False positives/negatives and Bayes rule for COVID-19 testing

Why both false positives and false negatives are bad for the COVID-19 tests. Why Bayes rule is important for these situations.

What is a false positive/negative anyway?

A disease-screening medical test, like the one used to detect whether you are infected with the dreaded COVID-19 virus, essentially gives you a YES/NO answer. But, here are some questions to think about.

  • Would you trust the answer unequivocally?
  • Is the probability of a wrong answer higher for a positive result than a negative result?
  • What is the cost of a mistake for a wrong answer? Are the costs the same for a ‘YES’ answer vs. a ‘NO’ answer?
  • Is it better to get multiple tests done to increase the probability of getting a correct diagnosis? Does it make more sense for a ‘YES’ answer vs. a ‘NO’ answer?

In fact, no test is 100% accurate. You may have seen on the news that there is a wide variation of accuracy in the tests that are being rapidly developed and deployed for COVID-19. But, it turns out even the term ‘accuracy’ means a very specific thing when it comes to medical tests.

If you think about it, there are four distinct scenarios, for a particular test outcome, with respect to a specific person.

  • You may be really infected, and the test says ‘YES’. This is called a TRUE POSITIVE (TP).
  • You may not be infected, but still, the test says ‘YES’. This is called a FALSE POSITIVE (FP).
  • You may not be infected, and the test says ‘NO’. This is called a TRUE NEGATIVE (TN).
  • You may be really infected, but the test says ‘NO’. This is called a FALSE NEGATIVE (FN).

Now, from a personal point of view, I would be happy with the performance of the test, if it can just detect the ‘right condition’ for me. That means if it has high TP and high TN, it does the job for me, personally. It is not only about detecting a positive COVID-19 patient with a ‘YES’ verdict, but it is also about correctly saying ‘NO’ for a COVID-19 negative patient.

…it turns out even the simple term ‘accuracy’ means a very specific thing when it comes to medical tests.

The exact terminology can vary a little bit, but, in almost all cases, the ‘accuracy’ measure will denote how well the test is doing with respect to the sum of TP and TN as a percentage of the total tests administered.

But a high accuracy is not the only metric by which a test should be judged. Equally important are the other measures like FP and FN numbers.

Why?

Because out of the four situations, described above, only one leads to non-action with no consequence i.e. the TN case. In this situation, you, after being tested, will go back home, without taxing the healthcare system and any long-term health repercussions.

All of the other three situations have a varying degree of costs (societal, medical, economic, whatever you want to call them) associated with them. And the total cost to the state or nation may well depend on how the test is performing on those metrics.

It is not only about detecting a positive COVID-19 patient with a ‘YES’ verdict, but it is also about correctly saying ‘NO’ for a COVID-19 negative patient.

Case of TRUE NEGATIVE (TN)

Let us cover the least expensive one first — the case of TN. As stated above, in this situation, you, after being tested, will go back home, without taxing the healthcare system and any long-term health repercussions. The only cost is the emotional toll on you while you wait for the test to be administered and for the result to come out.

Case of TRUE POSITIVE (TP)

This is a personally dreaded scenario (but not the worst one!). You have been detected as a COVID-19 positive patient and now the ordeal starts. Depending on your exact health situation, and the criticality of the symptoms, you may be advised to self-quarantine or check into a hospital. The costs are of course different in these two alternative situations. One taxes you and your immediate family more, whereas another one taxes the healthcare system significantly.

But, at least, you got a correct assessment! There is a worse outcome, which is the next case.

Case of FALSE NEGATIVE (FN)

In the case of COVID-19, this is definitely the worst-case situation. A person, with the pathogen in his/her lungs, will go untreated. Depending on the underlying health conditions, and many other physiological parameters, the outcome is not necessarily a fatality, but surely this has higher personal and societal cost than the TP case. If this happens for someone in the high-risk cohort, then a tragic (and possibly avoidable) loss of life can ensue with a high enough possibility.

