The SNP leader admitted the word "national" could be "hugely problematic".
Hospital Mortality Rates Down 16.5%
A target for cutting hospital deaths in Scotland has not yet been met, according to the latest figures.
The Scottish Patient Safety Programme was established with the aim of reducing hospital mortality rates by 15% by December 2012, and then by 20% by the end of 2015.
The most recent figures show that by the period July to September 2015, the rate for Scotland as a whole had fallen by 16.5%.
Mortality rates have fallen in 26 of the 29 hospitals participating in the safety programme since the October to December period in 2007 when recording began, with nine showing a reduction of more than 20%.
These include NHS Ayrshire and Arran's Crosshouse Hospital (35.3%), NHS Lanarkshire's Monklands District General Hospital (25%) and NHS Tayside's Ninewells Hospital (21.6%).
The Scottish Government said hospital death rates are now at the lowest recorded level.
Health Secretary Shona Robison said: "It is encouraging to see that our commitment to patient safety across the health service is delivering such strong results, especially at a time when our NHS is treating more people, with more complex needs, than ever before.
"The 16.5% drop in mortality rates shows the high standards in Scotland's NHS and is one of the reasons Scotland is emerging as a world-leader in delivering effective and safe care for patients.
"Scotland was the first country in the world to implement a national patient safety programme and is the only UK country publishing and driving improvement in our NHS through the use of mortality data in this way.''
Professor Jason Leitch, clinical director for NHS Scotland, added: "Our NHS is working to deliver the safest possible hospitals we can for Scotland, and today's figures show we are continuing in the right direction.
"The vast majority of the thousands of patients who come through Scotland's NHS every day are cared for safely and successfully by our hard-working front line staff. Across our NHS, these staff have put patient safety at the heart of everything they do. And this culture is helping the NHS to be open and honest where care falls short of what we expect, and ensure we learn the right lessons.
"However, there is always more we can do. Patient safety will always remain a top priority for NHS Scotland and we will continue to deliver safe, person-centred care to thousands of people across Scotland every day of the year.''
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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