Short way (quick)

If you have a VCF already, you can just use VCFtools in order to do a very simple linkage disequilibrium (LD) analysis: http://vcftools.sourceforge.net/documentation.html#ld

Long way (more flexibility and comprehensive)

Another, more roundabout approach would be to get your data from VCF to PLINK format, where you could do a more comprehensive analysis. You could have followed my tutorial (Produce PCA bi-plot for 1000 Genomes Phase III in VCF format (old) ), which includes the downloading of all 1000 Genomes Phase III data in VCF format and then converting them into PLINK format.

Here is further information for conducting LD analysis in PLINK:

• http://zzz.bwh.harvard.edu/plink/ld.shtml
• https://www.cog-genomics.org/plink/1.9/ld

If you follow my tutorial, you'll have the entire 1000 Genomes Phase III samples in PLINK, and from there you can easily filter in/out your samples of interest. See here for details: https://www.cog-genomics.org/plink/1.9/filter

For using a dataset correctly in PLINK, you should create a custom FAM file that matches your dataset and then specify this when performing LD analysis with --fam MyCustom.fam. A FAM file contains 7 columns:

1. Family ID (FID)
2. Individual ID (IID)
3. Paternal ID (PID)
4. Maternal ID (MID)
5. Gender (1, male; 2, female)
6. Phenotype/Disease status (1, control; 2, case/disease)

The file ftp://ftp.1000genomes.ebi.ac.uk/vol1/ftp/technical/working/20130606_sample_info/20130606_g1k.ped, which you'll get if you follow my tutorial, already contains this information, so, use that and filter out what you don't need.

Also, when reading your data from VCF/BCF into PLINK, it is critical that you specify a sample order file so that PLINK reads the samples in the order that you want and in the order that matches the samples as listed in your custom FAM. A sample command is:

plink --noweb \
  --bcf My.bcf \
  --keep-allele-order \
  --indiv-sort file SampleSort.list \
  --vcf-idspace-to _ \
  --const-fid \
  --allow-extra-chr 0 \
  --split-x b37 no-fail \
  --make-bed \
  --out PlinkDataForLD

The file mentioned in this command after the --indiv-sort file command-line parameter, SampleSort.list, contains 2 columns (FID IID), like this:

0  NA0165
0  NA0169
et cetera

Then, to do LD analysis in PLINK:

plink --file PlinkDataForLD \
  --r2 --ld-window-kb 1000 \
  --ld-window 100000 \
  --ld-window-r2 0 \
  --fam MyCustom.fam