Case of FALSE POSITIVE (FP)

This is the most dreaded scenario for the medical system, patient, who, in reality, does not have the virus, is declared positive. The outcome can be of varying nature here. The person may be temporarily admitted into the healthcare system, thereby overloading the system and, more importantly, occupying extremely limited resources, which could have served a truly positive patient. If the person is sent back home, he/she goes through enormous emotional upheaval — for nothing — as he/she is really not infected.

But a high accuracy is not the only metric by which a test should be judged. Equally important are the other measures like FP and FN numbers.

Statisticians have been doing these for a long time

Essentially, this kind of YES/NO test falls under the so-called binary classification systems. Statisticians have been dealing with these systems for a long time and they call the same metrics by a different set of names — Type-I and Type-II errors.

They even have a fancy name for a tabular representation of all the scenarios we discussed, it is called ‘Confusion Matrix’ and it looks like following,

Image source: Wikipedia (Creative Commons license)

The recent resurgence of machine learning systems and algorithms, many of which use some form of binary (or multi-class) classifiers (e.g. logistic regression, decision tree, support vector machines, and neural networks) at their core, have made this confusion matrix popular. It is one of the most widely used metrics for judging the performance of an ML system.

The great feature of this matrix is that once it is produced, we can calculate a number of useful metrics from just the four numbers,

Image source: Wikipedia (Creative Commons license)
Image source: Wikipedia (Creative Commons license)

Characteristics and variations of the specific biomedical test (or of the software algorithm in case of an ML system) will result in different numbers for these metrics. You can simply assign different costs to each of these metrics and tune the test/algorithm to minimize the overall cost.

In the specific case of COVID-19, however, we would not venture into such an exercise. Cost-benefit analyses of such a life-altering, global pandemic should be left to experts and policy-makers at the highest level. As data science practitioners, you will be empowered to know that the same tools, that you use in your ML algorithms or statistical modeling, are utilized for measuring the success of mission-critical medical testing and public health systems.

We will, however, further discuss the utility of these measures for more advanced analysis of the test results using Bayesian probability inference.

Bayes’ rule for COVID-19 tests?

A statistical method of seeking a second opinion

Bayes’ theorem (alternatively Bayes’ law or Bayes’ rule) has been called the most powerful rule of probability and statistics. It describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

Bayes’ rule formula

It is a powerful law of probability that brings in the concept of ‘subjectivity’ or ‘the degree of belief’ into the cold, hard statistical modeling. It lets us begin with a hypothesis and a certain degree of belief in that hypothesis, based on domain expertise or prior knowledge. Thereafter, we gather data and update our initial beliefs. If the data support the hypothesis then the probability goes up, if it does not match, then probability goes down.

In the domain of medical testing, this continuous update methodology means, we are never satisfied with one set of tests. We can calculate the probability of a person being infected from the test data, repeat the test again, feed the result from the previous test to the same formula again, and update our probability.

This is just like seeing a second (or a third) opinion from a doctor about the diagnosis of a disease.

Cost-benefit analyses of such a life-altering, global pandemic should be left to experts and policy-makers at the highest level. As data science practitioners, you will be empowered to know that the same tools, that you use in your ML algorithms or statistical modeling, are utilized for measuring the success of mission-critical public health systems.

The knowledge of false positives/negatives are directly applicable

How do you declare a person COVID-19 positive? After you get a positive result from the test.

But, as we discussed, every test result is uncertain to some extent. So, we cannot actually say with 100% certainty that a person is COVID-19 positive, we can only say with high enough probability. Now, if we cast the testing process in terms of probability, here are a few quantities we can write,

P(COVID-19 positive| test = positive): This denotes the probability that the person is really COVID-19 positive given that the test result is positive. It is called a conditional probability expression. We want to calculate this. Now, if you look at the Bayes’ rule formula above, you will recognize it to be equivalent to the posterior expression P(A|B).

P(test = positive|COVID-19 positive): This is the prior P(B|A) in the Bayes’ rule. This is nothing but sensitivity i.e. how many true positives (test results) are there among all the positive cases (in reality).

