(Adds family statement, coastguard comments)
MILAN/LOS ROQUES, Venezuela Jan 7 (Reuters) - The family of missing Italian fashion boss Vittorio Missoni said on Monday they still believed he was alive, three days after his plane disappeared off the coast of Venezuela.
The small twin-engine aircraft carrying Missoni, 58, his wife Maurizia Castiglioni, another couple and two Venezuelan crew members went missing on Friday after taking off from the island resort of Los Roques.
"We are full of hope and confidence for the work that the authorities have done so far. We will not give up," Missoni's sister Angela wrote in an emailed statement to the media.
"We believe Vittorio, Maurizia, Elda and Guido are still alive!" Angela also wrote on Twitter. "Please help us find them and bring them back home."
Missoni, a sports lover known for his informal looks and charming smile, is the oldest son of the founders of the fashion house famous for its exuberantly coloured knits featuring bold stripes and zigzags.
He is the firm's co-owner with siblings Luca and Angela, who handle the technical and design sides of the firm.
Luca Missoni, who is also a pilot, was flying over the area to help with the rescue effort together with Alberto Piantoni, chief executive of the fashion house, Angela said.
Venezuelan rescue divers were searching the aircraft's last determined location, while searches also continue on the ground.
Captain Raul Rivas, Coast Guard Commander in Los Roques, said the son of a jewellery designer and owner of an international hotel chain was also believed to be on board alongside Missoni, his wife and their friends Elda Scalvenzi and Guido Foresti.
The pilot of a Cessna 402 that took off a minute after the Britten Norman BN2 carrying Missoni said he saw the plane as it disappeared into a cloud.
"I saw them right in front of me as they were swallowed up by a huge cumulus cloud," pilot Enrique Rada told Turin daily La Stampa in an interview published on Monday. "It was a lightning bolt. It must have been a lightning bolt."
However Rivas said the weather conditions were favourable when the aircraft disappeared.
"The sun was good at that moment and the atmospheric conditions couldn't have been a determining factor if the aircraft had a problem," the captain said.
The company said it would go ahead with a Milan fashion show on Jan. 13 but the family may not attend. Family-owned Missoni posted sales of 70 million euros ($91 million) in 2011. ($1 = 0.7666 euros) (Reporting by Jennifer Clark and Antonella Ciancio in Milan; Additional reporting by Javier Andres Rojas in Los Roques and Andrew Cawthorne in Caracas; Editing by Tom Pfeiffer)