At First Minister’s Questions on Thursday, Mr Carlaw asked Ms Sturgeon how she would characterise her legal guarantee to treat people within 12 weeks being missed in a quarter of all cases.
The Treatment Time Guarantee was introduced by the First Minister in her previous role as Health Secretary in 2012.
Official figures for the last three months of 2018 indicate that across Scotland, 72.7% of people waiting for either inpatient or day treatment received it within 12 weeks - down from 80% in October to December 2017.
The First Minister responded to Mr Carlaw by indicating that the Scottish Government was investing “record sums” in the NHS and had pledged £850 million towards the Waiting Time Improvement Plan.
Ms Sturgeon said “I regret the fact that there are people who are not being treated within the Treatment Time Guarantee, but I would also remind Jackson Carlaw that since that guarantee was introduced, over 1.7 million patients received their treatment within the required timeframe - patients who perhaps would not have been treated within the 12 week timeframe had that guarantee not been in place”.
Mr Carlaw said: “Well frankly, the First Minister missing her legal guarantee in one in every four cases is surely an unqualified failure.”
The Scottish Conservative interim leader added that following a recruitment drive for radiologists set out by the-then Health Secretary Shona Robison last year, only five staff had been recruited.
“Why should we have any faith in this government’s promises now when we know previous, much-hyped promises have flopped?”, he said.
Ms Sturgeon said that radiology has been experiencing acute shortages worldwide and not just in Scotland.
“That is why we have increased training places in Scotland and it’s why we are acting to improve recruitment,” she said.
“It’s also worth noting that since this government took office, consultant radiologists have increased by 45.4% and by 2022 we’ll have increased specialty training places in radiology by approximately 75% from 2014 levels.
“The international radiology recruitment campaign, launched in 2018, generated interest from clinicians around the globe and health boards are now finalising a number of offers of appointment.”
Scottish Liberal Democrat leader Willie Rennie said: “It’s been eight years since this law was passed and it’s been eight years of excuses... it seems the longer that people have to wait, the bigger the excuse from the First Minister.
“Nicola Sturgeon told us her patients’ rights law was the way to cut waiting times but it is just flim flam.
“Tricking patients doesn’t get them treated any quicker. The law is broken 200 times every day. 13,000 were waiting - now it’s 18,000.”
Scottish Labour’s health spokeswoman Monica Lennon said: “This is a striking admission from Nicola Sturgeon, who has brought in a new Health Secretary to oversee a new waiting times plan, and it will hardly fill NHS staff with confidence.
“The reality is, there has been too much complacency from the Scottish Government on NHS performance, setting NHS staff targets and then not delivering the support and resources needed to deliver them.
“Nicola Sturgeon’s uncharacteristic straight answer reveals a lot about the condition of our health service.”