P(COVID-19 positive): This is the probability of a random person having been infected by the COVID-19 virus. In the domain of medical testing, this is called the ‘prevalence rate’. This is the piece of the information that is not test-specific but needs domain knowledge or broader statistical measure. For COVID-19, experts may say, after pouring over a lot of data from all over the world that the general prevalence rate is 0.1% i.e. 1 out of 1000 people may be infected with the virus. Of course, this number can change based on the country, health system, active social distancing measure, etc. This term appears in the numerator of the Bayes’ rule ( P(A) in the Bayes’ rule).

P(test=positive): This is the denominator in the Bayes’ rule equation i.e. P(B). This can be calculated as,

P(test=positive) = P(test=positive|COVID-19 positive)*P(COVID-19 positive)+P(test=positive|COVID-19 negative)*P(COVID-19 negative)

Clearly, this calculation takes into account the fact that we can get a positive test result both for a truly infected person or a FALSE POSITIVE for a non-infected person. The term P(test=positive|COVID-19 negative) is simply the FALSE POSITIVE rate calculated from the confusion matrix. The term P(test=positive|COVID-19 positive) is the sensitivity as appearing in the numerator (discussed above).

Therefore, we can see that all the characteristics of a medical test can be readily utilized in a Bayesian calculation.

But there is more to the Bayesian statistics than this!

It lets us begin with a hypothesis and a certain degree of belief in that hypothesis, based on domain expertise or prior knowledge. Thereafter, we gather data and update our initial beliefs. If the data support the hypothesis then the probability goes up, if it does not match, then probability goes down.

Chaining Bayes’ rule

The best thing about Bayesian inference is the ability to use prior knowledge in the form of a Prior probability term in the numerator of the Bayes’ theorem.

In this setting of COVID-19 testing, the prior knowledge is nothing but the computed probability of a test which is then fed back to the next test.

That means, for these cases, where the prevalence rate in the general population is low, one way to increase confidence in the test result is to prescribe subsequent test, if the first test result is positive, and apply chained Bayes computation.

A step-by-step example

Look at the following article to understand the same process in the context of a drug screening, which is exactly equivalent to the COVID-19 testing. This article goes through a numerical example and plots and charts to make the calculations clear and shows clearly how the characteristics of a particular test can impact the overall confidence in the test result.Bayes’ rule with a simple and practical exampleWe demonstrate simple yet practical examples of the application of the Bayes’ rule with Python code.towardsdatascience.com

That means, for these cases, where the prevalence rate in the general population is low, one way to increase confidence in the test result is to prescribe subsequent test, if the first test result is positive, and apply chained Bayes computation.

Summary

The greatest global crisis since World War II and the largest global pandemic since the 1918–19 Spanish Flu is upon us today. Everybody is looking at the daily rise of the death toll and the rapid, exponential spread of this novel strain of the virus.

Data scientists, like so many people from all other walks of life, may also be feeling anxious. It may be somewhat reassuring to know that the familiar tools of data science and statistical modeling are very much relevant for analyzing the critical testing and disease-related data.

The goal of this article was to give an overview of some of the basic concepts in this regard. When you see a discussion about COVID-19 testing and its accuracy, you should be asking these questions and judge the result in light of data-driven rationality.

Medical professionals and epidemiologists work with this kind of analysis all the time. It is time that we also share this knowledge and understanding as much as we can and apply it rightly for discussion or decision-making.

Stay safe, everybody!

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The economic effects of COVID-19 around the world

Latest developments:

  • China’s factory output posts sharpest plunge in three decades in Jan-Feb.
  • Unprecedented Federal Reserve move fails to calm markets.
  • US share trading halted; market falls 9% on Monday.
  • Spain, France follow Italy in imposing severe restrictions on movement.

Previous headlines:

  • UNCTAD warns of a $1 trillion cost to the world economy.
  • Cryptocurrencies plunge.
  • Italy’s entire population under quarantine measures.
  • Some key industries in Wuhan are told they can resume work.

