Governmental officials worldwide are currently evaluating exit strategies to end or reduce present restrictions on social interactions limiting the spread of SARS-CoV-2, the virus that causes covid-19. Governments must balance competing priorities; restrictions lower the risk of infection, but harm the economy and other aspects of health. 

A key challenge is that governments must relax restrictions as early as possible, but have limited evidence on how this will affect the transmission of SARS-CoV-2. Lifting the lockdown too early will lead to a second wave of infection and deaths, requiring a return to a policy of physical distancing. Few governments have faced a comparable decision since the 1918 influenza pandemic. Policy changes on physical distancing evolve rapidly and differ by country, so governments will find it hard to learn from the experiences of other countries. 

We propose a strategy where governments relax lockdown gradually, in a way that would both provide evidence on whether continued lockdown is needed, and ensure that the risks of infection are minimised and distributed fairly across society. A way to achieve this is alternating lifting restrictions for a limited period (for example, one day) on only half of the population at any one time. Such a policy could be implemented via an odds-and-evens policy based on house number. Government would alternate maintaining and relaxing stay-at-home orders between odd-and-even households. Governments could adapt policy for people without homes or with addresses without numbers.

Each group (odd or even) would be exposed to SARS-CoV-2 at different times, and analysing the average timing of infection would help understand the risks associated with relaxing lockdown. Governments could obtain robust evidence from a controlled experiment and then decide if lockdown should be lifted or continue.

Odd-and-evens polices have been used before. To reduce air pollution, many highly polluted cities (for example, Bogota and Beijing) have implemented odds-and-evens systems for car number plates restricting use to certain days. Importantly, to help control covid-19 several countries in South and Central America, for example, Panama and Peru, have adopted a gender-based approach to easing restrictions with men and women let out on alternate days. Others, such as Costa Rica, bases restrictions on car number plates, while Bolivia permits people out once weekly on Monday through Friday based on the last digit of the national ID number.

This policy would reduce the level and duration of population mixing compared with total relaxation of current policies. Rather than basing restrictions on individuals, using house numbers has the advantage of being applied to people living together and thereby reduces the risk of transmission within the household. An odds-and-evens policy would minimise harm, in line with the principle of non‐maleficence, a fundamental ethical principle that underlies public health policies and experiments. Relaxing restrictions would likely generate economic benefits by facilitating the opening of shops, businesses and schools. 

Relaxing restrictions on an odds-and-evens basis is a form of alternative allocation and one of the oldest methods of conducting controlled experiments. The Cochrane Collaboration defines this as a form of quasi-randomisation. Such an experiment has a cross-over design in that the restrictions on each group are lifted alternately. With large numbers, even short alternating periods such as a day should enable policy makers to detect a ‘saw-tooth’ pattern in health outcomes. Quasi-randomisation means that the proportion with previous infection, and risk factors for infection and its complications should be equal by group at onset; in addition, the same proportion of essential workers would be exempt from this policy.  

Patients’ addresses are routinely collected in almost all health care settings and recorded on death certificates. Most covid-19 cases could therefore be assigned to odd-and-even groups using routine data without identifying patients. It should be possible to set up systems rapidly to update analyses on a daily basis. Because the median incubation period is estimated to be five days, with first medical consultation taking place on average two days later, and hospitalisation five days later, results could be available in days.  Testing for covid would align with government policy; again, there is no reason to believe that testing would differ by and odd or even house number.  

Governments might also consider cycling lock-down over longer periods, for example, alternate weeks. Longer cycles increase the ability to attribute infection to exposure and may mean people are at home while most infectious, thereby reducing transmission. Balanced against these advantages are the ethical considerations of exposing one group to a potentially harmful policy for longer. Economic impacts may differ: in some instances it might be beneficial to have the same staff in the office or factory throughout the week to enable them to complete tasks. The design of the experiment could vary across or within countries and over time. Government may wish to pre-specify stopping criteria.

Implementing a controlled policy experiment would bring challenges, not least since some people would choose not to obey the rules. Cautious individuals may opt to continue physical isolation even on days when policy permits them to leave their homes. However, people living in even- and odd-numbered homes are likely to be equally adherent, so would not bias the results of the experiment. 

Governments are facing unprecedented decisions. An experimental transition period would signal to the public that the threat of covid-19 remains, and that life has not yet returned to normal;  the transition period may make it easier for the public to accept returning to a full lockdown if required. An odds-and-evens policy is one way to lift restrictions gradually and equitably as a controlled trial involving huge numbers of individuals. It would permit the economy to restart and provide a firm evidence-base on which to develop future policy decisions to combat the ongoing epidemic of covid-19.   

Philip Clarke is the Director of Health Economics Research Centre (HERC) at the University of Oxford; his interests include developing methods to value the benefits of improving access to health care, health inequalities and the use of simulation models in health economic evaluation. 

Laurence Roope is an economist and Senior Researcher at HERC. His interests include developing methods to measure poverty and inequality, and the economics of antimicrobial resistance. 

Adrian Barnett is a statistician and professor and is currently the president of the Statistical Society of Australia.  

Amanda Adler has a background in economics, medicine and epidemiology;  she is a clinician, the Professor of Diabetic Medicine and Health Policy at Oxford University, and a chair of a NICE Technology Appraisal Committee.

Competing interests: None declared

This piece was peer reviewed