Rafael Nadal was advised not to risk playing in Brisbane after suffering a small strain of his left thigh.
Though she was beaten in a Hopman Cup doubles clash that saw her take on Roger Federer, Serena Williams called it the "match of her career".
World number one Novak Djokovic started 2019 with a dominant performance in Doha.
Jelena Ostapenko was thrashed by Monica Niculescu in Shenzhen, while Venus Williams made a winning start to 2019.
Serena Williams said she did not want her mixed doubles clash with Roger Federer to end as she was "just warming up".
Sloane Stephens made a poor start to 2019, losing to the unseeded Johanna Konta in straight sets in Brisbane.
Andy Murray and Nick Kyrgios were among the winners at the Brisbane International on New Year's Day.
Andy Murray made an encouraging return against James Duckworth on New Year's Day, but says he is unsure how long his career will last.
Rafael Nadal just wants to remain healthy and happy in 2019, saying he was unfazed by the top ranking.
Andy Murray was too good for James Duckworth in the Brisbane International first round.