Have you read?

As the world grapples with the coronavirus, the economic impact is mounting – with the OECD warning the virus presents the biggest danger to the global economy since the 2008 financial crisis.

UNCTAD, the UN trade agency, warned of a slowdown of global growth to under 2% this year, effectively wiping $1 trillion off the value of the world economy.

poll of economists by the London School of Economics found 51% believed the world faces a major recession, even if COVID-19 kills no more people than seasonal flu. Only 5% said they did not think it would.

There are now some 170,000 confirmed cases of COVID-19 globally, the new coronavirus that emerged in Wuhan, China, in December and is spreading around the world.

Businesses are dealing with lost revenue and disrupted supply chains due to China’s factory shutdowns. Weeks after China imposed travel restrictions on million of its people, Italy placed quarantine measures on its entire population, with France and Spain imposing similar measures and many other European countries restricting movement and business activity. On 11 March, some key industries in Wuhan were told they can resume, a day after Chinese President Xi Jinping visited the city for the first time since the outbreak began.

Here are a few ways the outbreak is sending ripples around the world.

Predicted slump

China is the world’s second-largest economy and leading trading nation, so economic fallout from COVID-19 also threatens global growth.

Economists polled by Reuters on March 3-5 said the outbreak likely halved China’s economic growth in the current quarter compared with the previous three months.

The poll of more than 40 economists, based both in and outside mainland China, forecast growth to fall to a median of 3.5% this quarter from 6.0% in the fourth quarter of 2019, a full percentage point lower than predicted in a Feb. 14 poll.

“If you’re in a city which has been basically closed down or put (under) virtual house arrest, you’re not going to go out to the streets, you can’t go to the cinema, the restaurants…with all those sorts of things, economic activity will be substantially negatively affected,” said Rob Carnell, head of Asia-Pacific research at ING.

The Chinese economy is likely to be hit further by reduced global demand for its products due to the effect of the outbreak on economies around the world.

Data released on 16 March showed China’s factory production plunged at the sharpest pace in three decades in the first two months of the year – something which could mean an even greater economic slowdown than predicted in that poll.

“Judging by the data, the shock to China’s economic activity from the coronavirus epidemic is greater than the (2008) global financial crisis,” said Zhang Yi, chief economist at Zhonghai Shengrong Capital Management.

“These data suggest a small contraction in the first-quarter economy is a high probability event. Government policies would need to be focused on preventing large-scale bankruptcies and unemployment.”

Falling oil, stock prices; central bank action fails to calm markets

To combat the economic fallout, the US Federal Reserve on 15 March cut its key interest rate to near zero.

But the move, coordinated with central banks in Japan, Australia and New Zealand in a joint-effort not seen since the 2008 financial crisis, failed to shore up global investor sentiment, with oil prices dipping below $30 a barrel on 16 March, and a 9% slump in share values when Wall Street opened.

China is the world’s biggest oil importer. With coronavirus hitting manufacturing and travel, the Internationa Energy Agency (IEA) predicted the first drop in global oil demand in a decade.

“Covid-19 (coronavirus) has spread beyond China and our 2020 base case global oil demand forecast is cut by 1.1 mb/d. For the first time since 2009, demand is expected to fall year-on-year, by 90 kb/d,” the IEA said in its monthly report for March 2020.

On 9 March, oil prices lost as much as a third of their value – the biggest daily rout since the 1991 Gulf War, as Saudi Arabia and Russia signaled they would hike output in a market already awash with crude, after their three-year supply pact collapsed.

“A WHO declaration of global emergency and U.S.-EU traffic ban is dampening the global energy demand outlook, in conjunction with an intensified price war between Saudi and Russia,” Margaret Yang, market analyst at CMC Markets in Singapore, told Reuters.

“Bears are dominating the oil market and there might be more downside before a bottom can be reached.”

Anyone hoping cryptocurrencies might prove a safe haven was disappointed. Bitcoin lost more than 30% of its value in the five days to 12 March, Reuters reported, outpacing losses for stocks and oil.

