The Antlers keep being told that their new concept album, about a dying woman, is a life-changer. But how much of an ordeal did they go through themselves

The Hanbury Ballroom in Brighton was built in 1892 as a mausoleum for the Sassoon family. There's something fitting, then, in the subject matter chosen by the band playing to the packed crowd, happily jostling at the bar. The Antlers, from New York, are singing about a skeletal girl succumbing to terminal illness.

The subject is deeply personal to the band's singer, Peter Silberman, even if it is not literal. But he doesn't mind that it seems to have become seized on by people claiming it as their own. "The more it becomes theirs, the easier it is to continue on with and move forward," he says. "It's not the kind of thing I'd want to hold on to. A lot of people have approached us with stories of their own experiences when this album has either reminded them of something, or helped them get through something. Or maybe even made something harder to deal with. The fact that they're relating to it at all is something I'm happy about."

The songs the Antlers are performing in Brighton come from their debut album, Hospice. To the sound of emotive rock, with windy echoes of Arcade Fire and Neutral Milk Hotel, Silberman sings the story of a boy who feels obliged to stay with his abusive girlfriend when she starts to die of bone cancer. The songs run through the fallout: there's an abortion (Bear); raging arguments (Sylvia); the resignation of death and defeat (Two) and the death itself (Shiva), as the girl's monitors beep for the last time. It climaxes with the realisation that the passing is ultimately an act of catharsis. "Some people can't be saved," muses one of the last lines. The epic tone of the music offsets the lyrics, enabling the album to be both deeply personal yet also vague enough to mean different things to different people.

It's not really about cancer, though: the illness is a metaphor for bad love. Yet its strength derives from the fact that it rings absolutely, heartbreakingly true as a document of the disease, with descriptions so vivid ("those singing morphine alarms out of tune") that it's easy to imagine people mourning to it. And it's been written by a 23-year-old from an affluent background, who manages to engage with the subject without ever sounding self-pitying.

"Without going too specific, I think of it as the story of a relationship, being told through the metaphor of the hospital with two characters within it," Silberman says. "There's the patient and the caregiver and at the same time, there's all the people who have been shut out of the hospital. It's the disintegration of that dysfunctional relationship. It's rediscovering the importance of independence and standing up for yourself."

But such a personal work surely creates room for confusion about what is fiction and what is fact. "It's one thing if people decide the record is about something," he says. "It's another if they decide its something about my life. That's the only part I get uncomfortable about – if someone were to say matter-of-factly, 'So this record is about your dead girlfriend.' It's important to separate the person from what they're making."

Nevertheless, Hospice is like a first novel, in that – regardless of how true to his life it is – there is evidently a lot of Silberman in Hospice. It's even a novelistic album (unsurprisingly, given that his mother is a writer), similar in some ways to Sylvia Plath's The Bell Jar. Where that was about a troubled young girl from Massachusetts struggling to fit into New York life, Hospice was written after Silberman moved left Skidmore College, near Saratoga Springs in upstate New York, to move to the city. Compounding the apparent link, Hospice features a song called Sylvia with a chorus that runs: "Get your head out of the oven."

But there is no link. "I haven't actually read The Bell Jar," Silberman says. Oh. However, there is some Plath in there: "I was interested in how she's this antihero for so many young women who identify with her for better or for worse. It seems to be this very common touchstone."

The Sylvia that song refers to is actually Leonard Michaels's novel Sylvia, a fictionalised version of his relationship with his wife. Like Hospice, it told the story of a Manhattan couple descending into self-destructive violence and then suicide. "The end of that book hit really hard," Silberman told a US blog this year. "The last page of it is what inspired the song Epilogue, this sort of being haunted while trying to sleep by this thing from the past."

There was much romanticised speculation around the album on its release last year, based around the notion that – like a writer retreating to some fastness to purge his soul – Silberman had become an apartment-bound recluse while he made the record. But, he says, that wasn't exactly what happened.

"It was with the first announcement about the record and that's just … fucked us ever since," he sighs, just about managing not to roll his eyes.

So he left the house once or twice then? "It's not that it's not true, it's more that it's misconceived. It's that Bon Iver thing of going into the woods and making a record … going into a cabin and writing a book. It's not that. The record is about an isolating relationship between two people and how the outside world becomes cut off from that and how they become cut off from people they know and people they care about. That's what this is about, that's what the record is about. Again, it's not about me. It's not about me needing to withdraw or any self-imposed seclusion. I understand the confusion but I feel like I've repeated it and explained it so many times that it's pointless. It's a backstory, but it's not the right backstory."

Backstory aside, Hospice is notable for being a complete conceptual work, like its most obvious predecessor, In the Aeroplane Over the Sea by Neutral Milk Hotel, which tells a magical realist version of Anne Frank's story. Is there still space for people to make records as complete works?

"That's going to go down to the kind of albums that people choose to make. The iTunes model [of buying individual songs] makes it easier for a record to become popular very quickly, but I don't think it necessarily gives you that longevity. I'd prefer to make something that exists as a whole, even if it's not necessarily a narrative piece. I have a hard time going 'song, song, song, song' and then seeing what makes sense together. A lot of people just write songs and when they have 10 of them go, 'Well, this is an album now.' I think it's important to give thought about what belongs together."

The trouble with touring the album relentlessly – and doing interviews like this one – is that the magic of such a personal record might be reduced every time the band have to talk about it. After NMH's final gig in support of In the Aeroplane … their leader, Jeff Mangum, more or less disappeared from public view. He had, apparently, tired of people who felt his album had altered their lives and wanted him to explain it to them.

Has Silberman had enough of explaining? "No," he says, surprisingly. "The only thing that's weird about it is that it feels like it's a record I wrote when I was much younger, even though I wasn't that much younger. I started on it record when I was 21, but it feels like a lot longer ago. I feel like I've moved forward from it, but it doesn't mean I don't care about it any more."

It's a good job, because he's probably going to be talking about it for a long, long time.

Hospice is out now on French Kiss. The Antlers play the Scala, London, on 19 May, then touring