I feel this is an awfully obtuse question to ask, but strangely, this problem is poorly documented.
I would like to upgrade PHP, but there are several problems:
I think one simple way to do it, is:
1 - Check you where is your current PHP:
$ which php
$ /usr/local/bin/php
You see? Usually, our commands that we run is a link in /usr/local/bin so...
2 - Unlink this current link of PHP
unlink /usr/local/bin/php
If you prefere, before unlink it, check the path and then remove php files (do ls -al /usr/local/bin | grep php and then rm -rf into desired path)
3 - Install PHP 7.1
curl -s http://php-osx.liip.ch/install.sh | bash -s 7.1
4 - Create new link (using php 7.1 bin that you have installed)
ln /usr/local/php5-7.1.9-20170914-100859/bin/php /usr/local/bin/php
Like I said, its a simple way I think.