“We’ve seen de-risking across all asset markets,” said Jamie Farquhar, portfolio manager at London-based crypto firm NKB. “Bitcoin is certainly not immune to that.”

Impact on air travel

On 5 March – before the US travel ban was announced – the International Air Transport Association (IATA) predictied the COVID-19 outbreak could cost airlines $113 billion in lost revenue as fewer people take flights.

“The industry remains very fragile,” Brian Pearce, the IATA’s chief economist, told the Associated Press. “There are lots of airlines that have got relatively narrow profit margins and lots of debt and this could send some into a very difficult situation.”

On March 16, British Airways said it would cut flying capacity by at least 75% in April and May. Other UK airlines, including Virgin Atlantic and easyJet also announced drastic cuts.

Disruption to commerce

The shortage of products and parts from China is affecting companies around the world, as factories delayed opening after the Lunar New Year and workers stayed home to help reduce the spread of the virus.

Apple’s manufacturing partner in China, Foxconn, is facing a production delay. Some carmakers including Nissan and Hyundai temporarily closed factories outside China because they couldn’t get parts.

The pharmaceutical industry is also bracing for disruption to global production.

Many trade shows, cultural and sporting events across the world have been cancelled or postponed.

The travel and tourism industries were hit early on by economic disruption from the outbreak.

Besides the impact on airlines, the UN’s International Civil Aviation Organization (ICAO) forecasts that Japan could lose $1.29 billion of tourism revenue in the first quarter due to the drop in Chinese travellers, while Thailand could lose $1.15 billion.

iOS 14

iOS 14 rumors and features

Leaked iOS 14 code obtained by 9to5Mac gives us clues about many details with what to expect from Apple’s upcoming hardware refreshes, including a new iPad Pro, iPhone 9, and AirTags. Apple is also developing a new Apple TV remote. https://youtu.be/hbzNC3DmU6Q

Lastly, iOS 14 code offers new details on Apple’s upcoming AirTag item trackers. 9to5Mac has previously reported many details on AirTags, including the marketing name. iOS 14 code indicates that AirTags will be able to be set up in bulk through iOS and that there will be a user-replaceable battery, much like Tile item trackers.

Augmented Reality

We’ve also learned that Apple is developing a new augmented reality app for iOS.

Based on 9to5Mac code findings, Apple appears to be testing integrations with Apple Stores and Starbucks. For instance, users would be able to hold up their phone in an Apple Store and view information about the products on display, get pricing, and compare features.

The iPhone or iPad would know about what augmented reality experience to begin based on QR-code like tags in the area. It is possible that iBeacons or Apple’s AirTags could also act as the trigger.

Home Screen

iOS 14 will also include a new home screen list view option with Siri suggestions.

Furthermore, the list view will include several different sorting options and other details. For instance, you’ll be able to filter applications such that you see all apps that currently have unread notifications. There will also be support for filtering apps by recently used, giving you better awareness of the apps you use most and least often.

Finally, this new list view will include smart suggestions powered by Siri to suggest which applications you might be searching for based on time of day and location. For instance, the list view might recommend that you open the Music app when you arrive at the gym.

Accessibility

iOS 14 will also include a number of new accessibility features as well.

iOS 14 looks set to offer some major new accessibility improvements. Our code findings uncovered a new feature that will be able to detect important sounds like fire alarms, sirens, door knocks, doorbells, and crying babies. Presumably, iOS will translate these alerts into haptics for people who have hearing loss.

iOS 14 release date and beta schedule

If past years are any indication, a new version of iOS (iOS 14) will be released in the fall of 2020. It’s expected that a developer beta will be released in June at WWDC ’20. A public beta is also likely to follow a few weeks after the release of the developer beta.

Once Apple starts the beta program for iOS 14, it’s expected they will release updates every few weeks to eliminate bugs, polish new features, remove features that won’t make the shipping version, and more.

