effects on SMA and OTHER cases |
cm:bf |
BF for model of effects restricted to CM cases |
other:bf |
BF for model of effects restricted to OTHER cases |
sma:bf |
BF for model of effects restricted to SMA cases |
mean_bf |
Model-averaged BF for subphenotype effects for the specific mode, across a subset of models with weights as described in [1]. |
max_bf_model |
The model with the highest BF across all those those tested |
max_bf |
The highest BF |
best_posterior_model |
The model with the highest posterior weight, given the weights specified our manuscript [1] |
best_posterior |
The highest posterior weight |
2nd_best_posterior_model |
The model with the second highest posterior weight |
2nd_best_posterior |
The second highest posterior weight |
Per-population results, including estimated allele frequency estimates, IMPUTE info scores, and per-population association test results can be found in these files:
`MalariaGEN_case-control:[mode]:percohort.csv.gz`
`MalariaGEN_subphenotype:[mode]:percohort.csv.gz`
The following table lists columns common to these files in addition to those listed above:
Column | Description |
---|---|
(common columns) | As described above |
mode |
Assumed mode of inheritance; either “add”, “dom”, “rec”, or “het”. |
[population]:N |
Total sample size of non-missing genotypes in this population (computed as the sum of imputed genotype probabilities for non-missing genotypes) |
[population]:B_allele_frequency |
Estimated frequency of the ‘B’ (non-reference) allele in this population |
[population]:minor_predictor_count |
Minor predictor count in this population, as described below. |
[population]:all_info |
IMPUTE info measure computed across all samples in this population |
[population]:comment |
comment field, as output by SNPTEST. Values other than NA reflect potential model fit errors. |
[population]:trusted |
Indicator of whether the estimate for this population was included in meta-analysis, as described below. |
In the above, [population]
refers to the acronym
column in Table 1, i.e. is one of Gambia
, Mali
, BurkinaFaso
, Ghana
, Nigeria
, Cameroon
, Malawi
, Tanzania
, Kenya
, Vietnam
, or PNG
. Results are provided for all eleven populations.
The following table lists association test-related columns found in the case-control files:
Column | Description |
---|---|
[population]:beta_1:SM |
Estimated log odds ratio for effect of the non-reference allele on SM in this population, computed using logistic regression |
[population]:se_1 |
The estimated standard error for the effect size estimate in this population. |
[population]:pvalue |
The Wald test P-value against the null that the effect is zero in this population. |
The following table lists association test-related columns found in the subphenotype files:
Column | Description |
---|---|
[population]:beta_1:CM |
Estimated log odds ratio for effect of the non-reference allele on CM in this population, computed using multinomial logistic regression |
[population]:se_1 |
The estimated standard error for the effect size estimate in this population. |
[population]:beta_1:OTHER |
Estimated log odds ratio for effect of the non-reference allele on OTHER in this population |
[population]:se_2 |
The estimated standard error for the effect size estimate in this population. |
[population]:beta_1:SMA |
Estimated log odds ratio for effect of the non-reference allele on SMA in this population |
[population]:se_3 |
The estimated standard error for the effect size estimate in this population. |
[population]:cov_1,2 |
The estimated covariance between beta_1 and beta_2 in this population. |
[population]:cov_1,3 |
The estimated covariance between beta_1 and beta_3 in this population. |
[population]:cov_3,3 |
The estimated covariance between beta_2 and beta_3 in this population. |
[population]:pvalue |
P-value against the null that all three effects are zero in this population. |