How do you validate the PropTypes of a nested object in ReactJS?

You can use React.PropTypes.shape to validate properties:

propTypes: {
    data: React.PropTypes.shape({
      id: React.PropTypes.number.isRequired,
      title: React.PropTypes.string
    })
}

Update

As @Chris pointed out in comments, as of React version 15.5.0 React.PropTypes has moved to package prop-types.

import PropTypes from 'prop-types';    

propTypes: {
    data: PropTypes.shape({
      id: PropTypes.number.isRequired,
      title: PropTypes.string
    })
}

More info