As always, Apple recommends that you only run the developer beta version of iOS on devices solely dedicated to development.

iOS 14 compatible devices

iOS 13 was compatible with

  • iPhone XS
  • iPhone XS Max
  • iPhone XR
  • iPhone X
  • iPhone 8
  • iPhone 8 Plus
  • iPhone 7
  • iPhone 7 Plus
  • iPhone 6s
  • iPhone 6s Plus
  • iPhone SE
  • iPod touch (7th generation)

With iOS 14, it’s expected that Apple will drop support for at least the iPhone SE, but don’t be surprised if the iPhone 6s and 6s Plus also drop support.

Mockups imagine what the leaked iOS 14 home screen changes will look like

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As 9to5Mac reported on Tuesday, iOS 14 code indicates that Apple is working on changes to the iPhone home screen, including a new list view.

Instead of just the grid of app icons, there will be a new page or new mode so users can look at their apps in a top-to-bottom scrolling list. Now, some intrepid readers have made mockups of what that might look like.

Apple has traditionally not changed the home screen on iOS very much. The grid of apps is tried and tested, familiar to users, and dates all the way back to the original iPhone.

However, Apple has expanded the metaphor slightly over the years, like adding app folders with iOS 4 and redesigning the ‘page zero’ Spotlight screen to include Siri suggestions and widgets. In 2019, iPadOS 13 integrated the widget sidebar with the first home screen.

The changes expected to debut with iOS 14 are less a redesign and more an addition to what we already have. You can imagine some way to toggle between views (similar to the list view toggle on the Apple Watch) or simply swiping across to a new home screen page, which contains the list view.

Parker Ortolani mocked up what that screen could look like in his renders. A simple segmented control lets the user switch from seeing all apps A-Z, to apps sorted by recently used, and then only those with notifications that need attention. The Spotlight search field is on-screen ready to filter down the list. Ortolani also visualized how folders could be presented in the list, with an option to expand and see the apps inside.

You can see how a home screen page dedicated to apps with unread notifications could be very useful. 9to5Mac reported that the list view would combine an alphabetized list of installed apps with Siri suggestions. You can see in Ortolani’s mockup how the Workout app is being recommended based on current location, emphasized with a darker background appearance.

Another twist on this design can be seen in the mockups by iSpazio.net, again inspired by the 9to5Mac report. In this version, it feels closer to the watchOS approach — with a permanent mode toggle at the top of the screen. Users could tap on the list and grid icons to switch the home screen to those respective layouts.

iSpazio also imagined how Apple could make the list item for each app more useful, by providing a summary description for each item about why the user should open it. For instance, the Messages app is labeled ‘2 new Messages to read’, the Calendar app shows the next calendar event inline, and the Photos apps prompts the user to open it and look at significant Moments. These features could be enabled through iOS 14 extensions to the Siri suggestions and notifications APIs.

This week, 9to5Mac obtained iOS 14 internal source code and reported on a plethora of features in development at Apple from environmental noise alerts to a new wallpaper experience, new HomeKit features including Night Shift for smart lights, a new augmented reality app, and much more. Ortolani mocked up many of these features in this Twitter thread if you want to get a sense of how these iOS 14 features might come to fruition.

iOS 14 is expected to be announced in June, alongside previews of other major Apple software operating systems like watchOS 7 and macOS 10.16. This would usually happen on the WWDC keynote stage.

However due to the coronavirus outbreak, gatherings and conferences have been canceled across the industry and Apple is not expected to be holding a physical WWDC this year — although the company has yet to confirm its plans. We would expect a small scale media-only event in June to announce the new operating systems like iOS 14, with the developer sessions of WWDC simply streamed live online.

Stay tuned to 9to5Mac for more iOS 14 news soon!

Stunning iPhone 12 design video shows Apple’s new leaked color

  • Apple’s iPhone 12 will feature a major redesign, marking the first time in three years that Apple will release a new iPhone model with an updated design.
  • Both the iPhone 12 and iPhone 12 Pro models Apple releases in 2020 will feature a new look with flat metal edges reminiscent of the iPhone 5’s beloved design.
  • The higher-end iPhone 12 Pro and iPhone 12 Pro Max are expected to be made available in a totally new color that leaked recently, and now a new video imagines Apple’s upcoming new iPhone 12 Pro in the stunning new color.

