Q:

Are the first solo flights by a student pilot more dangerous?

The first solo flight is a nail-biting moment, not only for the student pilot, but also for the flight instructor who's sending him off.  In theory not having a CFI reduces the margin of safety compared to flights with an instructor (at the same point in a student's training).  I've also heard stories about mistakes and even crashes on first solo flights, and according to "Crashes of instructional flights" by Baker, Lamb, Li, and Dodd, solo flights account for about half of instructional flight crashes.
Yet even though the biggest safety measure- a CFI- is gone, are these student solo flights really more dangerous?  Are there any studies on accident rate among low time GA pilots vs (solo) students?  Also, are incidents more common in the first solo flights than at other parts of a student's pilot training? 

A:

There is no evidence to back the claim that the first solo ride of the student is more dangerous compared to the later ones.
US NIH conducted a study on the accidents with solo pilots, which doesn't indicate that first-time solo fliers are any more prone to accident than others. Aircraft accidents with student pilots flying solo: analysis of 390 cases by  Sjir Uitdewilligen and Alexander Johan de Voogt analyzed NTSB probable cause reports of 390 crashes that occurred in the period 2001 – 2005, concluding that,

Student pilots flying solo show fewer injuries and fatalities compared to general instructional flights while in our sample first-time solo student pilots did not feature any fatalities.

Note that this gives only the injuries and not the times the students got into accidents per se. Out of a total of 3811 accidents involving student pilots, 390 occurred while they were flying solo and around 50 involved first-time student solo pilots. Actually, student pilots themselves are prone to less accidents compared to others. From Comparative Analysis of Accident and Non-Accident Pilots by David C. Ison:

Most accidents (49.1%) were conducted with individuals holding a private pilot certificate. Second in incidence were commercial pilots (28.2%), followed by Airline Transport Pilots (ATPs) (13.7%), and student pilots (5.7%)
Considering that 20% of pilots hold a student certificate, these individuals have a disproportionally low accident occurrence.

The report also gives some additional insight into the reason the first-time solo fliers have lesser injuries:

... first-time solo pilots are commonly confined to the airport and practice their takeoff and landings. Such operations may result in accidents, but they will occur near to the ground with a lower risk of a fatality

The report also gives some data about higher experienced student pilots sustaining more injuries, though nothing conclusive, noting that,

... in 25 cases, student pilots were reported to have more than 100 and up to 322 h of flight experience. In the dataset, these pilots were significantly more often injured than students with less hours of flight experience.

It has to be noted that as the hours logged gets more, the students get into more demanding flights which may be reason for this increase in injuries.

A:

I couldn't find any analysis of first solo flights, but based on NTSB accident reports it looks like accidents are very rare. There are only 60 reports of fatal part 91 (GA) accidents with the words "first solo" in the report, and 492 non-fatal accidents. But many of those are false positives anyway, because they include reports with things like "with his first solo occurring about a month prior to the accident", so the real numbers are lower.
Training flights in general are very safe compared to other flights. In 2015, student pilots accounted for only 6.5% of non-commercial fixed-wing GA accidents. That's much lower than private (47.1%), commercial (26.6%) and even ATP (12.2%) certificate holders.
AOPA has a detailed report called Accidents During Flight Instruction that comments on student solo flight in general, but not on first solos specifically. It says:

Two-thirds of all fixed-wing training accidents come during primary
  instruction, and two-thirds of those are during the relatively few
  hours of solo flight by student pilots. However, fatalities on student
  solos are extremely rare.

And it does give some information about your question on first solos vs. other phases of instruction:

Two-thirds of all fatal fixed-wing accidents occurred during advanced
  instruction, less than half of them while pursuing a specific
  certificate, rating, or endorsement. Transition training, flight
  reviews, generic refresher training, and specialized instruction in
  areas such as mountain flying, aerobatics, and cropdusting
  collectively accounted for over 60 percent of all advanced dual
  accidents, including more than half the fatal accidents.

Other people have already commented on why student solo flights in general are relatively safe: the student is primed with plenty of recent training and instructor feedback, and the flight conditions are well controlled. 

A:

No.
Anytime you get on a car or airplane or any mode of transportation, it is dangerous. Yet most of those journeys end without any incident.
First solo is a very short flight, mostly of a few circuits of the traffic pattern. The instructor is watching and talking to the student. The student is well trained at that point and literally know what they are doing.
I think Simon's comment is very important and needs to be remembered, most accidents can happen when confidence and ego can outweigh wisdom and learning.
You should also notice that most of student's flying occur in VMC or better conditions. This includes both first solos and checkrides. Being the pilot in command, you can cancel the flight if you think any condition is not suitable.

