1. Individual Level Data

For analyses using individual-level data, the basic format for single trait is as follows:

• X is an $N \times P$ matrix with $N$ individuals and $P$ variants. Including variant names as column names is highly recommended, especially when working with multiple $X$ matrices and $Y$ vectors.
• Y is a length $N$ vector containing phenotype values for the same $N$ individuals as $X$.

The input format for multiple traits is similar, but X should be a list of genotype matrices, each corresponding to a different trait. Y should also be a list of phenotype vectors. For example:

• X = list(X1, X2, X3, X4, X5) where each Xi is a matrix for trait i - with the dimension of $N_i \times P_i$, where $N_i$ and $P_i$ do not need to be the same for different traits.
• Y = list(Y1, Y2, Y3, Y4, Y5) where each Yi is a vector for trait i - with $N_i$ individuals.

colocboost also offers flexible input options (see detailed usage with different input formats, refer to Individual Level Data Colocalization):

• Single $X$ matrix with $N \times P$, and $Y$ matrix with $N \times L$ for $L$ traits.
• Multiple $X$ matrices and unmatched $Y$ vectors with a mapping dictionary (example shown in section 3 below).

2. Summary Statistics

For analyses using summary statistics, the basic format for single trait is as follows:

• sumstat is a data frame with required columns z or (beta, sebeta), and optional columns but highly recommended n and variant.

data(Sumstat_5traits)
head(Sumstat_5traits$sumstat[[1]])
#>              z    n variant
#> 451 -1.0945531 1153    rs_1
#> 452 -0.4113347 1153    rs_2
#> 453 -0.4113347 1153    rs_3
#> 454 -0.7467923 1153    rs_4
#> 455 -0.3018575 1153    rs_5
#> 456 -0.5256479 1153    rs_6

- `z` or (`beta`, `sebeta`) - required: either z-score or (effect size and standard error)
- `n` - highly recommended: sample size for the summary statistics, it is highly recommendation to provide.
- `variant` - highly recommended: required if sumstat for different outcomes do not have the same number of variables (multiple sumstat and multiple LD).

• LD is a matrix of LD. This matrix does not need to contain the exact same variants as in sumstat, but the colnames and rownames of LD should include the variant names for proper alignment.

The input format for multiple traits is similar, but sumstat should be a list of data frames sumstat = list(sumstat1, sumstat2, sumstat3). The flexibility of input format for multiple traits is as follows (see detailed usage with different input formats, refer to Summary Statistics Colocalization):

• One LD matrix with a superset of variants in sumstat for all traits is allowed.
• Multiple LD matrices, each corresponding to a different trait, are also allowed for the trait-specific LD structure.
• Multiple LD matrices and unmatched sumstat data frames with a mapping dictionary are also allowed (example shown in section 3 below).

3. Optional: mapping between arbitrary input $X$ and $Y$

For analysis when including multiple genotype matrices X with unmatched arbitrary phenotype vectors Y, a mapping dictionary dict_YX is required to indicate the relationship between X and Y. Similarly, when multiple LD matrices with unmatched arbitrary multiple summary statistics sumstat are used, a mapping dictionary dict_sumstatLD is required to indicate the relationship between sumstat and LD.

For example, considering three genotype matrices X = list(X1, X2, X3) and 6 phenotype vectors Y = list(Y1, Y2, Y3, Y4, Y5, Y6), where

• X1 is for trait 1, trait 2, trait 3
• X2 is for trait 4, trait 5
• X3 is for trait 6

Then, you need to define a 6 by 2 matrix mapping dictionary dict_YX as follows:

• The first column should be c(1,2,3,4,5,6) for 6 traits.
• The second column should be c(1,1,1,2,2,3) for 3 genotype matrices.

Here, each row indicates the trait index and the corresponding genotype matrix index.

dict_YX <- cbind(c(1,2,3,4,5,6), c(1,1,1,2,2,3))
dict_YX
#>      [,1] [,2]
#> [1,]    1    1
#> [2,]    2    1
#> [3,]    3    1
#> [4,]    4    2
#> [5,]    5    2
#> [6,]    6    3

4. HyPrColoc compatible format: effect size and standard error matrices

ColocBoost also provides a flexibility to use HyPrColoc compatible format for summary statistics with and without LD matrix. For example, when analyze $L$ traits for the same $P$ variants with the specified effect size and standard error matrices:

• effect_est (required) is $P \times L$ matrix of variable regression coefficients (i.e. regression beta values) in the genomic region.
• effect_se (required) is $P \times L$ matrix of standard errors for the regression coefficients.
• effect_n (highly recommended) is either a scalar or a vector of sample sizes for estimating regression coefficients.
• LD (optional) is LD matrix for the $P$ variants. If it is not provided, it will apply LD-free ColocBoost.

See more details about HyPrColoc compatible format in Summary Statistics Colocalization).

See more details about data format to implement LD-free ColocBoost and LD-mismatch diagnosis in LD mismatch and LD-free Colocalization).