When it comes to Apple’s iPhone 12 release and its iPhone 9 release that was expected in the coming weeks, everything seems to be up in the air right now. A report just yesterday suggested that Apple will completely cancel its iPhone 9 release next month not because of manufacturing issues, but because the company doesn’t want to encourage people to gather en masse at its stores in light of the novel corona virus outbreak. As a reminder, the iPhone 9 is also referred to as “iPhone SE 2,” and it’s expected to be a lower-cost iPhone starting at $399 that uses the iPhone 8’s design with updated specs in line with the iPhone 11.

As far as Apple’s new flagship iPhone 12 and iPhone 12 Pro are concerned, things are even more unclear right now. Numerous reports suggest that the COVID-19 outbreak will force Apple to delay its iPhone 12 release until October or possibly November, though the company still might announce the phones in September. That doesn’t sound too terrible, but there’s one slight problem: many experts believe that the corona virus outbreak will continue to get worse and worse in the coming months. If it does, there’s no telling what might happen to Apple’s plans for the iPhone 12. As of Thursday morning, there are more than 120,000 confirmed cases of the COVID-19 corona virus and the spread isn’t expected to slow down anytime soon. Regardless of when Apple finally releases its iPhone 12 lineup, however, we already know plenty about the new design and features thanks to numerous leaks from reliable sources. Now, a new video helps visualize everything we’ve heard, and it also shows Apple’s new iPhone 12 Pro in the stunning new color that leaked earlier this year.

Most of what we know so far about Apple’s upcoming iPhone 12 and iPhone 12 Pro series smartphones comes from TF International Securities analyst Ming-Chi Kuo. He has been the most prolific and most accurate Apple insider for years, and he’s had plenty to say about the iPhone 12 series since even before the iPhone 11 was released.

According to Kuo’s reporting, Apple will release not three but four new flagship models this year. Two will be iPhone 12 models with different screen sizes, and then there will be a 6.1-inch iPhone 12 Pro and a 6.7-inch iPhone 12 Pro Max. All four phones will apparently feature OLED screens and 5G support, while the iPhone 12 Pro phones will get upgraded triple-lens rear camera systems with a new time of flight (ToF) sensor.

more recent iPhone 12 leak from a new source that has been active recently suggests that Apple’s upcoming new iPhone 12 models will get an even bigger camera upgrade than we thought. That leak also outlined some alleged new features and upgrades supposedly coming to Apple’s new iPhones, but the same source also had some interesting iPhone 12 tidbits to share back in January.

In the earlier leak, Max Weinbach claimed that Apple is planning to release the iPhone 12 Pro in an exciting new color that will replace Midnight Green in Apple’s current iPhone 11 Pro lineup. The new color is supposedly called Midnight Blue, and it will reportedly be a deep navy blue color that will be made available alongside Space Gray, Silver, and Gold. Deep navy blue sounds far more appealing than the dark green color that’s currently available, and now a new video created by YouTube channel Technizo attempts to visualize the iPhone 12 Pro in the stunning new color.

The majority of the video shows Apple’s leaked iPhone 12 Pro design in Space Gray, and it’s pretty close to what we expect to see later this year when Apple officially takes the wraps off of the iPhone 12 Pro. The one big mistake with this video is the same mistake we’ve seen in countless other iPhone 12 Pro visualizations — Apple’s new Pro models will have a triple-lens rear camera with an additional small ToF sensor added in. These renders, on the other hand, show a quad-lens camera.

The Midnight Blue iPhone 12 Pro makes its first appearance around the 53-second mark, and the hue shown in the video looks like it could indeed be pretty close to the real thing. We won’t know for certain until Apple unveils the iPhone 12 and iPhone 12 Pro this coming September, but you can check out the video below to tide you over in the meantime.

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